interpretation of conditionals in the suppression task · 2004-10-08 · interpret such conditional...

Interpretation of Conditionals in

the Suppression Task

Andrea Lechler

Master of Science

Artificial Intelligence

School of Informatics

University of Edinburgh

2004

Abstract

If people are presented with a conditional sentence and a corresponding categorical

premise, they easily make modus ponens inferences. But several studies have shown

that this valid inference of classical logic can be suppressed by adding another

conditional sentence containing an additional necessary condition. Although most

authors accounting for this suppression of inferences have stressed the importance of

interpretative processes, it has not been investigated sufficiently how subjects really

interpret such conditional sentences in practice. Thus, this dissertation examines

people’s interpretations in interviews, utilising statements similar to those used in

previous studies. The results indicate that there is a wider range of possible

interpretations than assumed in accounts of the suppression effect in the literature,

and that subjects do not always adopt the interpretations expected by experimenters.

Moreover, they show that there is often no clear-cut distinction between interpretation

and reasoning. This study investigates the influence of other factors like participants’

understanding of the task, character or the use of world knowledge. It also examines

the role of background or abnormality conditions and counterexamples for the meaning

of conditionals. The findings are used to assess other ways of accounting for the

suppression effect and conditional reasoning in general, like the theory of mental

models or probabilistic approaches.

i

Acknowledgements

First, I would like to thank my supervisor Keith Stenning for his helpful advice and

many fruitful discussions, and Levente Barczy for the good cooperation in doing

interviews for our projects. I want to express my appreciation to Wiebke Herding and

Daniel Dennis for their useful comments on my thesis and all other forms of support

they gave me during the project. I am also grateful to the DAAD (German Academic

Exchange Service) for funding my MSc course.

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Declaration

I declare that this thesis was composed by myself, that the work contained herein is

my own except where explicitly stated otherwise in the text, and that this work has not

been submitted for any other degree or professional qualification except as specified.

(Andrea Lechler)

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Table of Contents

1 Introduction 11.1 The suppression effect in conditional reasoning . . . . . . . . . . . . 1

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Method 92.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Different kinds of interpretations 183.1 Interpretations considered in previous studies . . . . . . . . . . . . . 18

3.2 A new categorisation . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.1 Independent statements . . . . . . . . . . . . . . . . . . . . . 22

3.2.2 Alternative conditions . . . . . . . . . . . . . . . . . . . . . 23

3.2.3 True antecedents . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.4 Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Subjects’ understanding of the suppression task 394.1 The role of instructions . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.3 Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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5 Involvement of world knowledge 55

6 Conditionals and counterexamples 62

7 Uncertainty in conditional reasoning 707.1 Uncertainty of the antecedent . . . . . . . . . . . . . . . . . . . . . . 70

7.2 True antecedents? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.3 Different types of assertion . . . . . . . . . . . . . . . . . . . . . . . 74

7.4 How can they be so sure? . . . . . . . . . . . . . . . . . . . . . . . . 80

8 Individual patterns of interpretation and reasoning 838.1 Effects of different experimental settings . . . . . . . . . . . . . . . . 83

8.2 Individual differences . . . . . . . . . . . . . . . . . . . . . . . . . . 85

8.2.1 Mental abilities . . . . . . . . . . . . . . . . . . . . . . . . . 86

8.2.2 Personality . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

9 Biconditionals 94

10 Conclusion 10110.1 The suppression effect . . . . . . . . . . . . . . . . . . . . . . . . . 101

10.1.1 Why did we observe less suppression? . . . . . . . . . . . . . 102

10.1.2 Why was there such a wide range of different conclusions? . . 102

10.1.3 Is there really suppression? . . . . . . . . . . . . . . . . . . . 103

10.2 General findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

10.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Bibliography 111

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Chapter 1

Introduction

1.1 The suppression effect in conditional reasoning

Everybody who has at least some knowledge of formal logic knows inference rules

like modus ponens:A � B A

BFrom the fact that A implies B and A holds, we can conclude that B holds. Many

psychologists have claimed that modus ponens is not only a rule of classical logic,

but is also employed in human reasoning, i.e. even people who have never heard of

formal logic have a corresponding mental rule. This poses the question as to which

representations this mental rule would operate on. In classical logic, modus ponens is

formulated for material implication, which is often translated into natural language by

means of ’if...then’ sentences. Indeed, modus ponens is often defined as an argument

of the form: if A then B, and A, therefore B. Does this mean that mental inference

rules like modus ponens operate on conditional sentences, or more precisely on their

mental representation? And what exactly is the meaning or the mental representation

of conditionals?

Byrne (1989) questioned these views by showing that the valid inferences modus

ponens and modus tollens1 can be suppressed if more context is provided.2 Before,

1If A then B, not B, therefore not A2The kind of experiment she deploys is hence called the ’suppression task’.

1

Chapter 1. Introduction 2

others had claimed that fallacies, such as ’denial of the antecedent’3 and ’affirmation

of the consequent’4, are not mental rules, but only implicatures or invited inferences

(Rumain et al. (1983); Markovits (1984); Markovits (1985)). They had showed

that these inferences are often not made if a second conditional is added to the

statement. Byrne replicated these results by presenting a second conditional containing

an alternative condition for the same consequent5, as in the following statement:

If she has an essay to write then she will study late in the library.If she has some textbooks to read then she will study late in the library.She does not have an essay to write.

Only a few subjects concluded that she will not study late in the library. Byrne extended

the experiment by introducing a second conditional with an “additional requirement

that must also hold” (p. 67):

If she has an essay to write then she will study late in the library.If the library stays open then she will study late in the library.She has an essay to write.

Now only 38% of subjects made modus ponens inferences, compared to 96% when

a simple conditional or two conditionals with alternative conditions were presented.

Byrne concludes that either there are no mental rules for the valid inferences, or that

suppression by itself tells us nothing about the existence or non-existenceof rules of inference in the mind (Byrne, 1989, p. 76)

She admits that the results can still be explained in terms of mental rules if one assumes

that the joint representation of both sentences makes the application of inference rules

impossible. Her proposal is that

Formal theories, therefore, need to be supplemented with a detailedaccount of the process of interpretation, because premises of the sameapparent logical form are represented in different ways depending on theirmeaning. (Byrne, 1989, p. 77)

3If A then B, not A, therefore not B4If A then B, B, therefore A5Although some scholars reject the terms ’antecedent’ and ’consequent’, I use them to refer to an

if-clause and the corresponding main clause. They make talking about conditional sentences easier, anddo not indicate preferences for any particular approach.


Yet, she rejects mental rules in favour of the mental model theory (see e.g. Johnson-

Laird and Byrne (1991)). Here, the idea is that people represent all possible states

of affairs which are consistent with their world knowledge and the content of the

sentences. A conclusion is only endorsed if there is no model which contradicts

it. Byrne explains the suppression effect by assuming that introducing alternative or

additional conditions results in subjects constructing different sets of models, which

provide different kinds of counterexamples. In subsequent papers (e.g. Byrne (1991);

Byrne et al. (1999); Johnson-Laird and Byrne (2002)) Byrne refined her approach, but

still stuck to these basic ideas.

This ’suppression effect’ described by Byrne has become one of the phenomena

every psychological theory of conditional reasoning has to account for.6As it has

not been considered in philosophical and linguistic approaches to conditionals, the

following review discusses only psychological studies. However, it is worth noting

that the use of language, in this case conditionals, in an artificial situation like Byrne’s

experiments can be interesting for linguists, too. Moreover, linguists tend to neglect the

close relationship between conditionals and reasoning. My account of the suppression

effect will try to bridge the gap between psychological and linguistic approaches.

Let us now examine what has been said about the suppression effect in cognitive

psychology. Many scholars accepted the mental model theory and made only slight

modifications to it (e.g. Dieussaert et al. (1999); Dieussaert et al. (2000)). There were,

however, many others who criticised Byrne’s approach and offered new explanations

for the suppression effect. Politzer and Braine (1991) defend their syntactic theory

of mental logic, and claim that, in contrast to the fallacies, the valid inferences are

suppressed due to inconsistencies within the premise set. Subjects cannot draw a

conclusion because the second conditional casts doubt on the truth of the first. They

also show how pragmatic processes yield the combined representation proposed by

Byrne (1989).

Although proponents of both mental logic (Politzer and Braine (1991)) and the

mental model theory (Byrne (1989)) emphasise the importance of interpretation, Chan

and Chua (1994) claim that “both theories have not offered a principled account of

6Others are syllogistic reasoning or Wason’s selection task.


the interpretive processes critical in reasoning” (p. 233) and do not consider content

and context effects sufficiently. According to them, people’s conclusions depend on

the relative salience or degree of necessity they assign to an additional requirement by

means of their world knowledge (or more precisely by so called “reasoning schemas”),

and on the order in which the sentences are presented. They observe an “increase in

suppression rate with increase in relative salience” (p. 231), and suggest a cognitive

model based on production rules which only allow a conclusion if the relative salience

of the second condition is low enough.

Other scholars point out that uncertainty of beliefs is an inherent feature of

human reasoning and must be accounted for by a theory of reasoning. Stevenson

and Over (1995) claim that adding an additional requirement to a conditional can

make it uncertain by decreasing the conditional probability of the consequent given

the antecedent, which leads to uncertain conclusions. They propose to extend the

mental model theory by a notion of conditional probability (see also Johnson-Laird

(1994); Oberauer and Wilhelm (2003)). George (1997) confirms the importance of

uncertainty in human reasoning, but he shows that none of the existing approaches

captures all the data in an adequate way. Oaksford and Chater (2001) reject logic

as a base of human reasoning and suggest a model solely based on probabilities.

They also consider the probability of exceptions, and explain the suppression of valid

inferences (and fallacies) by “high values of the exceptions parameter” (p. 352). While

this model mainly focuses on the reasoning process, Politzer and Bourmaud (2002)

try to combine the uncertainty approach with a more detailed pragmatic analysis.

They claim that suppression arises because the epistemic implicature that the second

condition might not be fulfilled reduces the believability of the first conditional. In their

approach, the conditional probability of the consequent given the antecedent indicates

the assertability of the conditional.

Stenning and van Lambalgen (2003b) come back to the idea of logic as a base of

human reasoning by stating that different logical models are appropriate for modelling

different tasks. They account for Byrne’s suppression data by representing conditionals

in a default logic that can be implemented by spreading activation networks. Like

others before them, they emphasise the importance of the interpretation process, which


they regard as “reasoning to an interpretation” (p. 11). It results in logical forms

which a uniform reasoning mechanism can be applied to. According to them, there

is no suppression of inference rules or mechanisms, but only a modification of the

representations they operate on. They show that this approach can account for Byrne’s

suppression data.

1.2 Objectives

The overall goal of my dissertation is to shed more light on the meaning of

conditionals. It was motivated by the work of Stenning and van Lambalgen (2003b).

As their approach emphasises the interpretative component, it is essential to know

whether the interpretations suggested by Byrne (1989) are really those that have to be

modelled. This is where my study tries to give answers. I want to show how people

really understand conditional sentences, especially statements that have been used to

elicit suppression effects. Although the importance of interpretation in reasoning has

been noted by many scholars, their claims about subjects’ interpretations are mostly

speculative and not based on systematic experiments. But even if they admit that

interpretation and reasoning cannot be treated separately, they often give an insufficient

account of the interpretation process and fail to consult linguistic theories on discourse

understanding. The involvement of linguistics rarely goes beyond mentioning Gricean

implicatures. Thus, another objective of this dissertation is to show how semantic and

pragmatic theories can help to gain a better understanding of the interpretation and

reasoning processes involved in the suppression task.

Besides showing which interpretations are possible, I want to examine what makes

people adopt one interpretation rather than another, and what determines how people

reason from conditional statements. These questions are strongly connected with the

way the suppression task is designed and with subjects’ assumptions about what they

are supposed to do. The goal of this dissertation is not to give an exhaustive analysis

of all relevant factors, but to show what has to be taken into consideration if one

wants to understand conditional reasoning. This work contains new ways of analysing

conditionals, so I will re-examine existing theories on conditional reasoning in the


light of my results. Special attention will be paid to the mental model theory and

probabilistic approaches to human reasoning.

1.3 Terminology

One of my goals is to gain more insight into the meaning or mental representation of

conditional sentences. By mental representation I do not mean the actual representation

of sentences or discourse in the brain. This term rather stands for the abstract structure

representing a conditional. But in order to examine and describe different ways of

interpreting conditional sentences, I need a certain notion of what a conditional or its

meaning is, which makes it difficult to investigate the meaning without any biases.

Thus, I try to introduce some underlying assumptions about the basic properties of

conditionals without fixing too many parameters.

In the literature, disagreement starts with the word ’conditional’. There have been

many different attempts to define this term, using words like ’possible’, ’hypothetical’,

or ’inference’. Wierzbicka (1997) claims that these concepts are more complex than

the “universal concept” IF, which she suggests for what we label with the term

’conditional’.7 According to her, it is more appropriate to define this concept by

some sample sentences illustrating its meaning and preventing confusion with other

concepts like WHEN. She suggests sentences containing events that can really happen

and specifying a particular time like

If it rains tomorrow, I will not go.

I think she is right in claiming that the simplicity of conditionals is often not recognised

and things are made more complicated than they actually are. However, the fact that

conditionals exist in all studied languages does not mean that there is only one way of

interpreting them and making inferences from them.

The literature8 usually makes the distinction between indicative conditionals like

the example above, and subjunctive or counterfactual conditionals like

7Wierzbicka suggests a set of universal semantic primitives which have equivalents in every languageand cannot be explained by other words.

8For comments on this distinction see e.g. Bennett (2003); Jackson (1987); Edgington (2001)


If it had rained, I would have stayed at home.

Wierzbicka (1997) even suggests the universal concept IF...WOULD for counterfac-

tuals. Only few authors like Dudman (1991) try to define conditionals in a way

that captures all occurring phenomena. This dissertation only deals with indicative

conditionals of the type introduced above9, i.e. without considering sentences like

If I didn’t have to work today, I would stay at home

which are sometimes treated as indicative and sometimes as counterfactual condition-

als. Thus, I restrict my attention to the type of conditional examined in the majority of

studies on the suppression of valid inferences. It is not clear whether my results about

the interpretation or meaning of these conditionals also apply to other types.

If we speak of a conditional correcting or denying another conditional10, we

implicitly state that the first sentence is considered to be false (or not true). So, if we

want to describe in which cases the second sentence can be understood as correcting

or denying the first, we need a notion of what it is for a conditional to be true or false.

This is a delicate and controversial issue, and it is not my intention to recapitulate the

whole discussion about whether conditionals are truth-functional or not. I rather want

to refer to the notion of necessary and sufficient conditions, which is a widespread

concept in the literature on conditionals. In these terms, a conditional sentence is

true if the antecedent is a sufficient condition for the consequent to hold.11 This

notion of sufficiency is generally relative to a certain context or to the assumption that

certain other conditions hold together with the antecedent. The relationship between

antecedent and consequent (i.e. the sufficiency of the antecedent) can also be defined

as enabling certain inferences, especially what is usually called modus ponens. Maybe

it is not only an inference rule operating on the representation of conditional sentences,

but itself a substantial part of the meaning of conditionals. This is what Stenning and

van Lambalgen (2003b) mean by stating that:

the conditional is often not so much a truth functional connective, as alicense for certain inferences (p. 14)

9This type of conditional is what I henceforth refer to as “conditional”.10See chapter 3.11Here we see again how difficult it is to define conditionals or the concept IF without being circular

and using words like ’if’ or ’condition’.


In their implementation of a neural network, they represent the relationship between

antecedent and consequent as a link between nodes, thus emphasising the fundamental

function of conditionals in representing discourse and reasoning on these representa-

tions.

The notion of the antecedent being a necessary condition for the consequent to hold

is not relevant in defining the meaning of conditional sentences as such. But we will

see later that it is important in interpreting the relationship between two conditionals

and in making inferences.

Chapter 2

Method

2.1 Motivation

Previous studies on the suppression effect were based on experiments where subjects

were presented with a sequence of sentences and asked what they could conclude.

In most cases, participants could only choose conclusions from a given list (Byrne

(1989); Byrne et al. (1999), Experiment 2-4; Stevenson and Over (1995); Stevenson

and Over (2001)), with the result that they only made inferences fitting into the

categories expected by the experimenters. But even when subjects could generate their

own answers, the analysis of these remained superficial. In their first experiment,

Byrne, Espino, and Santamaria (1999) gave participants the opportunity to draw

their own conclusions. But again, they only categorised the results in accordance

with the mental model theory and returned to the previous design in the remaining

experiments. Dieussaert et al. (2000) present a more detailed analysis of freely

produced conclusions. Dieussaert et al. (1999) make subjects even describe the

reasoning process in a think aloud study. The problem with their studies, however,

is that they focus on the reasoning process itself, especially on the deployment of

different reasoning strategies, but do not use the material to examine underlying

interpretations. Like many other studies, they accept the stance on interpretation

expressed in the mental model theory and build their own analysis upon it.

Another shortcoming of most studies on conditional reasoning is that they only

9

Chapter 2. Method 10

account for answers given by the majority of subjects, without explaining why there

is such a great variety of answers. Thus, they implicitly state that all other subjects

did not interpret and reason in a natural and representative way which would be worth

accounting for. Of course, there may be subjects who do not understand the task or

do not take it seriously, but it is not likely that this is such a significant percentage,

especially considering the fact that most subjects make the expected inferences in the

standard condition. Again, Dieussaert et al. (1999; 2000) constitute an exception, but

as said above their analysis does not attach enough significance to interpretation.

2.2 Design

This shows the need for a study which tries to account for different types of answers by

giving people the opportunity to express how they interpret conditional sentences. The

method I used within my project can be called ’interview’ rather than ’experiment’.1

I did some of the interviews2 together with Levente Barczy, who was investigating

how people’s understanding of the suppression task and the ontologies introduced

by the instructions determine which logic they use.3 The material was very similar

to that used in previous studies, we only changed it slightly to make the sentences

sound more natural, and added our own statements to examine certain factors, like the

role of the content or the formulation of the sentences, more systematically. Yet, the

way the sentences were presented and people were asked to draw conclusions differed

significantly from other experiments. After the presentation of a statement, subjects

were engaged in a conversation about how they understood the sentences and what

their conclusions were.

In contrast to most previous studies, I used a qualitative rather than a quantitative or

statistical research method. Some psychologists are sceptical about qualitative research

because it is very subjective and generalisations are not easily possible. It is also

objected that the results are not natural in the sense that they would not occur without

1Stenning and van Lambalgen (2003a) call a very similar method used in a study on Wason’sselection task ’socratic tutorial dialogue’. This terminology is misleading because the goal of theseconversations is not to make the participants learn.

2Subjects 13 to 26 in the excerpts presented below.3I will hence use the pronoun ’we’ when talking about the interviews.


the intervention of an experimenter. In our case, this could mean that the questions in

the interviews trigger interpretations or conclusions people would not come up with

naturally. But I think it is unlikely that people have a totally new way of understanding

natural language in the interviews, it is rather a question of which of the available

interpretations they adopt under such artificial conditions. Another issue is whether

the assertions people make can really be taken as evidence of mental processes. But

as I investigated possible outcomes of the interpretation and reasoning process and not

the mental process itself, this does not seem to be a big problem in my case. Moreover,

qualitative research seemed to be more adequate because I was not interested in the

percentage of subjects making a certain conclusion, I rather wanted to find out why

people come to their conclusions. There were no variables that could be evaluated

statistically because my goal was to determine the range of possible interpretations

and factors influencing which interpretations and conclusions people choose. The

interviews also gave the possibility to develop new hypotheses. Quantitative research

is often a testing of hypotheses in terms of predefined categories, but my goal was

to question the categorisation introduced by previous studies and show that other

interpretations are also possible. Of course, it is difficult to say why exactly people

choose a particular interpretation, but such interviews can at least show the existence of

certain interpretations. As with qualitative research in general, it is difficult to present

a comprehensive analysis of all the data because there is no numerical data to explain.

Another drawback is the danger of picking single quotations as evidence for one’s

hypothesis whilst withholding contradicting data. But sometimes qualitative research

may yield more honest data than quantitative methods that suggest a uniform pattern

of behaviour which can be described with numbers. That this is not always the case is

shown by previous studies on the suppression effect where analysing the percentages

of inferences led to wrong conclusions about the nature of reasoning. To sum, the

qualitative method used in this dissertation is a useful complement to quantitative

studies.

I try to combine a psychological with a linguistic analysis of the interpretation and

reasoning process. So, it is important to compare the method used in this dissertation

with the methods standardly employed in linguistic research. Some linguists rely only


on their own intuitions or those of their colleagues, but their intuitions may not be

correct. Others base their theories on the analysis of text and speech corpora, which

are likely to contain more natural and representative data. However, it is often difficult

to find enough significant data in corpora to investigate a particular phenomenon. I

would place the method I deployed somewhere between these two extremes. The

interviews are not perfect situations of natural language usage. Subjects are aware

that they are asked about their understanding of language and thus likely to reflect

upon their interpretation of the material. But asking others about their interpretations

in an indirect way goes beyond just consulting one’s own intuitions. Thus, this method

offers a way of gathering data on a specific phenomenon systematically, i.e. without

depending on rare appearances in corpora, and is at the same time a step away from a

mere armchair analysis of natural language.

My hypothesis was that people do not always interpret the presented conditional

statements in the way expected by the experimenters, and that this fact has to

be considered when interpreting the reasoning data. So, the first objective of the

interviews was to investigate which interpretations people adopt in the suppression

task. An obvious starting point was to use the material of previous studies to make

my results comparable and clarify their data. But the form of the statements -

two conditionals with the same consequent followed by one of the antecedents (the

categorical premise) - does not seem very natural and does not occur very often in

real written and spoken language. Thus, the question is whether this is an appropriate

way to examine how people usually interpret conditionals. Should we not use more

natural material, i.e. conditionals embedded in a broader discourse with the categorical

premise presented in a less marked way?

Firstly, it is important to note that experiments always constitute somewhat

artificial situations, so even more natural material could not make them really

natural. The deciding criterion of a good experiment is not naturalness, but that

it allows conclusions about the real world. In this study, using rather abstract

material is adequate because its interpretation is presumably based on the same

principles or processes as the interpretation of more realistic material. People try

to make sense of these sentences by using the mechanisms they use for interpreting


language in daily life. So, using more abstract, unnatural material might even be

better because the processes which are involved are easier to investigate. Factors

which might influence the interpretation process can be controlled more easily. For

instance, the degree to which people use their own world knowledge can be examined

systematically by varying the amount of context given to them. Conditionals presented

without any context might help to find out if there is a default interpretation for

conditionals. Adding further context may show which factors make people choose

another interpretation instead of or in addition to the default interpretation, and what

makes them doubt the truth of a conditional. Presenting two conditional sentences

together may also reveal different ways of interpreting natural language conditionals.

Of special interest is the case where the second conditional triggers a revision of the

first. This provides insight into the interpretation process itself, and allows conclusions

about the mental representations of conditionals.

Another source of information are the inferences people make from the presented

statements. They shed light on the role of natural language conditionals in human

reasoning and the relationship between the antecedent and the consequent, e.g.

whether the antecedent is a necessary or sufficient condition for the consequent to

be true. But the invitation to make inferences is also one of the drawbacks of this kind

of material. If people are presented with a conditional and a corresponding categorical

premise and asked what follows, their interpretation of the conditional will be such that

the truth of the antecedent implies the truth of the consequent. This does not permit us

to find out whether there are other interpretations of the conditional not allowing such

inferences. For this reason, I presented conditional sentences without a categorical

premise at the beginning of the conversation, and only added the categorical premise

after having interviewed subjects about their understanding of the conditional.

Participants were told that the sentences were part of a conversation they overheard,

or text messages on a mobile phone they had found. To find out what the default

interpretation of a conditional is, we asked them what they thought the discussion was

about, or why the messages had been sent. After the interviewees had been given

the categorical premise, we asked them what followed from the sentences and why

it followed. Sometimes we presented only one conditional and the corresponding


categorical premise at the beginning and asked subjects what they could conclude.

Then we gave them the second conditional to see whether the new information would

make them change their conclusion, and how they would interpret this sentence in

the context provided by the first two. As already mentioned above, we usually

presented one of the antecedents as a categorical premise, which means that we focused

our attention on modus ponens inferences. Since I was mainly interested in the

interpretation of conditionals, and not so much in the reasoning process, it seemed

legitimate to use only this kind of inference, which I assumed to be most obvious. This

permitted me to analyse the interpretation process without worrying about the type of

inference.

In order to investigate what role probabilities and uncertainty play in interpreting

conditionals, we also asked people how sure they were about their conclusion, or what

information they would need to be sure.

Another issue this dissertation explores is the relationship between the two

conditionals, especially between the two consequents. Subjects’ answers to questions

like ’How many people are saying these sentences?’ or ’Why is the second person

saying this in response to the first person?’, indicated what they thought the function

of the second conditional was.4 Making people rephrase the sentences was another

way of finding out how they interpreted the relation between the two sentences. We

asked them whether the sentences sounded natural, whether these were sentences they

would say, or, if not, how they would convey the same information using different

4However, these questions did not always have the intended effect, as the following excerpt shows:Subject 18A: Imagine you are sitting in a bus, and there are some people at the back of the bus having a discussion,and you want to find out what they are talking about. And you hear these sentences: If Rosa meets herfriend Liz, she goes to the cinema. If she has money for a cinema-ticket, she goes to the cinema. Shehas money for a cinema-ticket.(...)A: What do you think, how many different people are saying these sentences?S: When they are talking about that?A: Yeah.S: Maybe just two people.A: Why two?S: I don’t know, it’s not a big conversation, really, is it, or a discussion point.A: Who would say which sentence?S: I mean if it was like secondary school children, there might be more, there might be five or six, butwith adults it would just be a couple, I think.


words. These questions also elicited statements about subjects’ understanding of the

task and the naturalness of our material.

As the controversy about the role of exceptions and counterexamples in interpreting

conditionals is an essential part of the literature on conditional reasoning5, I wanted

to test the plausibility of different hypotheses by asking questions like ’What could

prevent her from being in the library?’ or ’Can you think of situations where she has

an essay to write, but isn’t in the library?’. This was also one way of gaining insight

into the involvement of world knowledge in interpreting the statements. Generally, it

is important to note that not all of our questions were intended to provide information

about one particular aspect of the interpretation and reasoning process. They often

mainly served the purpose of making people talk about the sentences, which we hoped

would reveal how they interpreted them.

2.3 Procedure

The design of the interviews as described in the previous section gives only a rough

overview of the presentation and questioning methods we used. This is due to

the fact that interviewing people requires flexibility and adapting the questions to

the interviewee. Moreover, our methods and materials continuously changed and

improved as we did the interviews. I started by interviewing friends to get a feeling

for how people reacted to my questions and how I could evoke information about their

understanding of the sentences. Most of the subsequent interviews were done at a

cafeteria at university, which means that most of our subjects were students. Yet, the

ages of our 30 interviewees ranged from 13 to 65. They had different occupations

and subjects of studies, which gave us the opportunity to examine the influence of

someone’s education and world knowledge on the interpretation and reasoning process.

Except for one, all subjects were native speakers of English and most of them did not

have any prior knowledge of linguistics or formal logic. We told the subjects that we

were interested in how they reasoned and how they interpreted sentences. As people

tended to be confused and uncertain about what they were expected to say, it was

5See chapter 6.


important to emphasise that there were no right or wrong answers and that the interview

was nothing like an intelligence or personality test. Then each person was presented

with three to five different statements in an interview of about 10 to 20 minutes.

2.4 Evaluation

It could be objected that people are biased by the way they interpret the first set

of sentences and the questions they are asked about it, and thus do not process the

following statements in a natural way.6 The presentation of several statements allows

us, however, to investigate this influence of the conversational context, and to examine

if there are individual preferences for certain kinds of interpretation. Of course, we

cannot even guarantee for the first statement that people interpret it in a natural and

unbiased way. It is not clear how strongly people are influenced by the experimental

character of the interview, and how conscious they are of the process which makes

them choose their interpretations. In some cases it was obvious that the subjects did not

interpret the sentences in a natural, unconscious way. It was notable that participants

with a linguistic or logical background often gave several possible interpretations.

Yet, the environment and character of the interviews were probably more similar

to a real life situation than the experiments in previous studies. The interviewees could

stay in familiar surroundings and were engaged in a conversation rather than asked

to solve an abstract task. But, as mentioned above, they were often suspicious and

thought we were interested in something different from what we told them. This effect

was more noticeable with two interviewers. Subjects were more relaxed when we

stopped asking them too much about the reasoning process and why they had changed

their conclusions.7

The results show that interviewing people about their understanding of conditional

statements helps to evaluate the results of experiments on conditional reasoning, and

to compare different approaches. This method gives the opportunity to ask further

questions if someone’s interpretation of the sentences is not clear from his conclusions.

6Indeed such effects could be observed. See chapter 8 for details.7As the interviews are numbered in chronological order, the excerpts presented in this dissertation

will allow the reader to follow the change of interviewing techniques.


A great advantage over the methods used in previous studies is that the types of answers

are not so restricted because subjects are encouraged to express themselves freely. This

helped us to get new ideas and not only to think in terms of previous hypotheses and

categories. Indeed, the interviews suggested types of interpretation that have not been

thought of before.8

8See section 3.2 for details.

Chapter 3

Different kinds of interpretations

3.1 Interpretations considered in previous studies

Byrne (1989) introduces two different ways of interpreting two consecutive condi-

tionals: the condition stated in the second conditional can be either an alternative

possibility or an additional requirement for the consequent to be true. She puts each

statement used in her experiments in one of these categories, and analyses the data

about inferences made according to this categorisation, thus assuming that subjects

always adopt one of these two interpretations. Subsequent studies on the suppression

effect kept this distinction and hardly thought about other possible interpretations. In

the few cases where other interpretations, e.g. the second conditional as a denial of the

first (Stevenson and Over (2001)), were taken into consideration, the authors did not try

to give a systematic account of possible interpretations. Yet, they are right in claiming

that Byrne’s two categories are not the only ones which have to be considered. I would

even say that her treatment of the second conditional as an additional requirement

is not precise enough. In order to account for all essential differences in people’s

conclusions, this category has to be subdivided again. Below, I will try to give a

more comprehensive description of the different ways subjects can interpret the second

conditional in the context provided by the first.

The second major flaw in how many scholars dealt with the issue of interpretation

is that they assumed subjects would adopt exactly the interpretation they deemed

18

Chapter 3. Different kinds of interpretations 19

most plausible themselves. Consequently, they analysed the reasoning data only

with regard to this interpretation. The inappropriateness of this assumption becomes

clear in Dieussaert et al.’s think aloud study (Dieussaert et al. (1999)) which uses

similar material as previous studies on the suppression effect. They take the following

statements as evidence for their amendment strategy, but do not analyse the relationship

between the two conditionals.

”1So she takes a domestic help, but this doesn’t mean that she earnsenough money, but one of the two conditions are fulfilled, so she takesa domestic help.”

”2 John goes out fishing, so there will be fish on the menu, whether hecatches one or not.”

(Dieussaert et al., 1999, p. 229)

Obviously, subjects have not adopted the intended interpretation of the second con-

ditional as an additional requirement, and this might have influenced their conclusions

to a greater extent than a particular reasoning strategy. The authors thought of the

possibility that subjects would not adopt the intended interpretation, so they made

other subjects score how ’alternative’ or ’additional’ the second antecedent is, and

chose their material based on this scoring. But they fail to use this fact to interpret the

results of their think aloud experiment: in the presentation of their results they keep the

original categorisation. This means that they do not consider the actual interpretation

of the sentences in their analysis.

The hypothesis that subjects often do not have the reading that was intended by

the authors of all these studies was confirmed in our interviews. In many cases where

the second condition was meant to be an additional requirement (in Byrne’s sense),

subjects interpreted it as an alternative, as can be seen in the following examples.3

1Based on the statement: If she goes out working, then the woman next door takes a housekeeper. Ifshe earns enough money, then the woman next door takes a housekeeper.

2Based on the statement: If Jan goes out fishing, then there is fish on the menu tonight. If Jan catchesa fish, then there is fish on the menu tonight.

3The following abbreviations or markers are used in the transcriptions of the interviews:S = subjectL = LeventeA = Andrea


This is probably one of the reasons why we did not observe many suppression effects

with modus ponens inferences and why others’ studies have not obtained uniform data.

Subject 17A: If Rosa meets her friend Liz, she goes to the cinema. If she has moneyfor a cinema ticket, she goes to the cinema. And you know: She has moneyfor a cinema ticket.S: Um, then she would go to the cinema, presumably, Um, again it’s justthe first sentence isn’t really relevant because she’s gonna have, if she hasthe money, and if she has the money, she goes, then she goes, whether shegoes with Liz or not is unclear.L: So, basically, she doesn’t need Liz around, as long as she has themoney?S: Yeah, if, the first two statements aren’t, are like two alternates and onlyone of them needs to be confirmed, and one of them is, so, she will go tothe cinema. But we don’t know whether she will be going with Liz or not.

Subject 1S: (reading)4 If Maria studies hard then she gets high grades in the exams.If Maria is intelligent then she gets high grades in the exams.She studies hard.A: What follows?S: Hm, that she will get high grades in the exams. But I guess it doesn’tsay whether she is intelligent or not. So she might get high grades anyway,even if she doesn’t study. Um...A: Do you think she will get high grades?S: Yes.A: Why can you say that?S: Because you said that if she does study hard then she will get goodgrades. And also if she is intelligent, she will get... There’s kind of twooptions, you said she does study hard...A: Does she have to be intelligent to get high grades?S: No, she can also just study hard.

Subject 20A: If Tom studies hard, he’ll pass. If he’s intelligent he’ll pass. And Tom

# = speech not intelligibleenclosed by * = not surecapital letters = pitch accent (I did not make a detailed prosodic analysis, pitch accents are only markedin cases where they seemed relevant for my purposes.)

4In some interviews, I made subjects read the sentences because I did not want my intonation toinfluence their interpretation.


is studying hard. What follows?S: Think it follows that he’ll pass, then. If he studies hard he’ll pass, andhe’s studyin’ hard so he’s gonna pass. It sounds like... it sounds like if he’sintelligent he doesn’t need to study hard to pass. But if he’s intelligent andhe’s studyin’ hard then he’ll pass. You know, the first one means he’ll passanyway, so he’s gonna pass no matter what, really.

3.2 A new categorisation

Interpretations of the conditional statements we are dealing with can be classified

along three different dimensions. One of them is the relation between antecedent and

consequent. In chapter one, I used the terms ’necessary’ and ’sufficient’ condition to

describe this relationship. They will also be used here to describe the different ways of

interpreting two successive conditional sentences.

Another variable is people’s stance on the coherence of the statement. Discourse

that people are confronted with in ’real life’ (as opposed to experiments or interviews)

is usually meant to be coherent, i.e. sentences refer to each other and are interpreted

in the context provided by the previous ones. But in the suppression task, people find

themselves in an unnatural situation and have to interpret sentences out of context. So,

it is possible that they do not always regard the sentences as part of a coherent text or

discourse, but interpret them as independent of each other. I will examine in the next

chapter how likely it is that people actually adopt this stance; but the fact that we found

examples of it in our interviews shows that it has to be considered in a description of

possible interpretations.

If people assume that a statement is coherent, they try to find an interpretation of it

that supports this assumption, so the interpretations of both sentences are more strongly

influenced by each other. I want to distinguish two types of coherent statements. In

a consistent statement, the function of adding the second conditional is to accept the

truth of the first conditional and add new information to the existing context. In an

inconsistent statement, the second sentence states that the first sentence (i.e. the current

context) is false and corrects it.

The following analysis will be based on the common classification of rhetorical

or discourse relations where this is possible, mainly referring to Asher and Lascarides


(2003). To explain the connection between two conditional sentences in terms of these

relations, we also need the notion of focus (See e.g. Kadmon (2001); Rooth (1996)),

which is used to describe the correlation between prosody and certain semantic or

pragmatic phenomena. The term focus usually denotes the syntactic constituent of

a sentence with the greatest prosodic prominence. The focused part of a sentence

answers the salient question in the current context and is chosen out of a set of

alternatives. The rest of the sentence, corresponding to this open question, is often

called background.

3.2.1 Independent statements

The first category comprises cases where the sentences are not treated as coherent. As

one is not assumed to be said in response to the other, this kind of interpretation is

always possible. It means that both antecedents are independent sufficient conditions

for the consequent to be true. In this case, subjects come up with an interpretation for

Byrne’s library example which is totally different from the one she expected, namely

that the student is in the library whenever it is open.

Subject 20L: Then the third message says, if the library is open, she’ll be in thelibrary. What do you think that means?S: Okay so it means that she’s gonna be working full out during the day, soshe’s gonna be working like all day, so she prefers to work in the library,so she’ll be in the library if it’s open, but if it’s not open obviously she’llbe working elsewhere, maybe.

Subject 23L: Hm, hm. Then you read the next message, which says: If the library isopen, she’ll be in the library.S: Um, yeah, then I think it was getting increasingly likely that she wasthere.L: What do you think that person meant?S: Um, just exactly what she, exactly what they said, really. That she canbe found most of the time in the library, um, she’s hard-working.


3.2.2 Alternative conditions

In all the types of interpretation described in the remainder of this chapter, people

assume that the statement is coherent. Very similar to the first category is the

interpretation of the second antecedent as an alternative sufficient condition from

which the same consequent follows. Here, subjects interpret the statement as consistent

and think that it makes sense to give two alternative situations from which the

consequent follows. The events or states denoted by the two antecedents often do not

overlap, although the main criterion is that they can both be interpreted as conditions

which are not necessary for the consequent to become true. For instance, the situations

’she has an essay to write’ and ’she has to copy papers’ may overlap, but they are

not both necessary for someone’s being in the library. It is, however, unlikely that

people interpret the conditional ’if the library is open....’ as an alternative condition

if they assume that the sentences are related. In terms of discourse relations, the

interpretation of the second conditional as introducing an alternative condition can

be explained by the relation parallel. Here, two sentences have a similar syntactic and

semantic structure, words like ’too’ often indicate that this relation holds. Indeed, if

subjects are asked to express the same information in their own words, they tend to

combine the two alternative conditions by ’or’, or add a word like ’also’ or ’too’ to the

second conditional. This can be seen in the following examples.

Subject 2A: Do you think someone would say both sentences together?S: I wouldn’t guess that someone would say this sentence - stop. And thenwould say that sentence - stop. He might say: if Maria is smart, or if shejust studies really hard, then she will get a high grade on the exams. Butshe studies hard, so she will get a high grade.

Subject 5A: What about the first one, how would you say that?S: If Mary has an essay deadline, then she will be in the library. She willbe in the library if she has to copy some papers, too. She has got an essaydeadline. That makes a bit more sense.

In one case where this type of interpretation was chosen the conditions were

joined by ’and’, which might be because the new conditional is a simplification of


a combination of the entire sentences (’if it is raining, she will get wet, and, if it is

snowing, she will get wet’).

Subject 3A: So, how would the sentence be if it was only one speaker?S: If it’s raining and snowing she will get wet.

In case of independent and parallel statements, both antecedents are interpreted as

sufficient and we have two separate conditionals. There should be no difference with

respect to modus ponens inferences, either. But despite their similarity, I think it is

justified to have two distinct categories because the interpretations are feasible under

different conditions and result from different assumptions about the coherence of the

statements.

3.2.3 True antecedents

An interesting case is Byrne’s category of conditionals introducing an additional

requirement (Byrne (1989)). Although she asks her subjects to assume that all

sentences are true, she only thinks of the interpretation of the second conditional as

correcting the first by making a necessary condition explicit. She does not expressly

talk of correction, but the fact that she considers the first condition as not sufficient

any longer indicates that this is the interpretation she means.5 However, many of

our subjects chose another interpretation for this kind of statement. As expected by

Byrne, they did not interpret the second antecedent as an alternative condition, but

as a condition that had to be satisfied to infer the truth of the consequent. Yet, this

did not keep them from concluding that the consequent held because they assumed

that the statement was consistent and the first conditional true. In this case, the

first antecedent is a sufficient condition in the present context and the truth of the

consequent cannot depend on the satisfaction of other conditions. It is assumed that all

conditions constituting the context in which the first antecedent is sufficient hold. This

results in people assuming that the second antecedent is true if they are told that the

first antecedent is true. The following excerpts illustrate this phenomenon.

5A more detailed discussion of correction follows in the next section.


Subject 2A: (...) You’re going to the cinema tonight to see ”Troy”. You know thatyour flatmate Susan wants to see it, too, so you would like to ask her ifshe is free tonight. But she isn’t at home and you can’t catch her on hermobile phone. So you ask your other flatmate Tom, ”Do you know whereSusan is?”.He says: “If she has an essay to write, she will be in the library.If she has to train for a competition, she will be in the gym.If the library stays open, she will be in the library.Oh, I remember her telling me that she has to hand in an essay next week.”So, where would you look for her now?S: In the library.A: Why?S: Because, you said: if she has an essay to write then she will be in thelibrary, and it stays open.A: Okay, so, do you know that it stays open?S: Didn’t the guy just say that it stays open? *While it* stays open.A: It says: if the library stays open, she will be in the library.S: Okay, then I would *go to* the library, I would beg that the library isopen.

Subject 36

A: “If she has an essay to write, then she will be in the library.If the library stays open, then she will be in the library.If she has to train for a competition then she will be in the gym.Oh, I remember her telling me that she has to hand in an essay tomorrow.”So, where would you look for her now?S: In the library?A: Are you sure she would be there?S: Yeah.A: Why?S: Because Tom says: she has an essay to hand in, so she will be in thelibrary.A: Well, what could prevent her from going there?S: If the library is shut. Or, if she has a competition, she will be in thegym.

Although the subject knows that the library being shut might be a reason for her not

being there, the second conditional does not influence her conclusion. This indicates

that she assumes the library is open.6Based on the same story.


Subject 13L: If Mary has an essay deadline, she studies late in the library.A: If the library stays open, she studies late in the library. Mary has anessay deadline.S: Hence, she would study in the library.A: Are you sure she will?S: If the library is open late.L: Okay, so, which is it?S: She will study in the library. If she has an essay deadline, she wouldstudy in the library.L: Ah, okay, that’s very good, what if it’s closed?S: Then she is fucked.L: Right, um....but, so wait, so she only studies late in the library if she hasan essay to write and the library is open.S: According to what the sentence says.(...)L: What do you think he is doing though? Why did he use like twosentences?S: Because he said something and just remembered something.L: Ah, okay, so, he corrected himself?S: Or just clarified.L: Okay, but certain logically we told you that she would study late in thelibrary if she has an essay deadline.S: Yes.L: Right? Okay. Then we told you that she would study late in the library.What do you think the additional, the second sentence about the librarystaying open like did to your understanding of the problem?S: It just added more inform..., it didn’t change # the problem really, itjust, an additional condition.

The conversation demonstrates that we did not expect this kind of interpretation

and thought people had misheard or forgotten the sentences, so we tried to find out

whether this was really how they understood the sentences. It was not always easy

to make them change their conclusion, which indicates that it was not only a result of

misunderstanding. This hypothesis is supported by the fact that a significant number of

subjects adopted this interpretation, i.e. regarded the second antecedent as true. Some

of them indeed changed their interpretation when our questions made them rethink

their answers. But this can be explained by the fact that they became more sceptical

and refused to assume the truth of an antecedent. The following examples demonstrate


this effect.

Subject 15A: If Mary studies hard, she’ll get a high grade in the exams.If Mary is intelligent, she’ll get a high grade in the exams.She studies hard.What follows now?S: She is intelligent and will get a high grade in the exam.L: Okay, so you changed your mind from before.S: Yes.L: Why?S: Because the wording changed.A: Do you think she is intelligent?S: I think that she works hard, and if that’s true I don’t think she’sintelligent. I think that she works hard.A: Do you think she’ll get high grades in the exam?S: If she works hard?L: Regardless of her intelligence?S: If you get high marks then you are a really intelligent person.A: So you think she’s intelligent?S: If she gets high marks, yeah.

Subject 14L: Okay. Next part is ah... If the red light is on, the rat is in the cage. Ifthe door is closed the rat is in the cage. And the red light is on.(...)S: So... the red light is on, and if it’s on the rat would be in the cage.L: Right.S: And now you are telling me the red light is on, and the door is closed?L: Well, I didn’t say that, no.S: You said the door is closed.L: Well, “If the door is closed, the rat is in the cage.” And now I just toldyou that the red light is on.S: I would still say... I would assume that the rat is still in the cage.Because you gave me the precondition that If the red light is on the ratis in the cage, and you gave me a second precondition that if the door isclosed the rat would be in the cage. And now you are telling me that thered light is on so I would go with the first precondition, I would assumethat the rat is in the cage. Again.A: Do you think the door is closed?S: Whah? I don’t know. I never thought about that. Am I confusing you?


One of these interviewees points to a way of analysing this type of interpretation.

He speaks of the second sentence as a clarification of the first, adding more information

to it. We can describe this more precisely by referring to the discourse relation elab-

oration. In contrast to Asher and Lascarides (2003), I refer to the focus background

distinction to make this relation applicable to conditionals. The consequent constitutes

the background, which is the same for both sentences. It is repeated to signal that the

function of the second sentence is to elaborate the first sentence. The second antecedent

is focused (through intonation or by its standing out from the background) because it

is the constituent that elaborates the corresponding constituent of the first sentence.

Asher and Lascarides (2003) state that the elaborating event is part of (i.e. temporally

included) in the elaborated event. Although this might be true in some of our examples,

their meaning postulate for elaboration is too restricted for our purposes because we do

not only talk about relations between single events. We can, however, say that the new

information is part of the first antecedent if this definition comprises tacitly assumed

conditions and inferences following from the event or situation that is expressed.

This definition also includes cases where the second conditional does not introduce

another separate situation or event, but states an inference from the first condition or

the exact meaning of words used in the first condition. For instance, the sentence ’she

has a history essay to write’ can elaborate the sentence ’she has an essay to write’ if the

person studies history, and from the fact that she has an essay to write, it follows that

she has a history essay to write because all her essays are history essays. The following

examples show that some participants in fact adopted this interpretation.

Subject 19L: Here is the next one: You hear that if Mary has a paper to write shewill be in the library. If she has a history paper to write, she will be inthe library. And you know that she has a paper to write. What can youconclude from that?S: That it’s a history paper.L: And she will be in the library?S: She will be in the library.#A: How can you know that she has a history paper to write?S: Because it says, she says: If she has a paper to write, she will be in thelibrary. And if she has paper, it’s *up to* history. So, I’m just concludingfrom the fact that she has a history paper.


A: Can you read the sentences again.L: Okay, you are not wrong or anything. You hear that, if Mary has a paperto write she will be in the library. If she has a history paper to write, shewill be in the library. And you know that she has a paper to write. So, doyou think the same, that she has a...S: She must be studying history.

Subject 18L: Who do you think would say these sentences?S: Ah, one of her friends probably, another student. Ah, they are talkingabout papers, an essay, a dissertation or something. And someone issaying: and she has a history paper to write, so the other person wouldbe giving more information, and not just a paper, but a history paper.(presentation of sentences)S: Well, I think it’s just kind of repeating itself. It could maybe just saythat she had a history paper. If she has a paper, she..., you would say: IFshe has a paper to write, she will be in the library. Yes, she has a historypaper, so she will be there.L: Well, she doesn’t have a history, you only know that she has A paper towrite.S: A paper, right. You are just thinking about her, IF she has a historypaper.

However, this analysis does not capture cases where modus ponens inferences are

made from the second conditional and the first is assumed to be true. Byrne et al.

(1999) got suppression effects similar to the standard case when they presented the

second antecedent as a categorical premise, which suggests that this case has to be

considered, too.7 More evidence is provided by our interviews, e.g. by the following

excerpt.

Subject 188

A: And can you draw any conclusion from that, what follows?S: Well, # she has money for the cinema, so I suppose, she goes to thecinema, with her friend.A: Can you think of situations where she has money for a cinema ticket,

7Their experimental setting does, however, not allow conclusions about subjects’ actualinterpretations. They might have endorsed modus ponens for other reasons, e.g. because they interpretedthe antecedents as two alternative conditions.

8Based on the statement: If Rosa meets her friend Liz, she goes to the cinema. If she has money fora cinema, she goes to the cinema. She has money for a cinema-ticket.


but she doesn’t go to the cinema?S: She has seen the cinema, the film before. Or, um, she goes to anotherform of entertainment.9

Here, the second antecedent is treated as a sufficient and the first as a complemen-

tary necessary condition for the truth of the consequent. Thus, we have the reverse

situation. As we cannot analyse the first antecedent as elaborating the second, we have

to find a more general description of the phenomenon. In both cases, the antecedent

from which the modus ponens inference is made is sufficient within a certain context.

People assume that all necessary background conditions constituting this context

hold. The other antecedent is interpreted as one of these background conditions and

thus assumed to be true. In the case of elaboration, the second antecedent is not a

sufficient condition on its own, but only one of the complementary conditions assumed

to hold in uttering the first conditional. Yet, the last excerpt shows that it can be

the starting point of modus ponens inferences. This suggests that a deciding factor

is the context in which the antecedent is a sufficient condition for the truth of the

consequent. Instead of saying that the second antecedent elaborates the first, one could

understand the first antecedent as providing the context in which the second is uttered

and meant to be a sufficient condition. Which antecedent is assumed to be true also

depends on the information provided by the categorical premise and how it is used in

making inferences. This shows that it is difficult to draw a clear distinction between

interpretation and reasoning. People’s interpretation of the statements depends on

how they reason from them. This interaction between interpretation and reasoning

processes might be one reason why the observed phenomena are hard to account for

by means of general discourse relations.

As human reasoning can be very efficient, it is also impossible to distinguish

between natural language interpretation and reasoning by measuring reaction times.

Thus, stating the truth of an antecedent might be the result of reasoning. People

might infer the truth of the antecedent from the truth of the consequent, which was

inferred from the truth of the first antecedent with modus ponens. This inference is

possible because the second antecedent is a necessary condition for the truth of the

9Based on the statement: If Rosa meets her friend Liz, she goes to the cinema. If she has money fora cinema, she goes to the cinema. She has money for a cinema-ticket.


consequent.10

It is also difficult to examine how people actually come to an interpretation, e.g.

how they connect the two antecedents by the notion of necessity. We can only

investigate which connection they finally see between the two antecedents, and how

this interpretation is used in different ways according to people’s attitude towards the

consistency of the discourse. People’s assumptions about the truth of the sentences

can be considered as the main difference between this category and correcting an

antecedent. As they are subject to change, it is not always possible to decide which of

these interpretations someone has adopted. Yet, it is important to make the distinction.

3.2.4 Correction

In case of a correction, the second conditional contradicts the first, i.e. the whole

statement is inconsistent. By making an implicitly assumed condition explicit, it claims

that the first antecedent is not sufficient, that there is another condition which also has

to hold for the consequent to be true. But this is only one kind of correction. Again,

referring to the general description of the discourse relation can help to define these

cases more precisely. Correction is one of Asher and Lascarides’ divergent relations

(Asher and Lascarides (2003)), involving a contradiction between sentences and a

revision of the current context (as opposed to a monotonic update, where information is

only added to the context). This relation also uses the focus background structure of the

sentences to make clear which part of the first sentence is corrected by the second. But

now the focused part of the second conditional is not added to the corresponding part of

the first conditional, but replaces it. How this principle works is obvious in cases where

the second condition is a subset of the first condition (e.g. ’history essay’ vs ’essay’).

The second sentence claims that the first condition is not strong enough, and thus not

sufficient, and has to be replaced by another one. Similarly, the second conditional

can claim that the first antecedent is not relevant for the truth of the consequent at

all, or even implies the negation of the consequent, and thus has to be replaced by

a new sufficient condition. This is only possible if the corrected antecedent is not

necessary, or not necessarily assumed to hold in the other antecedent (e.g. in ’If she

10This kind of interpretation will be discussed in more detail in chapter 9.


forgets her umbrella, she will get wet’ the first condition that it is raining has to hold

for the sentence to make sense at all). A special case is the situation where the event or

situation in the first antecedent is a subset of the second one. Then the first condition is

still sufficient, but it can be widened without loosing its sufficiency, or, in other words,

it is only sufficient because it is a subset of another sufficient condition. Examples for

interpretation as correction can be found in the following excerpts from interviews.

Subject 16A: You have a medical student saying: If Bill has aids, he will make agood recovery. And the situation is: Bill has aids.(...) A: If you also had a professor of medicine saying: If Bill has cholera,he will make a good recovery?(...)A: What do you think why the professor is saying that, in this situation?S: The if cholera part?A: Yeah.S: I think he’s saying you can’t recover from aids. But if he had cholera,then *he’d have a* chance to recover.A: Ah, okay.L: So, it’s like giving an alternative?S: Yeah...L: Like he wishes he had cholera.S: Or if he had aids and then contracted cholera, then he’s saying yourcholera could improve but he’s not saying your aids could.

Subject 23A: Why do you think the professor is saying that: If Bill has cholera, hewill make a good recovery?S: Um...A: In response to what the student says.S: Um, it could be a, it could be a sarcastic comment, um, it couldbe interpreted in different ways, it could be interpreted as mocking themedical student, lack of knowledge, as they are in a position above themand they # know more about medicine than a medical student, they maybe saying: the fact, if he has AIDS, the fact he’s gonna make a goodrecovery is extremely unlikely, so it’s also saying, that comment couldbe interpreted as sarcastic. Um...

Subject 211

A: Okay, so what can you conclude here?11Based on the story: Rose and James are discussing if they should allow her little daughter to go to

a hill walk with her class on the next day.


S: That she is going to get wet and might get sick againA: Do you think she will get wet if it is raining?S: Well, the dad says that she won’t get wet, but an umbrella isn’t alwaysthe best against the rain, especially not in Edinburgh. (laughing) Anumbrella, she might not even use it.

In these cases, the second sentence states the first antecedent is not a sufficient

condition and even implies the negation of the consequent. It introduces another

necessary condition replacing the first one.

It is, however, less obvious how these principles apply if the second antecedent

introduces an additional necessary condition. Then the first condition is not just

replaced; it still has to hold. Yet, we can say that a new sufficient antecedent, consisting

of both conditions, replaces the first one. The second antecedent could then be analysed

as an ellipsis, where the first condition is contained, but not realised on the surface.

There is evidence for the fact that people treat both conditions as part of the same

antecedent. If subjects rephrase the sentences, many join the conditions by ’and’ (often

emphasised), which means that now both conditions have to hold for the consequent

to be true.

Subject 16L: Okay. If Maria studies hard, she will get a high grade in the exams.If she is intelligent, she will get a high grade in the exams.And she studies hard. Therefore...S: Therefore, um, if you are intelligent AND you study hard, then yes, youshould get a high grade.

Subject 11S: (reading) If John goes fishing, he will have a fish supper.If John catches fish, he will have a fish supper.John is almost always lucky when he goes fishing.John is going fishing.A: So, what follows here?S: Um, if he, he is going fishing, and if he catches anything, he is going tohave a fish supper. Um, and he almost always catches some fish, but that

Rose: I’m not sure if we should let her go. She still hasn’t fully recovered from her cold. It depends onthe weather. If it is raining she will get wet.James: If it is snowing she will get wet. She will have her umbrella against the rain, but I know that shecouldn’t resist snowball fights.Rose: Here’s the weather forecast. They say there will be rain tomorrow.


doesn’t guarantee that, even though he’s going fishing that doesn’t meanhe’s gonna catch any fish, or have a fish supper.

There is another important distinction I want to point to. In most previous studies,

a second necessary condition was one which was obviously necessary or part of the

assumptions made in uttering the first conditional. The reason for using this kind

of material was probably that subjects could easily infer by means of their world

knowledge that it was meant to be an additional requirement.12 Yet, this is only a

special way of introducing an additional condition. It can be described as casting doubt

on the satisfaction of the necessary condition. Due to its uncertainty in the present

situation it cannot be assumed to hold, and is thus made explicit. But especially in

cases where the first conditional denotes a general lawlike relationship or habit, this

does not mean that its general truth is denied. The speaker of the second sentence can

still accept that this relationship usually holds, he just points to a possible exception or

abnormality in the present situation. So, the second sentence questions the adequacy

of the first sentence for a particular situation, not its truth in general. This shows again

the importance of considering the context in which a conditional is uttered and meant

to be true.

The difference to other cases becomes clear in the following example: The sentence

’If Mary has an essay deadline, she will be in the computer lab’ suggests that she

usually writes her essays in the computer lab. But if we add the statement ’If the

library is closed, she will be in the computer lab’, the hearer gets the impression that

she usually or under normal conditions writes her essays in the library, she is only in

the computer lab if the library is closed. So, this means that the first sentence is not true

because the connection it is expressing does not hold in all the situations it suggests to

hold.

As previous studies did not treat statements where an assumption was made explicit

as inconsistent, it is necessary to note which notion of inconsistency is employed

here. Inconsistency is often used to describe contradictions that can be expressed by

classical logic. But in our case, there is no overt contradiction between propositions,

the correcting sentence rather questions the satisfaction of assumed background12At least, this is what the experimenters assumed; as shown above subjects did not always adopt the

same interpretation.


conditions. As just noted, the second speaker can even accept the first conditional

as generally true and just doubt its adequacy in the current context. This might be

the reason why the inconsistency within the statement is not so obvious. I think it

is legitimate to speak of correction if an additional necessary condition whose truth

is uncertain is introduced. It must, however, be considered that there are different

kinds of correction, like casting doubt on something in contrast to denying it, and that

inconsistencies are not always perceived to the same degree. This might also affect the

acceptance of a correction by the first speaker. The adaptation of a statement to the

present context might be easier to accept than the denial of the whole sentence.

3.2.5 Summary

The last example shows once more how all the research in this area is biased by Byrne

(1989) and her categories of interpretation. I do not want to claim that my classification

is complete and comprises all ways in which two consecutive conditionals can

be interpreted. Conditional sentences are a phenomenon too complex to give an

exhaustive categorisation of the content they can convey. But I think this overview

contains the essential cases that are necessary to explain the suppression effect. Thus,

let us recapitulate them.

The first category comprises interpretations where the two conditionals are treated

as separate, independent statements. However, people usually believe that all sentences

are part of a coherent discourse and refer to each other. Therefore, with respect to all

the other categories we consider, we can classify the possible interpretations along two

orthogonal dimensions: the consistency of the statement and the relationship between

antecedents and consequents. If the sentences are assumed to be consistent and both are

not necessary for the truth of the consequent, the two antecedents are often treated as

alternative conditions. Another possibility in case of a consistent statement is that one

of the antecedents is a necessary condition for the consequent and assumed to be true.

In case of an inconsistent statement, the second sentence is interpreted as correcting

the first. Here, the sufficiency of the first antecedent is denied and it is replaced by

the second antecedent. Again, the necessity of the second antecedent is an important

factor, but it does not provide a distinction as clear-cut as in the case of consistent


statements. If the second antecedent is a necessary condition, it can be interpreted as

an additional requirement, triggering a modification of the first antecedent. If the first

antecedent is not a necessary condition, it can be understood as implying the negation

of the consequent.

Now, we can also state more clearly what the flaw of Byrne’s categorisation is. She

only considers the relationship between antecedents and consequents and neglects the

consistency of the statements as another essential dimension.

It is also interesting to compare this classification with Stenning and van Lam-

balgen (2003b). The observation that there is no clear-cut distinction between

interpretation and reasoning processes corresponds to their claim of “reasoning to an

interpretation”. Their goal is to model interpretations they believe to be consistent with

the cases described by Byrne, not to give an account of all possible interpretations.

Like her, they have only one category of additional necessary conditions without

considering the consistency of the statement as a distinguishing factor. Their final

representation of the statements only represents the relationship between the two

antecedents. Thus, their analysis is coarser grained than the one presented here.

The question is whether their logic can express these finer distinctions. This would

require modelling a person’s view on the consistency of the discourse and representing

contradictions within a statement prior to the process of accommodation. In their

current model of a credulous interpretation, corrections are always accepted and settled

between the speakers. Such an intermediate stage would also make it possible to model

the case where one of the antecedents is assumed to be true.

It is important to note that these are only interpretations derived from the presented

material, which does not mean that subjects actually believe the truth of the sentences

and base their conclusion on these interpretations. Yet, there is evidence for the fact

that subjects adopt one of the interpretations before distancing themselves from it. This

means that they know what the intended interpretation is, independent from their belief

in its truth.

Subject 6S: (reading) If it is raining, Jane will get wet.If she forgets her umbrella, she will get wet.It is raining.


A: So, what follows?S: Jane will get wet.A: Okay. Are you sure?S: Well, yes.A: What could prevent her from becoming wet?S: Not raining. You know, that’s # she’s not gonna get wet. If it’s raining,whether she has got an umbrella or not, she’ll still get wet.

Here, the second conditional is interpreted as an additional necessary condition,

but the subject does not believe that this factor is relevant, so he does not consider this

condition in his conclusion.


s

Chapter 4

Subjects’ understanding of the

suppression task

4.1 The role of instructions

Previous studies have taken into consideration that the task instructions and the

way the conditional statements are introduced influence how subjects interpret the

sentences and draw conclusions. In the original experiment, Byrne (1989) asked

participants to “assume that the premises were true” and to choose a conclusion that

“follows from the sentences” (p. 68). This instruction is not in accordance with

her assumption that subjects often interpret the second conditional as introducing

an additional requirement, and thus as a correction of the first, stating that it is not

true. Another problem is that it is not clear whether she wants to examine how

subjects understand such conditionals naturally, or whether she wants them to treat

the statements as an abstract logical task. She claims to be interested in “everyday

reasoning”, but presumes that her subjects adopt a classical notion of valid inferences,

i.e. “the conclusion is true (...) in any state of affairs in which the premises are true”

(p. 77), a principle that is fundamental in the mental model theory. This raises the

question what subjects’ definition of a conclusion is. Do they really have this idea

of valid inferences? Byrne (1989) herself admits that there was a “departure from

strict validity” (p. 75) when the conditionals were presented as part of a discourse and

39

Chapter 4. Subjects’ understanding of the suppression task 40

thus typical of usage in daily life. Nevertheless, she sticks to her notion of validity

in modelling human reasoning within the mental model theory. Her remarks point,

however, to the fact that there are different ways of processing the statements in order

to find a conclusion.

Stevenson and Over (1995) say that by presenting their material as a conversation

they “encourage the subjects to treat the premises in the same way as any other

statements that vary in their believability” (p. 628).1 Stevenson and Over (2001)

even claim “that in a conversational context, where one conditional is followed by an

alternative conditional, each being uttered by a different speaker, then reasoners will

pragmatically infer that the alternative is intended as a correction of the original” (p.

377). So, they notice that the interpretation of the second conditional as an alternative

(in Byrne’s terms) is not the only possible interpretation for their statements, but they

do not realise that the second sentence can correct the first one in different ways (as

we saw above), and that interpretations other than correction cannot be excluded.

They assume that in a conversation the second sentence is always interpreted as a

correction although the fact that many of their subjects made modus ponens inferences

is a hint that this is not the case. Their explanation is that subjects do not believe

the second speaker because he has less expertise than the first speaker, and so do not

accept the correction. Our interviews show that subjects do often not even consider the

possibility that the second conditional could be a correction of the first. Even when we

changed the example so that the first sentence definitely contradicted people’s world

knowledge (“If Bill has AIDS he will make a good recovery” instead of “If Bill has

typhoid he will make a good recovery”), many subjects were unable to say why the

second sentence could have been uttered in response to the first, or gave a reason

other than correction2. This shows the need for finding out what the implications for

interpretation and reasoning really are if people perceive the statements as part of a

discourse, and which alternative modes of processing can be adopted.

I think in analysing subjects’ understanding of the task it is important to distinguish

1The assumption that people assign statements in discourse different degrees of believability leadsthem to the idea that the meaning of conditional sentences is closely linked to the conditional probabilityof the consequent given the antecedent.

2Examples will be given below.


between the way they interpret sentences to get their meaning, and the way they draw

conclusions. Although interpretation is an important factor in reasoning and should

not be neglected, we cannot assume that people always reason from their natural

interpretation of the sentences. They might think that they are confronted with a special

way of using language and expected to treat the sentences independent of their natural

meaning.

4.2 Interpretation

When human beings read text or hear speech in their own language, they usually

process them automatically, i.e. besides recognising the fragment as sentences of their

language they try to grasp their content and assign them a certain meaning. Thus,

we can assume that subjects paying attention to the material we present them always

have an interpretation of it. Yet, we saw that subjects can come up with very different

interpretations, which is partly due to their attitude towards the material.

An important factor is the special form of the material used in the suppression task.

When asked if the sentences sounded natural and if they would convey their content in

the same way, subjects usually did not perceive them as natural. We got more positive

answers after we had slightly changed the formulation of the sentences (e.g. changed

the tenses, contracted subject and verb, introduced anaphora and ellipses, made fewer

repetitions of words). Yet, many subjects were disturbed by the categorical premise

because it was worded in the same way as one of the conditions and stated as certain

what had been unknown or uncertain before. We got similar reactions when the second

antecedent contained a condition that must have been assumed to hold in uttering the

first conditional. It seemed to be a widespread assumption that a conditional is only

uttered if the speaker does not know whether the antecedent is true. This became

apparent when we asked participants how many people could say the sentences. As

the following excerpts exhibit, they often assumed more than one speaker.

Subject 4S: (reading) If it is raining then she will get wet.If it is snowing then she will get wet.It IS raining.


(...)A: Or what do you think how many speakers say these sentences?S: Um, the first sentence could be one speaker. And then the secondsentence could be another speaker. And then the third sentence could bethe first, the original speaker. Or it could be one speaker who has realisedafter saying the second sentence that it is in fact raining.A: Okay, so they could all be said by one speaker?S: Yeah, if they are not looking out of the window, so or if they are notoutside, then they could be said by one speaker, and then they go on andactually see that it is raining.

Subject 24L: Another question is: how many people do you think would be sayingthese things?S: More than one, I think.L: More than one.S: Yeah, because you wouldn’t say, I don’t think you would say: If she hasenough money, she’ll go, and also, also you’d say that at the same time asknowing she got her salary.

Subject 5S: (reading) If Mary has an essay deadline, she will be in the library.If she has to copy some papers, she will be in the library.She has an essay deadline.(...)A: What do you think how many speakers say these sentences?S: Um... I think three.A: Why?S: Because the first one doesn’t know that she has an essay deadline. Thesecond one gives a different reason why she’d be in the library, that doesn’tfollow from the first. The third one is supplying information that the othertwo couldn’t have known.(...)S: (reading) If John practices a lot then he will become a good pianist.Of course only if he is musically gifted.John practices a lot.(...)S: I guess you assume that he does have some kind of musical gift becausethe first person says that, then if it’s not the same person who is sayingthe second thing, then perhaps the assumption there is that he has musicaltalent because then that’s the only thing they are talking about. If the firstperson is saying the first two things then they don’t know and therefore


the first sentence doesn’t really necessarily make sense. But if the secondperson is saying “Of course only if he is musically gifted”, then maybe thefirst person knows he already is, that’s already there.

The conflict between introducing information as unknown in an antecedent while

stating its truth in another sentence leads to a certain tension within a statement. In

a discourse this tension can be relieved easily by attributing the sentences to different

speakers. It is, however, not clear what people make of it if they do not get the hint to

treat the sentences as part of a discourse. One possibility is that they cannot make sense

of the sentences taken together. Another possibility may be that they do not perceive

any tension because they assume the truth of one antecedent.3

Although we did not explicitly give the instruction to assume the truth of the

premises, most of our participants believed that all sentences were true or correct,

and based their interpretation on this assumption. In our interviews, we presented

most of the statements as part of a conversation. Here, subjects tended to assume that

the presented discourse is coherent and consistent, and that every participant makes a

relevant contribution.

Subject 23S: If you take the first two sentences as true, you’re saying the green light,if you, if you, if I was just to assume the truth, I mean if I was to assume thetruth of these two, then I think it’s most likely that these two are connectedas well.

A sentence being relevant can mean that it answers the salient question in the given

context. Participants thought that a conditional is uttered because the condition in the

antecedent is a possible event or situation.They tried to find a relevant interpretation of

the statement (quoted above, about Bill having AIDS) by assuming that the question is

which disease Bill has.

Subject 19A: In which situation would the sentence be uttered?S: Alright. I supposed if he developed cholera from, through, I don’t know,aids, it weakens the immune system, so he may develop cholera, I suppose.

3See section 3.2.3 for a description of this kind of interpretation and section 7.2 for a discussion ofuncertain versus true antecedents.


L: So, do you think he would have said it if he thought that Bill hasdeveloped cholera?S: Yes. Because there’s no #, no interest in anybody. If it’s no value, it’sjust saying something, then it’s not relevant.L: So do you think there would be a case where it would be relevant,maybe?S: If he had, he was likely to develop cholera, as well as aids. I suppose inthese # countries they do it as well, don’t they? There might be a chanceof him developing cholera, as well as aids.

Subject 25S: Um, no, the professor thinks if he’s got cholera, he’ll make a goodrecovery. Um, the professor doesn’t seem to think he’s got aids, for somereason or other, the student thinks that, the medical student thinks that.Um, the professor doesn’t seem to make any reference to aids, at all.Cholera seems to be what he thinks the boy has got.

In cases where they cannot find an interpretation in which the relevance of a

statement is obvious, some participants, especially those who do not have much

imagination, find it difficult to come up with a meaningful interpretation. The result

is that they treat the sentences as unrelated because it still allows them to assume that

both sentences are true. Even if a statement is obviously false, as in the following

example, most subjects do not easily think of the possibility of correction. This shows

that the default stance in interpreting discourse is to assume that all speakers tell the

truth.

Subject 14L: Okay, next one. The second part of that is, the medical student says IfBill has aids, he will make a good recovery. And, an actual professor ofmedicine says If Bill has cholera he will make a good recovery. But Billhas aids.S: Wait so... What’s the link? There’s no link.L: So you’re not... would you change your mind?S: No, there’s no link, between the second sentence and the first. BecauseBill has aids, why are you telling me about this person talking aboutcholera. It’s not relevant,L: I guess the way it would be relevant is that the medical student isnot competent but the professor of medicine is. And cholera is a seriousillness.S: Yeah, but Bill has aids. He doesn’t have cholera, so... what’s the...


okay, yeah, I would trust the professor of medicine, I would have trust inthat doctor. But he is talking about cholera, he’s not talking about aids,and Bill has aids so... what’s the relevance between the two? So... You’reasking me in reference to the second statement itself. So, okay, I get whatyou’re trying to say. So Bill may... Bill may or may not recover from aids,if he has cholera. Is that what you’re trying to get me to say?L: I’m not trying to get you to say anything.S: I’m sorry, it just doesn’t make sense to me, the second one. I mean, it’sa serious disease, but he has aids, so what’s the... There’s no relevance.

Subject 22L: A medical student says: If Bill has aids, he will eventually be fullyhealthy. And the situation is that Bill has aids.(...)L: Suppose then, you heard a professor of medicine say: If Bill hascholera, he will eventually be fully healthy.(...)L: Is the medical student present at the time?S: The one who said about aids?L: Yes.S: I don’t know, it’s hardly related. It could be, might not be, it doesn’t tellyou.A: If he said it in a response to what the medical student was saying? Whywould he say it then?S: He wouldn’t, I don’t think. So, the medical student says: If he’s gotaids, he will be healthy. He has aids. And then the other one says: If he’sgot cholera, he will be healthy. He has cholera.L: The medical student didn’t say, by the way, that Bill has aids. You justhave to know...S: Oh, you know. Ah, okay, if he’s got aids, he will be healthy. And thenthe professor says: if he’s got cholera, he will be healthy. They are justsaying random sentences on each other. I don’t know # would saying it, itis weird. I don’t know, they wouldn’t say it, I don’t think.L: Can you imagine a situation where there would be an # to say it?S: Well, if he had a symptom, if the patient, Bill, had symptoms that were,you know, shown by aids or cholera, but he could be mistaken, I don’tknow if that’s possible, but... um, then maybe the medical professor, youknow, the student: If he’s got aids, he will be healthy. The professor wouldjust look at him and gonna be think: But, anyway, he’ll go away, ah, whatif he has cholera, he will also be healthy # He wouldn’t say it, I don’t think,there will never ever be a situation where he would say it.

As a consequence of my questions, the following participant eventually found an


interpretation where the second conditional corrects the first. But she doubts that this

is the intended reading because it means that the first sentence is wrong.

Subject 7A: What do you think how many speakers say that?S: Um, I’m not sure, is that supposed to be some sort of response to...?A: What do you think?S: It seems like two, sort of, saying, a statement of one person wouldsay: if she has to copy papers she will be in the library. It sounds liketwo alternatives to one thing that you could say, but I don’t know if it’ssupposed to be two people talking to each other. I guess I would assumesome * they are talking to, but it doesn’t sound like a conversation.*A: Do you think one person could say that?S: Yeah. Or it could be, I suppose it could be a reply to it, if she has tocopy papers she will be in the library.A: How would you say that? What would sound more natural?S: Um, I suppose if you read it as an alternative, then * If she has to copyPAPERS, she will be in the library. But I don’t know if that is what itmeans at all, if she has to copy papers she will be in the library. Thatwould be suggesting that the first statement was wrong.

So, the effect of presenting sentences as a conversation is not that one is interpreted

as correcting the other. People rather assume that both are true, and try to find an

interpretation where they are both relevant. In contrast, presenting the sentences as

text messages sent by different people who did not know of each other makes many

subjects interpret the sentences separately and independently. In this case, the second

conditional is not interpreted as correction or elaboration of the first conditional, even

if this interpretation would very likely in a conversational context as in the following

example. In the first excerpt the second condition is interpreted as a correction, in the

second it is understood as an independent condition.

Subject 10S: (reading) If Mary has an essay deadline, she studies late in the library.If the library stays open, she studies late in the library.A: So, what do you think they are talking about?S: Mary, having an essay deadline, and, as long as the library is open, andshe is going to study in the library to meet up.A: If you hear then this sentence: Mary has an essay deadline. What elsedo you know then? What can you conclude?


S: That she definitely has an essay deadline, so she is going to study latein the library.A: What do you think how many speakers say these sentences?S: Three.A: Why?S: Because one would say: if she’s got a deadline, then she studies late.The other one would say: Yes, but only if the library is open. And theother one is saying: she does have an essay deadline. So, that applies.A: Would you be sure that she is in the library?S: Only if the library is open. They were not sure that the library is open.

Subject 23L: Hm, hm. Then you read the next message, which says: If the library isopen, she’ll be in the library.S: Um, yeah, then I think it was getting increasingly likely that she wasthere.L: What do you think that person meant?S: Um, just exactly what she, exactly what they said, really. That she canbe found most of the time in the library, um, she’s hard-working.

Subject 20L: Then the third message says, If the library is open, she’ll be in thelibrary. What do you think that means?S: Okay so it means that she’s gonna be working full out during the day, soshe’s gonna be working like all day, so she prefers to work in the library,so she’ll be in the library if it’s open, but if it’s not open obviously she’llbe working elsewhere, maybe.

Of course, it is difficult to make people interpret sentences which are presented

together totally independent from each other. Even if sentences are presented as

messages from people who did not know of each other and thus one is not a direct

response to the other, subjects assume that they are somehow related. For instance,

they assume that both messages are answers to the same question, which is of course

very obvious, given the fact that they share the same consequent.

Subject 20L: The addition of the third sentence, if the library is open, she’ll be inthe library, do you think that influences where she’ll be at all? Like, youropinion of where she’ll be.S: Yeah, cause like I said before it implies that she’s working, she’s got alot of work to do, cause you know, in a normal day, if the library is open,


you’re not gonna be there automatically, so this person is saying if thelibrary is open she’ll be there, so that implies she’s got a lot of work on.So yeah, it influences your judgement of where she’s gonna be. Librariesare open most of the day as well, so it’s not like... Unless its a weekendL: So pretty much that sentence, “if the library is open, she’ll be in thelibrary”, is influencing you to think that its more likely.S: Its influenced by the other one as well, that one on its own wouldn’t beas powerful.A: What do you think the whole thing was about, why do you think allthese messages were sent? Are they somehow related?S: The person who owns the phone, texted a number of people asking themthe whereabouts of Mary. And people are replying about it, so maybe itslike three different messages from three different people maybe its like thesame person, in a backwards and forwards replying, you know.L: Do you think they were all answering the same questions?S: I think they’re all answering the same questions, all about where Maryis, so...

This subject thinks that all messages answer the question “Where is Mary?”.

Although he does not really interpret the sentences as directly related, he says that

they both influence his reasoning. It is probably a general property of human language

understanding that the interpretation of a sentence is influenced by the context in which

it is uttered, even if it is not meant to refer to it.

Does this help us in predicting which interpretations are most likely to be adopted

by subjects? Is there something like a default interpretation? As subjects tend to treat

both sentences as true and part of a coherent discourse, the second conditional is most

likely to be interpreted as introducing an alternative condition or assumed to be true.

Which one is chosen in a particular situation depends to a great extent on the content

of the sentences. If it allows us to regard the two conditions as alternative options, this

interpretation is probably the preferred one. But if the content of the two conditions

is strongly connected or one of them is necessary, it is rather treated as an elaboration

or clarification. Of course, this requires that people have enough knowledge about the

domain and use this knowledge in interpreting the sentences. These factors will be

discussed in the next chapter.

An interesting observation in our interviews was that many subjects changed their

interpretation as a reaction to our questions. When we asked them if they were sure


about their conclusion or what could prevent the consequent from being true, they

became more sceptical and started thinking about counterexamples. As a consequence,

they often treated the second sentence as a correction. The following excerpts show

some examples.

Subject 1A: (...) If she has an essay to write, she will be in the library.If she has to train for a competition, she will be in the gym.If the library stays open, then she will be in the library.Then he says: I remember her telling me that she has to hand in an essaynext week. So, where would you look for her.S: In the library.A: Are you sure you would find her there?S: Um, but he said that ... (laughs) that if she had an essay to write she willbe in the library. Or if it’s open, I guess, so it depends, it depends. (...)A: What aboutIf John practises a lot then he will become a good pianist.Of course only if he is musically gifted.John practises a lot. What follows?S: He will be good in playing the piano. If he practises a lot ... if he is justgifted he will be good in it anyway, but he still has to practise.A: What if he only practises? S: Um, if he is not gifted? # he still could ifhe practises a lot.A: (reading sentences again)S: Okay, yeah, he can only be a good pianist if he is musically gifted,and practises a lot. So, John practises a lot, but it doesn’t tell us if he ismusically gifted or not. So, he might not be a good piano player.

Subject 15L: If Rosa meets her friend Liz, she goes to the cinema.If she has money for a cinema ticket, she goes to the cinema.And she has money for a cinema ticket. Therefore...S: Therefore she will go to the cinema.L: Regardless whether she meets Rosa?S: Can you repeat that?L: If Rosa meets her friend Liz, she goes to the cinema. If she has moneyfor a cinema ticket, she goes to the cinema. And she has money for acinema ticket.S: So then no, she would want to wait for her... for her friend.L: But why, I mean we said that if she has money for a cinema ticket thenshe just goes to the cinema.


S: But I don’t think she would want to go alone. She is waiting for herfriend.

4.3 Reasoning

In the previous section we saw that the material used in the suppression task is often

perceived as unnatural. Another interesting question is how natural it is to draw

conclusions from this kind of material. Our interviews showed that the task is not

as clear as is assumed by many authors of previous studies. When we asked subjects

what followed from one or two conditionals and a categorical premise, or whether they

could draw any conclusion, some made inferences other than modus ponens or were

not sure what they were expected to do:

Subject 16L: If Mary has an essay deadline, she studies late in the library.And she has an essay deadline. Therefore...S: Therefore, she must be close to her deadline. Is that what you werelooking for?L: Well, where do you, where do you think she’ll be?S: Okay, sorry. Could you say that again?L: If Mary has an essay deadline, she studies late in the library. Mary hasan essay deadline.S: So, she’s in the library?

This can be explained easily, as every segment of natural language allows a great

number of different kinds of inferences (e.g. lexical or conversational inferences) and

the ones based on ’if’-sentences are only one option subjects face - although the form

of the statements gives them a special weight in this case. Especially subjects knowing

tasks of a similar form like syllogisms or riddles based on classical logic will favour

this kind of inference. But if the statements are embedded in a broader context and

not presented in written form, this similarity may not be so obvious. The fact that

we could observe other kinds of inferences might also indicate that there are ways of

interpreting a conditional which do not so strongly lead subjects to conclude the truth

of the consequent from the truth of the antecedent.


Subject 17A: Imagine you are sitting in a bus, and there are some people at the backof the bus, having a discussion, and you want to find out what they aretalking about, and you hear them say: If Mary has an essay deadline, shestudies late in the library. So, what do you think they are talking about?S: Um, probably talking about someone who is not in that group, who,and what they do for studying, so they might be talking about what theyare doing for studying, and they are saying: Well, Mary does that - as anexample of what other people might...A: And then you hear the sentence: Mary has an essay deadline. Whatfollows then, what can you conclude?S: Um, well, that Mary is a student, and, or, yeah, Mary is a student andhas a deadline coming up, and possibly they would have a deadline aswell.A: Hm. And if you take both sentences together: If Mary has an essaydeadline, she studies late in the library. And: Mary has an essay deadline.S: Now they are probably talking about why Mary is not there, why Marycan’t be with them. I think it is, she will be studying late in the librarywhile they are on the bus.

After we had given subjects hints as to which kind of inference we expected,

they were able to make modus ponens inferences, and started making them by

themselves in the following examples. This shows that there are different kinds of

inferences from conditionals, and that subjects can switch between different modes

of reasoning. The inferences in the last two examples can be explained by general

principles of conversation like the Gricean maxims. The subjects want to make an

informative contribution to the discourse, but modus ponens inferences do not add new

information. Thus, they do not usually occur in speech, and are not an obvious answer

for participants perceiving the task as a natural conversation. But not all participants

regarded the material as a fragment of natural language they would encounter in daily

life. There is evidence that subjects often understood the sentences as an abstract

problem they had to solve. Although we told them before that we were interested in

how they understood the sentences and that there were no right or wrong answers, the

form of the material and the request to draw conclusions suggested this kind of task.

Subject 12A: Are these sentences you would say?S: No, no.


A: How would you say that?S: I would probably say: John likes a lot of fish. I’m not sure, theywouldn’t, I don’t know anyone who goes fishing, so it wouldn’t naturallycome to me.A: Why do you think it doesn’t sound natural?S: Cause it’s very sort of: If John goes fishing (every word emphasised),he will have a fish supper. If John CATCHES a fish, he will have a fishsupper. John is almost lucky when he goes fishing. It sounds like sortof a maths problem. Like a maths problem, like when Jason goes to thelibrary, he picks up three books. You know what I mean? Very sort of #and everything.A: So, what would sound more natural then?S: I don’t know. Um...*It’s hard to say* because it sounds like a riddle,like a problem, as opposed to like a story.

Subject 25L: That’s good, I think we’re done, thanks very much. What do you thinkthe experiment was about?S: Um, logic perhaps, you know, if this and if that, then what would that #gonna be about?

Subject 17L: What do you think of the questions? Like what do you think is goingon?S: Well, I was thinking before you read the questions that it was gonna be,um, like some sort of, um, *hot-doing* thing where you would # makethat suppositions and then have to change it, like constantly, but either I’malways right or I never know # what actually changed to, because there’snot that many changes that have been going on in it. So, I don’t know whatyou’re gonna looking for.L: Hm, hm. Still you don’t know?S: Um, no, not really.L: Hm, hm. Does the sort of what make you more sceptical of us as thespeakers, as we went on?S: Um, how do you mean?L: Well, in the first one you answered the question pretty quickly andpretty shortly, and after that you gave more and more reasons.S: Well, I think it’s just sort of fitting it more into context as it goeson. Although in terms of the wording, as I said they are worded in a,like a logical argument # all humans are mortal, men are humans kind ofthing, which isn’t so conversational, but I’ve been trying to fit them intoconversation, which presumably is why I’ve said more about what’s going


on in the context.L: Ah, so you think it’s about implications, things like that?S: Um , quite possibly #, since I’ve been trying to look for implications,then I hope what it’s about, yeah.

How does this understanding of the task influence the reasoning process? In one

case, we made the mistake of asking the subject before the interview whether she had

knowledge of formal logic. This made her try to relate the given sentences with the

content of her logic classes and to translate them into formulae of classical logic.

But there can also be other, less extreme consequences. One is that subjects’ do

not adopt the goal of making an informative, relevant contribution to the discourse.

They accept that their task is to say what obviously follows from the given sentences.

Another consequence might be that subjects do not necessarily base their conclusion

on their natural interpretation of the sentences. They are used to similar tasks in maths

or other subjects, so they abstract away from the concrete meaning of the sentences

and do not try to embed them in a broader context. In this case, the content of the

sentences and subjects’ world knowledge might only play a minor role. But as our

questions encouraged subjects to use their world knowledge and make up a context for

the statement, it is difficult to pinpoint the exact implications of this attitude on the

reasoning process. The interaction of abstracting and concretising became apparent in

the last excerpt.

Of course, not every subject adopted one of these extreme positions. There is prob-

ably rather a continuum of different stances in treating the material. Argumentation,

for instance, is a form of discourse lying between the two positions described above.

It excludes certain kinds of Gricean implicatures, but it is not as abstract as a logical

task.

What are now the conclusions subjects draw if their reasoning is based on the type

of inference conditionals invite to? At this point, we come again across the question

what subjects consider as a valid argument. Do they really have the classical notion of

validity as the mental model theory claims? This would mean that they only endorse a

conclusion if they cannot find a counterexample to it. The role of counterexamples will

be discussed in more detail in chapter 6, but we can already note here that subjects drew

conclusions although they could readily find counterexamples to them. This suggests


rather a non-monotonic notion of validity, where a conclusion only has to hold in

all preferred models (see Stenning and van Lambalgen (2003b)). Unfortunately, the

interviews do not yield sufficient data to examine how subjects’ understanding of the

task influences their notion of a valid argument.

As we saw above, subjects usually assumed that all premises were true. This is

also illustrated by the next example.

Subject 17L: So, you basically didn’t change your mind when you heard the secondsentence?S: Well, no, because it doesn’t alter the first two, if both of the first twoare correct anyway, then it’s just another criteria which she doesn’t haveto meet together.

But even if they interpreted one sentence as stating that the other one is false,

they had no difficulties in drawing a conclusion. This shows that assuming the truth

of all premises is not necessary for deriving a true conclusion, as is the case with

the classical notion of validity and soundness. If subjects base their inferences on

their interpretation of the statements, then their conclusion rather follows from their

interpretation of the discourse as a whole

Chapter 5

Involvement of world knowledge

As we saw above, there are several possible interpretations of the conditional

statements used in studies on the suppression effect. Yet, previous studies often assume

that all subjects come up with the same interpretation. The meaning of the sentences

is supposed to be clear because the second conditional reminds people of the inherent

properties of a situation described by the first conditional. The underlying assumption

is that world knowledge is used to get this interpretation. But people’s knowledge

about particular topics differs, and they use their world knowledge to different degrees.

Although each statement is more likely to be interpreted in one way rather than another,

there is still room for individual differences

Many subjects think they are expected only to use the semantic content of the

sentences to solve the problem, so they try to exclude their world knowledge. This is

illustrated by the following example.

Subject 4S: (reading) If John practises a lot then he will become a good pianist.If he is musically gifted then he will become a good pianist.He practises a lot.A: What follows here?S: Um.... first it looks like... um... if he practises a lot then he will bea good pianist. It doesn’t specify that he has to practise a lot and bemusically gifted to become a good pianist. So I would say that he willbecome a good pianist, just by practising a lot.A: So you think it’s not necessary to be musically gifted to be a goodpianist?

55

Chapter 5. Involvement of world knowledge 56

S: *From these* sentences, it’s not me personally speaking, I would sayyes.A: Okay.S: But from these sentences... it doesn’t say: if John practises a lot ANDhe is musically gifted, he will become a good pianist. *They are eachother* mutually exclusive, so separate sentences.

We tried to find sentences which did not require the use of world knowledge or

for which several interpretations were equally possible, but it turned out that it is very

difficult to find such neutral sentences. Nevertheless, it was possible to examine the

influence of world knowledge on the interpretation process. Its involvement became

clear when people changed their interpretation as in the following case.

Subject 12S: (reading) If John goes fishing, he will have a fish supper.If John catches fish, he will have a fish supper.John is almost always lucky when he goes fishing.John is going fishing.A: So, what follows here?S: There’s a good chance of having a fish supper.A: What could prevent him here from having a fish supper?S: If he doesn’t catch a fish.A: Okay, so what...S: Well, ah, not, not necessarily actually, he is going fishing, so he mighthave bought fish supper.A: So, do you think... So, if you know that he catches fish, do you knowthen for sure that he will have a fish supper?S: Well, it says of John: if he goes fishing, he WILL have a fish supper, sohe may have fish supper, even if he doesn’t catch fish.A: Which information do you need to be sure that he will have a fishsupper?S: Um..., that he is going fishing, I don’t know.

It could also be observed that some statements allowed more interpretations than

others, so people had to use their world knowledge to a greater extent for finding and

justifying an interpretation. This was the case for the following statement from Byrne

et al. (1999):

If Maria studies hard then she gets a high grade in the examinations.If she is intelligent then she gets a high grade in the examinations.


She studies hard.1

The authors expected people to interpret the second condition as an additional

requirement, but lots of our subjects understood it as an alternative or assumed it was

true. Their interpretation mainly depended on their idea of the relationship between

intelligence, hard work and good marks, as illustrated by the next example.

Subject 2S: (reading) If Maria studies hard then she gets a high grade in the exams.If Maria is intelligent then she gets a high grade in the exams.She studies hard.A: What follows?S: That she will get a high grade in the exams.A: Could you think of situations where she studies hard but she doesn’tget high grades?S: If something catastrophic happens, like she was on the way to her examsand she had a car crash, and so she was so # and upset that she couldn’tthink while she was doing her exam.(laughing)A: Do you think she is intelligent?S: Well, it depends, because she might not, intelligence might not comeeasily to her, but if she works hard and learns well, then that’s anotherform of intelligence... She is not born with it, but she studies hard andgains wisdom.A: Do you think you have to study hard to get high grades?S: Some people don’t have to study at all and they get high grades.

Although we tried to make the formulation of the second conditional less ambigu-

ous, the following subject changed her interpretation when she started to deploy her

own knowledge.

Subject 11S: (reading) If Maria studies hard, she will get a high grade in the exams.Of course, only if she is intelligent.She studies hard.A: What follows here?S: Um...She does study hard, so, but that doesn’t necessarily mean that shewill get a high grade.A: Why not?S: Because it says: Of course, only if she is intelligent. But if she studies

1We presented the sentences in a slightly modified form to make them seem more natural.


hard, there’s not any reason for her not getting a good grade.A: What if she is not intelligent?S: Um, well maybe she is not intelligent, but maybe she can memorisethings well, and then maybe she could, she could still do well in the exam,I guess. Um, I don’t really know what else to say about that, really.

The next subject even stated explicitly that she interpreted the statements based on

her own experience because it was a familiar topic to her.

Subject 14A: If Mary studies hard she gets a high grades in the exams.Mary is studying hard. What follows?S: Okay, but then... well... so she is studying hard. I wouldn’t assume...she MAY get hight grades.A: Why MAY?S: Uhm... I don’t know, maybe as a student I, you know, I think... It’slike a personal experience thing, like you may study hard but you may notnecessarily get high grades at the same time, because... so I would say, sheMAY get high grades on the exam.L: Like uh... you’re not really believing enough?S: Like what do you mean?L: Well, we said if she studies hard then she’s gonna get high grades. So Iguess... I mean you’re...S: Yeah butL: Your knowledge as a student.S: Well, it’s not that simple isn’t it, because when you talk about say, therat. What’s the first one, the photocopying thing... To me these are likevery strange, am I confusing you, these are like very strange situations.But now where you’re studying, I don’t know it’s just a different situation.And not...L: Is it like less specific maybe?S: Yyyyyyeah. In a sense. In a sense that’s specific. Like to me, let’s saythe rat and the whatever is... it’s like to me is like a no brainer, it’s likedirectly related, but now, no. I don’t really think so. Now I would say she,I would say she may get high grades. Or she will probably get high grades.But I won’t say she will. You get what I’m trying to say?(...)L: No, that’s fine. Okay, you wanna do the next one? The second bitof what she was... If Mary studies hard, she gets a high grade on theexams. Of course, only if she’s intelligent. And she is studying hard.Then therefore...S: So I’m supposed to interpret... so I would say... I would say she will


get high grades if she’s studying hard and if she’s intelligent.L: Okay, so you changed your mind from before.S: From before as in...L: From before, last time you said “maybe if she gets high grades she’ll...”S: Yeah, because... Yeah I was thinking like... that is what I had in mind.I didn’t say it, but you could be dumb and you could be studying reallyhard, but it doesn’t mean you would get high grades. But... maybe like Isaid if you compare with the previous two situations this is something I’mmore familiar with, you know that... so now I’m like, if she’s intelligentand she studies hard, I think, yeah I would think she will get high grades.

It is also interesting to examine cases where the given statement is not consistent

with a subject’s world knowledge. Johnson-Laird and Byrne (2002) claim that

reasoners change the representations of conditionals if they contradict their world

knowledge. This modification of mental models might prevent inferences which would

have been possible otherwise. I think, however, that there is a basic mechanism of

drawing inferences from conditionals, independent of people’s world knowledge. If a

conclusion contradicts their world knowledge, they discard it and say that they cannot

draw a conclusion, or qualify their conclusion by means of probabilistic terms. For

people not used to solving abstract tasks, this might even be the case if the conclusion

does not follow from their world knowledge, without there being a real inconsistency.2

By saying that Bill will not make a good recovery, the following subjects show that

this is the conclusion which would follow from the sentences if they did not use their

own knowledge about AIDS.

Subject 16A: You have a medical student saying: If Bill has aids, he will make agood recovery. And the situation is: Bill has aids. Can you draw anyconclusion?S: I don’t think he’ll make a good recovery.A: Why not?S: Because you don’t recover from aids.

Subject 22L: A medical student says: If Bill has aids, he will eventually be fully

2Luria (1979) reports of peasants in Uzbekistan and Kirghizia who refused to make inferences fromsyllogisms if they had never been in the country that the statement was about. One of their participantsstated: “Your words can be answered only by someone who was there, and if a person wasn’t there, hecan’t say anything on the basis of your words.”


healthy. And the situation is that Bill has aids.S: Then the medical student is lying. Unless they discovered a # cure orsome. And Bill is healthy?L: No, Bill has aids.S: Then, it doesn’t, it’s not logical. But if you just took it as *faith*value, and didn’t have a clue what *you are all* about, then you couldsay: Bill will eventually be healthy. But it doesn’t, it’s not based onknowing the world, having background knowledge. If you just didn’tknow anything, then, if it was the first sentence you ever heard, but youunderstood English, then you would believe he’s gonna be healthy.

Another interesting observation is that the use of world knowledge and the use of

probabilistic terms often occur together in our interviews. So, probabilities are not part

of the basic meaning of conditionals, they are added to make them agree with people’s

world knowledge. An example is the following excerpt.3

Subject 6A: You’re going to the cinema tonight to see ”Troy”. You know that yourflatmate Susan wants to see it, too, so you would like to ask her if she isfree tonight. But she isn’t at home and you can’t catch her on her mobilephone. So you ask your other flatmate Tom and his girlfriend Jenny: ”Doyou know where Susan is?”.Tom says: If she has an essay to write, she will be in the library.Jenny says: If the library stays open, then she will be in the library.And during the last days, she was quite often in the gym to train for hercompetition.Then Tom says: Oh, I remember her telling me that she has to hand in anessay next week.So, where would you look for her?S: Um, it is # a good chance of finding her in the library. # Maybe shecould be by the gym, as well.A: Okay, so what could prevent her from being in the library?S: Well, she could be in the pub, you know. (laughing) There’s a whole,an infinite number of possibilities...#A: So, is there any information you would need to decide where she is?S: Well, it’d be interesting to know how conscientious as a student shewas. You know, if she doesn’t give her # Say, she is a first year student,and she’s got a week for an essay deadline. She is probably not gonna bein the library. But if she is a final year student and she wants to stay on fora PhD, she will probably stay in the library, working really hard.

3This topic will be discussed in more detail in chapter 7.


Stevenson and Over (2001) show how the expertise of the speakers influences their

subjects’ interpretations of conditionals. They say that “reasoners make inferences

about the likelihood of a proposition based on the expertise of the speaker” (p. 377),

i.e. experts are more believed than novices. But I think this is again a matter of

world knowledge, namely the knowledge someone has of a person’s experience and

expertise in a particular domain. Our interviews show that people sometimes distance

themselves from a speaker and do not believe him, but they still know which conclusion

his utterance suggests, they can draw a conclusion “according to what he is saying”.

Subject 19A: A medical student says: If Bill has aids, he will eventually be fullyhealthy. And the situation is: Bill has aids. What follows here?S: Well, according to the medical student, he will be fully healthy.

Subject 11S: (reading) Professor of medicine: If Bill has aids, he will make a goodrecovery.Medical student: If Bill has cholera, he will make a good recovery.Situation: Bill has aids.A: What follows here?S: It’s implied that he will make a good recovery, from the first sentence.Um, but that’s based only on what that professor is saying.A: What do you think, why is the student saying the second sentence?S: Um, maybe, it doesn’t really seem to relate to the fact that he has aids.Maybe... I don’t know.A: So, can you be sure that he will make a good recovery?S: No, you can’t just from what that first sentence says. It’s assumed thathe would, but you couldn’t say that for sure.A: Why not?S: Well, that’s just not from the sentences, just from... Um, I don’t know,I don’t think you could make an assumption like that.

Chapter 6

Conditionals and counterexamples

Mental model theorists claim that the suppression of inferences is strongly related to

the “availability of counterexamples”. Byrne et al. (1999) say that “a conclusion is

valid if there are no counterexamples to it, that is, if there are no situations in which

the premises are true but the conclusion is false” (p. 350). But what they actually

mean are not real situations, but mental models of the premises, in accordance with

the classical notion of validity. Their “key suggestion is that the provision of an

alternative or additional antecedent enables people to represent counterexamples to

conclusions explicitly” (Byrne et al., 1999, p. 352). This means the representation

of several conditionals can contain models in which the categorical premise is true

but the consequent of a corresponding conditional is false. According to the mental

model theory, the existence of such models makes people suppress a conclusion. Thus,

they say the suppression of inferences does not depend on whether people can think

of general counterexamples, but solely on the content of the conditionals, especially

on the relationship between the two antecedents. Only because they think that this

relationship is interpreted by means of world knowledge (which is, as we have seen

above, only partly true), Byrne et al. (1999) can claim that “the role of background

knowledge in the suppression effect is that it provides ready-made counterexamples to

putative conclusions” (p. 369). This shows that their terminology is a bit confusing

since the words ’counterexample’ and ’background knowledge’ do not suggest what

the mental model approach really is about.

The above quotation also points to another open question within the mental model

62

Chapter 6. Conditionals and counterexamples 63

theory, namely which conclusions people have counterexamples to. Which are the

conclusions “they are considering” or “that would otherwise be endorsed” (Byrne

et al., 1999, p. 371)? The mental model theory does not explain which mechanism

makes people choose such a putative conclusion.1 Does this suggest that there is a

basic mechanism of making inferences from conditionals which is prior to considering

mental models?

Although these inconsistencies within the mental model approach already cast

doubt on its appropriateness for explaining the suppression effect, there remain several

claims which have to be examined empirically. Let us regard cases where participants

in our interviews did not draw a modus ponens conclusion because an additional

requirement was not satisfied.2 The first thing to note is that many subjects interpreted

Byrne’s examples in one of the other ways described above (i.e. they interpreted

the second antecedent as an alternative condition or assumed it was true). And

even those who interpreted the second conditional as a correction often only did so

when our questions started making them more sceptical. But although the way they

interpreted the sentences was affected by our questions, it is legitimate to examine

how they reasoned from this interpretation. Another important point is that subjects

never refused to conclude anything at all because of an additional requirement. Yet,

conclusions were often qualified by modal expressions or conditions. So, the essential

question is whether these modifications indicate that people’s reasoning is based on

finding counterexamples, or rather counter-models. This hypothesis would predict

that subjects, having such a counter-model in mind, point to the possibility of the

second condition not being fulfilled, and thus, the consequent not being true. But

this was usually not the case. People rather used the positive (as opposed to the

negated) form of the additional condition and the consequent. Instead of saying that the

consequent might not be true, they gave conditions for its being true. Others modified

the consequent by a modal operator while still speaking of it in an affirmative way.

Subject 251An exception might be Dieussaert et al.’s (2000) amendment strategy where a conclusion based on

the first conditional is modified if new information in form of a second conditional is added.2I restrict my attention to these cases because this is what the mental model theory tries to explain

by means of counterexamples. There are, of course, other reasons for people not to draw a conclusionbased on modus ponens, e.g. if it contradicts their world knowledge (see previous chapter).


L: Okay, go on to the next one then: If Rosa meets her friend, she’ll go tothe cinema. If she has enough money for a ticket, she’ll go. And she gother salary this week. Can you conclude anything from those?S: Well, she should be able to go to the cinema if she meets her friends, sheneeds her friends, she needs money, and she’s just been paid her salary, soshe’s got the friends, then she’s got, she needs to go to the cinema, I wouldthink.(...)A: Again three sentences: If the green light is on, the rabbit is in the cage.If the door is closed, the rabbit is in the cage. I can see that the green lightis on. So, imagine that’s a conversation, you hear these sentences, whatcan you conclude now?S: What I conclude? If the cage door is shut, then the rabbit is in the cage.Again, you’ve met one of the two criteria for the rabbit being in the cage.The green light is on, fine, the rabbit is in the cage. Um, but we don’tknow whether or not the door is open or not. If the door’s shut, then that’sit, we got it for sure, the rabbit is definitely in the cage.

Subject 233

L: Okay, and do you think she will end up going to the cinema?S: Ahm..., if her friends are around, she has the money, so...ahm, thenthere’s one person if this is a different person to that person and they aresaying, you know these two people have contrasting opinions, then sheobviously has enough money, but she needs to meet her friends, as well,so, the friends would need to be around.

Subject 10S: (reading) If Maria studies hard, she will get a high grade in the exams.If she is intelligent, she will get a high grade in the exams.She studies hard.A: So, what follows here?S: That she will get a high grade, assuming that she is intelligent, as well.Because to get a high grade she needs to study hard and be intelligent, andit only says that she studies hard. So if Mary is intelligent as well, she willget a high grade.

Subject 3S: (reading) If John practises a lot, then he will become a good pianist.Of course only if he is musically gifted.John practises a lot.A: What follows here?

3Based on the same statement.


S: He MIGHT become a good pianist.A: Why? What reasons are there why he shouldn’t...S: Well, I don’t know if he is musically gifted. And the statement is thathe will only become a good pianist if he is musically gifted, as well aspractises a lot.

The following two conclusions are the ones which are closest to the mental model

approach. But it is not clear if this can be taken as evidence for the existence of a

model in which the second condition and the consequent are false.

Subject 2S: (reading) If John practises a lot, then he will become a good pianist.Of course only if he is musically gifted.John practises a lot.A: What follows here?S: So, he might become a good pianist.A: What could prevent him from becoming a good pianist?S: Because he might not be musically gifted. So, maybe, no matter howmuch he practises, he just can’t understand rhythms and, or dynamics, andso no matter how *much* he practises, it *just* sounds crappy.

Subject 1S: Okay, yeah, he can only be a good pianist if he is musically gifted,and practises a lot. So, John practises a lot, but it doesn’t tell us if he ismusically gifted or not. So, he might not be a good piano player.

Another way of testing the hypothesis of the mental model theory is to check

which kind of counterexample people come up with, i.e. what they think could be

reasons for the consequent not being true in cases where the categorical premise is

true. Therefore, we asked participants in our interviews questions like “What could

prevent her from going to the library?”, or “Can you think of situations where she

has an essay to write, but she doesn’t go to the library?”. The goal was to examine

whether the type of counterexample the mental model approach is based on is related

to people’s interpretation of the sentences and whether it really makes people suppress

conclusions. Of course, the fact that people find counterexamples when they are

explicitly asked for such does not guarantee that they were aware of these situations

while choosing a conclusion. The mental model theory makes only claims about

“explicitly represented” counterexamples. Yet, the observation that subjects usually


did not have to think about this question very long shows that the counterexamples

were easily available. Indeed, many subjects gave the negation of the second condition

as a reason for the consequent not being true.

Subject 25S: Could you read me *the same* again, please?L: Sure. If Mary has an essay to write, she’ll be in the library. If the libraryis open, she’ll be in the library. Mary has an essay deadline tomorrow.S: Presumably she’s in the library, doing her essay.L: Hm, hm. Do you think anything could prevent her from being in thelibrary?S: Well, if the library was shut, I suppose.L: Hm.S: The second one said: If it’s open, that’s where she’ll be, it might beshut.

Subject 3A: (...) If she has an essay to write, then she will be in the library.If the library stays open, then she will be in the library.If she has to train for a competition then she will be in the gym.Oh, I remember her telling me that she has to hand in an essay tomorrow.So, where would you look for her now?S: In the library?A: Are you sure she would be there?S: Yeah.A: Why?S: Because Tom says: she has an essay to hand in, so she will be in thelibrary.A: Well, what could prevent her from going there?S: If the library is shut. Or, if she has a competition, she will be in thegym.

People who only give these conditions as exceptions or counterexamples are

often those who try to exclude their world knowledge and adopt something like a

closed world assumption. Others, who use their world knowledge in interpreting the

sentences, often talk of situations not mentioned in the text. There also seems to be a

correlation between the type of counterexample a person gives and her interpretation of

the second conditional. Subjects interpreting the second conditional as an elaboration

are less likely to think of the possibility that its antecedent might not be true. As they


assume it is true, it does not affect their reasoning. The following excerpts illustrate

this effect.

Subject 2A: (...) “If she has an essay to write, she will be in the library.If she has to train for a competition, she will be in the gym.If the library stays open, then she will be in the library.Oh, I remember her telling me that she has to hand in an essay next week.”So, where would you look for her now?S: In the library.A: Why?S: Because, you said: if she has an essay to write then she will be in thelibrary, and it stays open.A: Okay, so, do you know that it stays open?S: Didn’t the guy just say that it stays open? *While it* Stays open.A: It says: if the library stays open, she will be in the library.S: Okay, then I would *go to* the library, I would beg that the library isopen.A: Okay. Could you think of any situations where she has an essay towrite, but she isn’t in the library?S: Just random ones, like if she was going to the library, and then she sawhere boyfriend and they decided to go out for coffee instead (laughing)....If she is a procrastinator, she would be in the library.

Subject 18A: Imagine you are sitting in a bus, and there are some people at the backof the bus having a discussion, and you want to find out what they aretalking about. And you hear these sentences: If Rosa meets her friend Liz,she goes to the cinema. If she has money for a cinema-ticket, she goes tothe cinema. She has money for a cinema-ticket.(...)A: And can you draw any conclusion from that, what follows?S: Well, # she has money for the cinema, so I suppose, she goes to thecinema, with her friend.A: Can you think of situations where she has money for a cinema ticket,but she doesn’t go to the cinema?S: She has seen the cinema, the film before. Or, um, she goes to anotherform of entertainment.

Subject 19L: Here is the next one: You hear that, if Mary has a paper to write shewill be in the library. If she has a history paper to write, she will be in


the library. And you know that she has a paper to write. What can youconclude from that?(...)A: Are you sure she will be there?S: Oh no, I’m not sure she WILL be there. If she’s writing a paper, thenshe WILL be there. She might be on a coffee bar, having a coffee.

Similarly, subjects who understand the second antecedent as presenting an alterna-

tive condition and not as another necessary condition, do not see it as a reason for the

consequent not to be true.

Subject 17A: (...) If Maria studies hard, she will get a high grade in the exams.If she is intelligent, she will get a high grade in the exams.She studies hard. Would you draw the same conclusion?(...)A: Can you think of a situation where she studies hard but she doesn’t geta high grade?S: Um..., no, well, if the first two sentences are correct, then if she studieshard she will always get high unless that person’s wrong or she’s studyingfor the wrong exam, or some other situation like that, but assuming that’scorrect, then yeah, she would, she would automatically get honour, yeah,she would be expected to get a high grade.

Subjects usually did not have difficulties finding a situation where the consequent

would not be true. If no condition was mentioned whose absence could be used

as such, then they easily came up with other situations. Yet, there was no obvious

correlation between the availability of counterexamples, no matter of which type, and

the suppression of inferences. As the above examples show, subjects who were aware

of events that could prevent the consequent from being true still made modus ponens

inferences.

Thus, the interviews provide rather evidence against the mental model account of

counterexamples. Does this mean that counterexamples are not important in analysing

conditionals, or do they play a different role? Stenning and van Lambalgen (2003b)

say that “especially in the case of lawlike conditionals, such a counterexample is not

used to discard the conditional, but to look for an abnormality” (p. 14). They describe

the meaning of conditionals as “If A, and nothing abnormal is the case, then B” (p. 14).


This is similar to Politzer and Bourmaud’s analysis following authors like Ramsey or

Goodman:

Conditionals are typically uttered with an implicit ceteris paribus assump-tion to the effect that the normal conditions of the world (the satisfactionof the CNCs [complementary necessary conditions] that belong to sharedknowledge) hold. (Politzer and Bourmaud, 2002, p. 366)

In both approaches, someone uttering a conditional knows that there are coun-

terexamples or exceptions, but this knowledge does not prevent him from uttering the

conditional as a “license for inferences” (Stenning and van Lambalgen, 2003b, p. 14)

or with a “guarantee that an inference can be made” (Politzer and Bourmaud, 2002,

p. 366). This idea is confirmed by the findings of our interviews as described above.

Subjects often knew that a conclusion was only possible under certain conditions, but

they assumed that these conditions held and thus made the inference. What exactly,

however, is the difference between the absence of abnormalities and the satisfaction

of all complementary necessary conditions? The notion of abnormalities seems to be

easier to grasp. Checking that nothing abnormal holds is more feasible than checking

that all necessary conditions hold, given the fact that their number is extremely or

infinitely large. The following excerpt seems to support this hypothesis. Here, the

subject has no exact idea of which conditions have to be satisfied for the system to

work correctly, he only assumes that no exceptional events happen.

Subject 8S: (reading) If the red light is on, the rat is in the cage.If the door is closed, the rat is in the cage.The red light is on.A: What follows here?S: The red light is on, so the rat is in the cage. As long as the system isworking correctly, the red light being on will indicate the rat is in the cage.A: Is there anything that could prevent her from being in the cage?S: Um, if the system is not working correctly, if it’s human operated, andsomebody has left the light on in error, or if it’s a *sound* or some otherarrangement that has gone faulty, then the light could be on without therat being in the cage. So, there are situations where that could happen, butassuming that everything is working correctly, then you have to go by thestatements to say that the rat is in the cage, you have to assume...

Chapter 7

Uncertainty in conditional reasoning

In chapter 5, we saw that the use of world knowledge often makes people express

uncertainty about a conclusion or put it in probabilistic terms. Through the use of

world knowledge, some subjects came to doubt the believability of the speaker, which

was also a source of uncertainty about the conclusion (Stevenson and Over (2001)).

But there are yet other reasons for uncertainty in conditional reasoning, which will be

discussed in the following.

7.1 Uncertainty of the antecedent

Many recent studies on conditional reasoning claim that conditional sentences express

a high conditional probability of the consequent given the antecedent. They say the

variation in this probability leads to different degrees of certainty of the conditional

and inferences derived from it. Among other phenomena, they try to explain the

suppression effect in probabilistic terms. Stevenson and Over (1995) say that the

introduction of an additional requirement reduces the conditional probability of the

consequent given the antecedent, which produces uncertainty in valid inferences. An

alternative condition, however, reduces the conditional probability of the antecedent

given the consequent, which produces uncertainty in fallacies.

A similar approach can be found in Politzer and Bourmaud (2002). They conclude

from the fact that ”the assertability conditions of if differ from its truth conditions”

70

Chapter 7. Uncertainty in conditional reasoning 71

and ”asserting a conditional serves various pragmatic purposes” (p. 369) that the

conditional belief in C given that A is a measure of the assertability of ”if A, C”.1

They show that ”the introduction of a complementary necessary condition into the

context (by cancelling the assumption of its satisfaction) decreases the assertability of

the conditional” (p. 370). This result is yielded by assuming that the representation

changes from A &�N � 2 � C to A & N1 � C.3 The authors say that this lowers

the degree of belief in the conditional premise. But I think the degree of belief in the

original conditional is not relevant any longer because the conditional has changed.

If A is given, the main factor the conclusion depends on is the truth of N1. Thus, it

would be more plausible to relate certainty of conclusions to the certainty with which

these conditions hold. If subjects are not given any information about that (as in Byrne

(1989)), we can expect answers like ”I don’t know, he may / might, it depends”. But

if we say something about the degree of certainty, we can expect the answer to include

this degree, because the main factor the truth of the consequent depends on is the truth

of the conditions in the antecedent.

The hypothesis that the certainty of a conclusion depends to a great extent on the

certainty with which the necessary conditions hold is supported by our interviews.

Subjects are sure about the validity of their conclusions if they can be sure that the

necessary conditions hold.

Subject 25A: Again three sentences: If the green light is on, the rabbit is in the cage.If the door is closed, the rabbit is in the cage. I can see that the green lightis on. So, imagine that’s a conversation, you hear these sentences, whatcan you conclude now?S: What I conclude? If the cage door is shut, then the rabbit is in the cage.Again, you’ve met one of the two criteria for the rabbit being in the cage.The green light is on, fine, the rabbit is in the cage. Um, but we don’tknow whether or not the door is open or not. If the door’s shut, then that’sit, we got it for sure, the rabbit is definitely in the cage.

1This analysis is based on suggestions by Lewis (1986) and Jackson (1987). The latter treats if-sentences as entailing conventional implicatures. Arguments against this approach can be found inBennett (2003).

2 � N � stands for the necessary conditions which are all satisfied.3This is the same as A & N1 & � N �� C. N1 is the necessary condition whose satisfaction is

doubted.


A: So, you are not sure now?S: I’m not sure because I don’t know whether the door is open or not.The point about the door being open or not hasn’t been cleared up to mysatisfaction. The point about the green light has been cleared up to mysatisfaction, but not the point about whether the door is open or not. Ifthe door is open, I’m not sure the rabbit’s in the cage, it’s probably #somewhere else by this time.

Subject 19L: Here is the next one: You hear that, if Mary has a paper to write shewill be in the library. If she has a history paper to write, she will be in thelibrary. And you know that she has a paper to write.A: Are you sure she will be there?S: Oh no, I’m not sure she WILL be there. If she’s writing a paper, thenshe WILL be there. She might be on a coffee bar, having a coffee.

Subject 10S: (reading) If Mary has an essay deadline, she studies late in the library.If the library stays open, she studies late in the library.(...)A: Would you be sure that she is in the library?S: Only if the library is open. They were not sure that the library is open.A: If you know that the library is open?S: Then yeah, because she has a deadline.

7.2 True antecedents?

This analysis presupposes that someone uttering a conditional does not know whether

the antecedent is true. When examining subjects’ understanding of the task, we

saw that many participants indeed treated the antecedent as uncertain.4 Yet, there

were others who did not interpret it as unknown but assumed its truth. How can

these contrasting findings be explained? Let us start by consulting the literature on

conditionals.

Most approaches only account for conditionals with uncertain antecedents. There

are, however, some cases where true antecedents are considered. It might be helpful to

look at Bennett (2003):4See section 4.2.


Again, when my colleague hears me say that I have applied for leave, hemay say ’If you have applied, I’m going to apply too’(...) This is not aconditional, either. My colleague means ’Because you have applied, I’mgoing to apply’, and he uses ’if’ because he is still digesting the newsabout my application. Had he known about it for a month, that use of ’if’would be unnatural. (p. 5)

He gives an example of an ’if’-sentence where the antecedent is known to be true, but

excludes it from his analysis by stating that it is not a conditional. This quotation points

to an important feature of conditional sentences that was already mentioned in chapter

3. Conditionals are always uttered in a certain context and it is difficult to assign them

a meaning out of context. The fact that the sentence could not be uttered in the same

way a month later does not imply that it is not a conditional, it rather means that it is

not appropriate in this context. In the described situation, the antecedent is part of the

common ground and used to anchor the information in the consequent to it. As the

antecedent is known to be true, it can be inferred that the consequent is true as well.

The fact that the inference is part of the meaning of the sentence shows again that it is

difficult to keep apart interpretation and reasoning.

This becomes also apparent in Johnson-Laird and Byrne’s (2002) classification

of conditionals. The authors introduce separate categories of interpretation for cases

where the truth of the antecedent or the falsity of the consequent are known to speaker

and hearer and make them exclude certain combinations of antecedent and consequent

(or sets of possibilities in Johnson-Laird and Byrne’s terms). One of their examples is:

“If my name’s Alex then Viv is engaged”, uttered in a situation where it is known that

the speaker’s name is Alex, in order to emphasise that Viv is engaged. They assign the

construction of a mental representation entirely to the interpretation process, but I think

that this process cannot be analysed independently from reasoning. Incidentally, I think

the foregoing cases also show that it is difficult to distinguish between implicatures, i.e.

pragmatic inferences, and inferences in reasoning.

Another phenomenon illustrating the smooth transition between interpretation and

reasoning can be found in Bonnefon and Hilton (2004). The authors demonstrate that

subjects conclude from consequential conditionals with a positive outcome, like “If

Cedric takes this new job, his life will improve in every respect”, that the antecedent is


true. This inference is not really part of the meaning of the sentence, but the experiment

does not constitute a reasoning task in the conventional sense, either.

In the first two examples from the literature, the knowledge that the antecedent

is true is part of the common ground at the utterance time of the conditional. In the

last case, the truth of the antecedent is inferred from the positive effect it will have.

The situation in our interviews is slightly different. Here, antecedents are assumed

to be true because they are among the background conditions of another conditional

which is used for modus ponens inferences. Although this assumption originates

from the reasoning process, it becomes part of subjects interpretation of the statement.

So, we encounter again the context-sensitivity of interpretations and the difficulty of

distinguishing between interpretation and reasoning.

There is yet another explanation for the apparent conflict between the general

uncertainty of antecedents and the assumption that they are true. If the second

conditional elaborates the first in the way described above, it is not an entire antecedent

which is assumed to be true, but only part of it, namely a complementary necessary

condition. The actual sufficient condition of the new antecedent is still interpreted as

uncertain (unless it is given as a categorical premise).

7.3 Different types of assertion

Another source of uncertainty in people’s conclusions is the uncertainty associated

with different types of sentences or predications, independent of the modifications

caused by adding new premises. For instance, conditionals are often predictions

about events in the future, and it is an inherent feature of predictions that they are not

certain. This uncertainty is sometimes made explicit by adding modal operators like

’probably’ or ’likely’. Thus, Johnson-Laird and Byrne (2002) have no reason to treat ’if

a then possibly b’ as a special type of ’basic conditional’ in classifying interpretations

of conditionals. Uncertainty of predictions can also depend on the content, which

shows again the strong relation between world knowledge and uncertainty in reasoning.

Medical examples in our interviews indicate that subjects are more reluctant to make

inferences in this domain. Other conditionals describe habits of human beings, and as


every habit has exceptions there is no certainty that the event described always happens.

Ontological conditionals expressing facts about the world are more certain, but this is

the kind of conditional sentence scholars are usually not interested in (e.g. ”If he is in

Scotland, then he is in Europe” has a similar degree of uncertainty as ”Scotland lies in

Europe”).

Subject 23L: Can you from the messages [first conditional and categorical premise]tell where she is? You want me to read the messages again?S: Um..., well, I mean, she could be in the library, but as I say it depends,it depends, I’m not sure, I’m not entirely sure.A: Why not?S: Um... because, I’m just trying, I’m trying to order my thoughts, um...,well, as I said, if she can’t be contacted then its not entirely certain thatshe’ll be..., I mean if the friend is saying she has an essay to write, wheredo you think she is? And they are saying, well, she’s likely to be in thelibrary, maybe that doesn’t necessarily mean that she’s gonna done that.L: Just because friends are not reliable?S: Yeah, or she may not be that predictable.

This subject points to the difficulty of predicting another person’s actions in the

future. The following excerpt makes clear that people are more certain in making

predictions about technical systems than in foretelling someone else’s behaviour.

Subject 26L: According to that person then. I’ll do the next one. That was good. Youoverhear the following conversation on a bus, and you hear the followingsnippets. The first bit is, if Rosa meets her friends, she’ll go to the cinema.If She has enough money for a ticket, she’ll go. And, She got her salarythis week.(...)L: And uh... Do you think she’s going to go, or not?S: You don’t know if she’s going to go or not. You know that she’s gotthe means to go. But whether or not she goes you don’t know from that.Because it’s not her saying it.L: Oh, okay. You think it’s possible that the friends are making it all up,then.S: Yeah.(...)A: If the green light is on, the rabbit is in the cage. If the door is closed,


the rabbit is in the cage. What do you think these sentences are about?(...)A: So if the green light is on... Can you know then? What follows?S: Right... Yeah. Well. Probably, yeah. You would. You would imagine itwould be there if that things says it would be there... The green light bein’on.L: But you don’t believe this in the situation where the door is closed.S: If it too... If the light... Actually, I can’t see how the two sentencesmight be related. But if the door was closed and the green light is oneyou’d assume that the rabbit was there, I’d imagine.L: What if the door wasn’t closed?S: If it wasn’t closed, and the green light was still on, I don’t suppose thatwould matter, would it?L: The door or the green light?S: Like, the door being closed. If the green light is there, it says it mustbe.(...)S: Well, without seeing inside it, and without having the wee light thing,how are you gonna know that it’s there? Just because the door’s closed?L: So you think the light is a better... Yeah, why do you think that a lightis a more reliable indicator?S: Well, if it’s in full working order and it does what it says it’s gonna dothen, why not?

My approach is close to Dudman’s analysis of conditionals (Dudman (1991)).5

His basic idea is that the ’if’-clause is only a modification or complication of the

main clause. In sentences talking about habits, it constitutes a modification or closer

specification of the habit. In projective messages, which contain an auxiliary and

whose time is later than their tense, the ’if’-clause is a constituent of the predicate. The

speaker’s verdict about future events is based on a fantasy starting at a particular time.

In the case of conditionals this fantasy contains the satisfaction of the ’if’-clause. Most

of the sentences we used in our interviews contained ’will’ followed by an infinitive in

the consequent. According to him, ’will’ is just one modal auxiliary among others

which can be used in the main clause. So, the modal character of a conditional,

or its degree of uncertainty, depends on the modal auxiliary which is chosen. The

5Other scholars, e.g. Bennett (2003), disagree with his approach because he questions the commondistinction between counterfactual and indicative conditionals. However, his work contains someinteresting ideas about the meaning of conditionals in general.


hypothetical character of some conditionals can be explained by the fact that the main

clause is a projective message and by the properties of ’will’. This would mean that we

have to model different modalities and treat ’will’ as one modality among others like

’may’ or ’can’. One problem with Dudman’s approach is that he only considers the

dimension of time as a factor of uncertainty and as a basis for his ’fantasies’, i.e. the

speaker does not know what will happen in future. But other dimensions like location

(e.g. as in “If he is at the beach now, he will have fish and chips for lunch”) or non-

availability of information (e.g. as in “If you are thinking of the same person as me,

...”) can also be a cause of uncertainty. The deciding factor is that the speaker does not

have information about the ’truth’ of the event or state in the ’if’-clause at the utterance

time.

In this context, it is interesting to have a closer look at the relationship between

conditionals describing habits or general laws on the one hand, and on the other

hand conditionals making predictions for the occurrence of a particular event. The

statements used in previous studies on the suppression effect and in our interviews

can all be interpreted as belonging to one or either of these two types. Presumably,

they were chosen for reasoning experiments because the occurrence of the event in

the consequent does not depend on a certain action or commitment of the speaker or

hearer, as with other speech act types like threat or promise. The following example

shows that for these speech act types the degree of uncertainty is even higher.

Subject 17A: Can you think of a situation where she studies hard but she doesn’t geta high grade?S: Um..., no, well, if the first two sentences are correct, then if she studieshard she will always get high unless that person’s wrong or she’s studyingfor the wrong exam, or some other situation like that, but assuming that’scorrect, then yeah, she would, she would automatically get honour, yeah,she would be expected to get a high grade.L: Can you think of a situation where these sentences would be uttered?Like what would be the point?S: Well, um, sort, like a school, um, parents’ night, it could be a teacherexplaining to the parents that she has to study hard, so they’d be usingthat as a sort of character to make them encourage study hard, which kindof undermines the certainty of the statement as well, because it might notbe true, they might just hope that she studies hard, they are just trying to


convince her to do, convince them to convince her.

But the interpretation of a conditional as a promise or encouragement is an

exception in our interviews, usually people interpreted the sentences as describing

habits or predictions in a particular situation. Thus, the first question is what makes

people choose one of these readings. Sometimes the content allows only the event-

related interpretation because it describes an event that cannot occur repeatedly. In

cases where the events in the antecedent or consequent are modified by a temporal

phrase, it is clear which reading is preferred. “If she has an essay deadline tomorrow,

she will be in the library” refers to one particular event, whereas “If she has an essay

to write, she is usually in the library” describes a habit.6 But apart from the episode of

John going fishing from Stevenson and Over (1995), where the certainty of a statement

was deliberately modified by temporal adverbs7, the statements we used contained no

temporal indicators. Another important factor is the tense of the main clause. Whereas

some tenses like ’will’ followed by an infinitive can be used both to describe habits

and to make predictions for future events, the simple present is an indicator for a habit

because it is usually not used for predictions8.

In order to find out whether there was a default interpretation, I presented a

conditional without a categorical premise to subjects at the beginning of the interview,

and asked them what they thought the discussion where it was uttered was about. In the

case of Mary writing her essay in the library, most people reckoned that the conditional

answered the question where she was and thus referred to a unique situation.

Subject 8A: Imagine you are sitting in a bus, and there are some people at the backwho have an argument, and you would like to find out what they are talkingabout. And then you hear these two sentences, maybe you can read themaloud.S: (reading) If Mary has an essay deadline, she will be in the library.If Mary has to copy papers, she will be in the library.A: So, what do you think they are talking about?S: And this is a discussion at the back of the bus?

6As Langacker (1997) notes, a temporal adverb can also specify the “overall episode of temporaryhabituality” (p. 196), a dimension that is not relevant here.

7See the next section for a discussion of this example.8There are exceptions like schedule related predictions, e.g. “The next train leaves in half an hour”.


A: You hear these sentences in a bus, and you want to know what peopleare talking about.S: They are wondering, I would say, if Mary is ... where Mary is or whatshe would be doing, I suppose. Hypothesising whether Mary would beable to come with them or something along those lines I would imagine.

Only few subjects thought that it was describing her studying habits.

Subject 17A: Imagine you are sitting in a bus, and there are some people at the backof the bus, having a discussion, and you want to find out what they aretalking about, and you hear them say: If Mary has an essay deadline, shestudies late in the library. So, what do you think they are talking about?S: Um, probably talking about someone who is not in that group, who,and what they do for studying, so they might be talking about what theyare doing for studying, and they are saying: Well, Mary does that - as anexample of what other people might...

But the following excerpt shows that there is not always a clear-cut distinction

between both types of interpretation.

Subject 23S: Um, someone is looking for Mary... and it’s from someone who wouldknow that she’s in the library, if she has an essay, from one of her friends,I guess.L: Hm, okay.S: Someone who knows that she does her essays in the library.

The subject thinks that although the salient question in context is about a particular

event, the answer describes a general habit. This poses the question what the relation

between both types of interpretation is. In his essays on generics and habituals in

general, Langacker (1997) presents some useful ideas. He treats generics and habituals

as “general validity predications” describing multiple occurrences of a certain event

type. Whilst for habituals distribution across time is dominating9, for generics the

set of potential participants is the salient parameter10. In contrast to repetitives,

habituals are not about actual instances of the described event type, they rather convey

9As in “Mary writes her essays in the library”.10As in “Students write their essays in the library”.


structural knowledge of the world. Yet, they can be obtained by generalising from

multiple actual and real instances of an event type. Interesting for our purposes is

that this general knowledge can then be used to make predictions for actual, non-

real events in the future. As the knowledge of general laws is often the basis for

making predictions, habitual and event-related conditionals are inextricably connected.

Langacker’s approach is also helpful in explaining the uncertainty occurring in

interpreting conditionals. Events described in general validity predications usually

do not happen continuously, their occurrence depends on certain conditions, which

he calls “enabling conditions”. In the case of conditional sentences, some of these

conditions are made explicit in the ’if’-clause. But the fact that these explicit

conditions are satisfied does not mean that all the other enabling conditions hold as

well in a particular situation. And as already mentioned above, every general rule can

have exceptions.

7.4 How can they be so sure?

The above examples show that people can have doubt about the truth of their

conclusions. But reviewing the huge literature about the uncertainty of assertions

in general, it is surprising how sure they usually are that the consequent is true if

they are told that the necessary conditions hold. One reason might be the assumption

that all other necessary conditions hold or that there are no abnormalities. This is

strongly related to a closed world assumption, where only the stated conditions matter.

Examples of this phenomenon are given in the following excerpts.

Subject 5S: (reading) If Mary has an essay deadline, she will be in the library.If she has to copy some papers, she will be in the library.She has an essay deadline.A: So, what follows from that? Which conclusion can you draw?S: Um, that she will be in the library.A: Are you sure she will be there?S: Yes, because the first sentence is about having an essay deadline, tellingus that she will be in the library.


Subject 7S: (reading) Professor of Medicine: If Bill has typhoid, he will make agood recovery.First year medical student: If Bill has cholera, he will make a goodrecovery.Situation: Bill has typhoid.A: What follows?S: That he shall make a good recovery, he WILL make a good recovery.A: Are you sure?S: Um, yeah, I guess. The professor of medicine says he will make a goodrecovery if he has it, and he does have it. I suppose the only problem is:could he have cholera as well. If he had cholera as well then... oh know,he will make a good recovery. He will make a good recovery either way.So, he will make a good recovery. I was thinking that it said he wouldn’t.

The next chapter discusses how degrees of certainty depend on the personality of a

subject. Secure, self-confident people are more likely to be sure about their conclusions

than self-conscious people.

Certainty about a statement can also be triggered by the form of the presented

material. An interesting example of how an experimental design can have the reverse

effect is the following statement.

If John goes fishing, he will have a fish supper.John almost always catches a fish when he goes fishing.John goes fishing. (Stevenson and Over (1995))

The authors thought that subjects would interpret the fact that John catches fish as

an additional necessary condition for John having a fish supper, and that the conclusion

would be uncertain because this condition is not always fulfilled. But many subjects

said that he would always have a fish supper, and if he did not catch a fish, he would

get it from somewhere else. The adverbial phrase ”almost always” in the second clause

seems to make people infer that the first sentence ”always” holds.

Subject 17L: Hm, hm, okay. Now, next time you hear the two sentences together:If John goes fishing, he will have a fish supper. And also: John almostalways catches some fish when he goes fishing. And John is going fishing.So, what do you conclude after that?S: Um, that John must buy fish suppers from a shop, because if he always


has a fish supper then it’s not necessarily a fish he catches himself if heonly sometimes catches fish.

Subject 5S: (reading) If John goes fishing, he will have a fish supper.John almost always catches some fish when he goes fishing.John goes fishing.A: So, what follows here?S: That he will have a fish supper, but that he is not necessarily going tocatch the fish that he is going to eat.A: So, where would he have the fish from?S: From a restaurant, from somewhere else, or from someone else whocatches them. Because if he always has a fish supper when he goes fishing,but he only sometimes catches fish, then he is not always gonna be eatingthe fish he has cooked.

If subjects had the intended interpretation, then it was again obvious that the

certainty of their conclusion only depended on the certainty of the second condition:

Subject 10S: (reading) If John goes fishing, he will have a fish supper.John almost always catches some fish when he goes fishing.John is going fishing.A: So, what can you conclude here?S: That John is going fishing, and because he catch..., he usually catchesfish when he goes fishing, he will have a fish supper.A: So, would you be sure here that he will have a fish supper?S: It’s quite likely. It’s not definite because he almost always catches somefish, but it’s highly possible.A: So, what could prevent him from having a fish supper?S: If he doesn’t catch any fish.

Chapter 8

Individual patterns of interpretation

and reasoning

A striking finding of our interviews were the big differences between subjects. A single

participant often had the same kind of interpretation for all or almost all the statements

he was given. This is an aspect that has been ignored in previous studies, none of them

carried out a within-subject analysis. Yet, such an analysis promises to provide more

knowledge of which factors influence the interpretation and reasoning process. It also

prevents the experimenters from being satisfied with only accounting for conclusions

made by the majority of subjects. Some differences in subjects’ answers can be

explained by differences in the design of the interviews. Others are more likely to

be caused by individual differences. Although there is not always a clear distinction,

the two phenomena will be treated separately.

8.1 Effects of different experimental settings

Subjects were always presented a set of statements within one interview. The content

of the statements and the order in which they were presented varied from subject to

subject. This enabled us to examine whether the interpretation of the sentences was

influenced by these variables. Indeed, it could be observed that people’s interpretation

of later statements was often biased by the earlier ones. If the content of the earlier ones

83

Chapter 8. Individual patterns of interpretation and reasoning 84

indicated very clearly that the second antecedent contained an additional necessary

requirement, then this kind of interpretation was transferred to subsequent cases —

even if it was not an obvious interpretation for all the statements. This effect is

illustrated by the following example. The first statement that the participant was

presented with was about Mary being in the library if she has an essay to write and if

the library is open. Like most people the subject understood the library being open as a

necessary condition for Mary being in the library. In the following two statements1 she

interpreted again the second antecedent as an additional requirement. Although some

others understood these statements in the same way, many had another interpretation,

which suggests that the participant was biased by the first example. This becomes even

more obvious in the following excerpt. Though the described interpretation is not the

first one she comes up with, she manages to get this reading for the statement after

thinking about it again. She was the only subject to interpret the sentences in this way.

Subject 10S: (reading) Medical student: If Bill has aids, he will make a goodrecovery.Professor of medicine: If Bill has cholera, he will make a good recovery.Situation: Bill has aids.A: So, what follows here?S: That he will make a good recovery.A: So, can you be sure that he will make a good recovery?S: Um, going by what’s in the sentence, then yes, because it says: if heHAS aids, he will make a good recovery, and he DOES have aids.A: Why do you think the professor of medicine says the second sentence?S: I don’t know. Maybe in case he has cholera, as well. Or maybe theydisagree with the fact that if he has aids and gets.... Maybe they think ifhe has aids and he gets cholera, he will make a good recovery. But, theprofessor of medicine might not think he can just make a good recovery ifhe only has aids.

For the last statement2, she interpreted again both antecedents as stating necessary

conditions for the consequent to be true. It has to be noted that her interpretation was1If John goes fishing, he will have a fish supper. John almost always catches some fish when he goes

fishing. John is going fishing.And: If Maria studies hard, she will get a high grade in the exams. If she is intelligent, she will get ahigh grade in the exams. She studies hard.

2If Rosa meets her friend Liz, she goes to the cinema. If she has money for a cinema ticket, she goesto the cinema. She has money for a cinema ticket.


not exactly the same in all five cases. Whilst she had assumed the second antecedent

to be true in the first statement, she became more sceptical as the conversation went

on and switched to understanding it as a correction. Once more it is shown that the

two types of interpretation are closely related and mainly differ in a person’s stance on

the consistency of a statement. This makes it often difficult to decide which one was

chosen.

Analogous effects could be found for more subjects, although similar material did

not elicit such a behaviour in other cases. This suggests that individual differences

also play a role in how likely the interpretation of sentences is to be biased by previous

statements.

8.2 Individual differences

The study of individual differences (in personality, mood, motivation, and abilities)

is an important branch of psychology. In order to understand and predict human

behaviour it is essential to know about general laws and individual differences.3

In studying human reasoning however, it is often assumed that all human beings

reason in a similar way. Scholars do not take into consideration that reasoning

processes are influenced by a person’s particular cognitive skills, and that someone’s

behaviour in an experimental setting may depend on his personality or the mood he is

in.

If one wants to examine the influence of individual differences on a certain

cognitive task, it is common to perform tests of relevant characteristics prior to the

actual experiments. Statistical analyses reveal whether there are really correlations

between the tested factors and subjects’ performance in the experiments. As I have

not run such tests on the participants of my interviews, I can only try to derive from

subjects’ behaviour and the information they gave in a questionnaire (e.g. age, studies,

occupation, former knowledge of logic or linguistics) which individual parameters

might be relevant in interpreting the conditional statements and reasoning from them.

3I refer to Cooper (2002) for a useful introduction to individual differences. Stanovich (1999) showsthat individual differences are an important factor in the rationality debate, i.e. in deciding whether thereare normative models in human reasoning.


Instead of conducting statistical analyses, I want to describe conspicuous answering

patterns in relation to individual characteristics. The following analyses are fairly

intuitive and not meant to present conclusive empirical evidence. They shall rather

give an idea of what kind of factors have to be taken into consideration in studies of

interpretation and reasoning.

8.2.1 Mental abilities

As already mentioned above, subjects can have different ideas of what they are

supposed to do. One possibility is to understand the presented statements as a logical

task or a riddle. Solving such tasks requires a certain degree of abstract and logical4

thinking, so people possessing this ability are more likely to take such a stance. Of

course, most people in our society are literate and learnt at school things like how to

analyse a text or how to solve abstract maths problems. University students, which

constituted the majority of our subjects (as in many studies on reasoning), are usually

above average in such skills, both because of their studies and their intelligence5. But

most had different subjects of studies, and some were not students, so it was possible

to observe some differences in logical and abstract thinking.

One subject doing a PhD in Bioinformatics treated the statements as a logical task

and tried to reason only from what the sentences said. She tried to exclude her own

world knowledge, which led to contradictions in some cases because the statements

are designed to be interpreted using background knowledge.

Subject 4S: (reading) If John practises a lot then he will become a good pianist.If he is musically gifted then he will become a good pianist.He practises a lot.A: What follows here?S: Um.... first it looks like... um... if he practises a lot then he will bea good pianist. It doesn’t specify that he has to practise a lot and bemusically gifted to become a good pianist. So I would say that he willbecome a good pianist, just by practising a lot.

4’Logical’ is here used in its common meaning.5This term is also used in a very common way, I do not want to plunge deeper into the question as

to what is intelligence.


A: So you think it’s not necessary to be musically gifted to be a goodpianist?S: *From these* sentences, it’s not me personally speaking, I would sayyes.A: Okay.S: But from these sentences... it doesn’t say: if John practises a lot ANDhe is musically gifted, he will become a good pianist. *They are eachother* mutually exclusive, so separate sentences.A: Okay. What about these sentences.S: (reading) If Maria studies hard then she will get a high grade in theexams.Of course, only if she is intelligent.She studies hard.A: So, what follows here?S: Although they are separate sentences, the second one refers to the firstone. So, it implies that... you don’t know necessarily that she will a highgrade in her exams because you don’t know whether she is intelligent.A: Okay.S: (reading) If Helen meets her boyfriend, they will go to the cinema.If she has enough money, she will go to the cinema.She doesn’t go to the cinema.A: Can you conclude anything?S:... Either she doesn’t meet her boyfriend or she doesn’t have enoughmoney. It doesn’t have to be both, it’s just either.A: So, if you know that she meets her boyfriend, can you concludeanything from that?S: Um, ....A: You just know that she meets her boyfriend.S: Okay, I, well since that’s separate sentences, yeah, she will go to thecinema.A: Could you think of any situations where she meets her boyfriend andshe doesn’t go to the cinema?S: She doesn’t, she doesn’t have any money. But again, these are separate.A: So, what happens if she meets her boyfriend and she doesn’t haveenough money?S: Um.... I suppose she doesn’t go. That might contradict my answers ofcourse.

In contrast, subjects without academic background seemed to treat the sentences

more like a natural discourse. They did not abstract away from the content of the

sentences or try to exclude their world knowledge. This became obvious in the way


they interpreted the second sentence. Two subjects, who seemed to be less experienced

in solving abstract tasks, interpreted the second conditional as an elaboration of the

first, which suggests that this is a common interpretation in daily life. The following

excerpts (discussed earlier) illustrate this point.

Subject 19L: Here is the next one: You hear that, if Mary has a paper to write shewill be in the library. If she has a history paper to write, she will be inthe library. And you know that she has a paper to write. What can youconclude from that?S: That it’s a history paper.L: And she will be in the library?S: She will be in the library.#A: How can you know that she has a history paper to write?S: Because it says, she says: If she has a paper to write, she will be in thelibrary. And if she has paper, it’s *up to* history. So, I’m just concludingfrom the fact that she has a history paper.A: Can you read the sentences again.L: Okay, you are not wrong or anything. You hear that, if Mary has a paperto write she will be in the library. If she has a history paper to write, shewill be in the library. And you know that she has a paper to write. So, doyou think the same, that she has a...S: She must be studying history.

Subject 18L: Who do you think would say these sentences?S: Ah, one of her friends probably, another student. Ah, they are talkingabout papers, an essay, a dissertation or something. And someone issaying: and she has a history paper to write, so the other person wouldbe giving more information, and not just a paper, but a history paper.(...)L: No, it’s: If Mary has a paper to write, she will be in the library. Andthis one is: If she has a history paper to write, she will be in the library.S: Well, I think it’s just kind of repeating itself. It could maybe just saythat she had a history paper. If she has a paper, she..., you would say: IFshe has a paper to write, she will be in the library. Yes, she has a historypaper, so she will be there.


8.2.2 Personality

Although it is difficult to make a statement about someone’s character after speaking to

him for less than half an hour, subjects’ behaviour in the conversations allows a coarse

classification according to their degree of self-confidence. Therefore, I compared the

answers given by very secure people to those given by rather self-conscious people.

Indeed, this variable seems to influence how people understand the task and interpret

the sentences.

Insecure people were usually more afraid of misunderstanding the task or giving

wrong answers.6 Thus, they adhered to the presented material and hesitated to involve

their own ideas or knowledge. Assuming that there were correct answers, they tried

to relate the sentences by finding a meaningful interpretation. Their general attitude

in interpreting the sentences can be described as credulous and cooperative.7 They

tried to find an interpretation in which the statement was consistent and all sentences

made relevant contributions to the discourse. They were also more likely to find

the sentences natural or make them sound natural through slight modifications. The

following excerpts will illustrate these claims.

Subject 1A: (...)If she has an essay to write, she will be in the library.If she has to train for a competition, she will be in the gym.If the library stays open, then she will be in the library.Then he says: I remember her telling me that she has to hand in an essaynext week.So, where would you look for her.S: In the library.A: Are you sure you would find her there?S: Um, but he said that ... (laughs) that if she had an essay to write she willbe in the library. Or if it’s open, I guess, so it depends, it dependsA: What could be reasons for her not to be in the library? Could you thinkof situations where she has an essay to write but she isn’t in the library.S: If the library is closed. Or, if she has something else to do? I don’tknow. Can she have two things at once? A competition as well? Sorry, I

6They did not always believe us when we told them we did not expect any particular answers.7A similar stance could be found with friends, presumably because they wanted to help me in doing

the interviews.


don’t want to do it wrong.(...)S: It’s really strange because I don’t know what I’m supposed to say.

This subject wants to give the right answers and sticks to the presented material

without bringing in her own ideas. The same phenomenon can also be observed for the

following participant. Here, the perception of the task as a personality test also reveals

the fear of being shown up and revealing hidden aspects of his character.

Subject 21L: If the red light is on, the rat is in the cage. The red light is on. What canyou conclude from that?S: The rat is in the cage. I don’t know...L: Okay, and then you hear in a different experiment now. If the red lightis on, the rat is in the cage. If the door is closed, the rat is in the cage. Theright light is on. What can you conclude?S: The door is open. Is that right?L: There is no right or wrong answer or anything. We are just wonderinghow you’d reason if we heard these things.S: I guess the rat is in the cage, again.L: Why, because the ...S: The light is still on. And... yeah.A: Do you think the door is closed?S: Yeah. I don’t know.L: It’s okay if you don’t know it.S: I don’t know, really. I’m hopeless at these things.L: It’s not an intelligence test, or anything. And these don’t get harder oranything.(...)A: Can you think of a situation where people would say these sentences?What do you have in mind when you hear them?S: Uh... sounds just like... kinda like a quiz.L: Like we’re... what do you mean like a quiz?S: I don’t know... Just like a personality test.L: It’s not a personality test or anything. We’re just interested in what youhave to say about it.S: Is this for a psychology thing?L: Do you think it is?S: I think it is.

The difference between secure and insecure people becomes apparent in the


statement about John going fishing8. As noted above, many subjects did not

interpret the condition that John catches a fish as necessary for him to have a fish

supper. Interestingly, this interpretation was mainly adopted by self-confident subjects,

who questioned the naturalness and consistency of the material and interpreted the

presented situations by means of their own world knowledge. Insecure people,

however, more often interpreted the statement in the way intended by Stevenson and

Over (1995). In the following, I want to contrast the two opposed interpretations,

starting with the intended one.

Subject 11S: (reading) If John goes fishing, he will have a fish supper.If John catches fish, he will have a fish supper.John is almost always lucky when he goes fishing.John is going fishing.A: So, what follows here?S: Um, if he, he is going fishing, and if he catches anything, he is going tohave a fish supper. Um, and he almost always catches some fish, but thatdoesn’t guarantee that, even though he’s going fishing that doesn’t meanhe’s gonna catch any fish, or have a fish supper.A: So, which information would you need to know if he will have a fishsupper?S: If he was successful in catching any fish when he went.A: So, then you could be sure that he will have a fish supper?S: Yes, because the first sentence says: if he is going fishing, then he willhave a fish supper. Or, I guess that is: if he catches some fish.... Is thatwhat you are looking for? Do you want that I speak more about that?

This participant, who shows obvious signs of insecurity at the end of the excerpt,

interprets the second antecedent as an additional requirement. In contrast to the next

person, she does not retrieve alternative possibilities or exceptions from her world

knowledge.

Subject 12S: (reading) If John goes fishing, he will have a fish supper.If John catches fish, he will have a fish supper.John is almost always lucky when he goes fishing.John is going fishing.

8Cf section 7.4.


A: So, what follows here?S: There’s a good chance of having a fish supper.A: What could prevent him here from having a fish supper?S: If he doesn’t catch a fish.A: Okay, so what...S: Well, ah, not, not necessarily actually, he is going fishing, so he mighthave bought fish supper.A: So, do you think... So, if you know that he catches fish, do you knowthen for sure that he will have a fish supper?S: Well, it says of John: if he goes fishing, he WILL have a fish supper, sohe may have fish supper, even if he doesn’t catch fish.A: Which information do you need to be sure that he will have a fishsupper?S: Um..., that he is going fishing, I don’t know.

Although the person has the same interpretation at the beginning, she feels free to

distance herself from the content of the statement and bring in her own ideas about the

topic.

In general, self-confident people show a tendency to question the content of the

statements and the conclusions that can be inferred from them. Even if they know

what the intended interpretation is, they are not always willing to accept it and to base

their reasoning on it. Their attitude towards the experimental setting can be described

as critical or sceptical. They are not afraid of getting it wrong because they rely on

their own abilities. Thus, they do not assume that the sentences must necessarily make

sense, and make less effort to relate them and find a meaningful interpretation.

Subject 6A: (...)Tom says: If she has an essay to write, she will be in the library.Jenny says: If the library stays open, then she will be in the library.And during the last days, she was quite often in the gym to train for hercompetition.Then Tom says: Oh, I remember her telling me that she has to hand in anessay next week.So, where would you look for her?S: Um, it is # a good chance of finding her in the library. # Maybe shecould be by the gym, as well.I: Okay, so what could prevent her from being in the library?S: Well, she could be in the pub, you know. (laughing) There’s a whole,an infinite number of possibilities...#


I: So, is there any information you would need to decide where she is?S: Well, it’d be interesting to know how conscientious as a student shewas. You know, if she doesn’t give her # Say, she is a first year student,and she’s got a week for an essay deadline. She is probably not gonna bein the library. But if she is a final year student and she wants to stay on fora PhD, she will probably stay in the library, working really hard.(...)S: (reading) If it is raining, Jane will get wet.If she forgets her umbrella, she will get wet.It is raining.A: So, what follows?S: Jane will get wet.A: Okay. Are you sure?S: Well, yes.A: What could prevent her from becoming wet?S: Not raining. You know, that’s # she’s not gonna get wet. If it’s raining,whether she has got an umbrella or not, she’ll still get wet.(...)S: (reading) If John practises a lot then he will become a good pianist.If he is musically gifted then he will become a good pianist.He practises a lot.A: So, what can you conclude here?S: John is an improving pianist.

Again, it can be observed that the answers go beyond the content of the statements

and comprise original ideas. The subject does not understand the statements as a

serious task, he rather tries to treat them in a humorous way. It is also conspicuous

how sure he is about the correctness of his conclusions. The question whether he is

sure cannot make him doubt his own reasoning abilities or world knowledge.

This shows that self-confidence plays a special role in the kind of method we

were deploying, where people can be made even more insecure by questioning their

answers. But I think many of the effects shown above can also occur in more

conventional experiments, so self-confidence is a factor that has to be included in

analysing reasoning data.

Chapter 9

Biconditionals

In the literature, it is often claimed that there are different kinds of conditionals, even

within the type of indicative conditionals we are considering in this work.1 One distinct

kind of conditional which is often discussed is the ’biconditional’, which describes

sentences with a conditional connection in both directions. Although this seems to

be a simple concept, there is disagreement on which sentences are interpreted as

biconditionals and how such a bidirectional conditional relation is derived. Sentences

starting with ’if and only if’ are often equated with biconditionals, but it needs to be

examined whether they really are a distinct type of conditional. The importance of

biconditionals might be overestimated as a consequence of their use in formal logic,

where ’if and only if’ stands for a bidirectional material implication. It is unclear

whether a biconditional interpretation is qualitatively different from the interpretations

of conditionals discussed so far. In the following, I want to present different views

on this topic in the literature, and argue that biconditionals are conditionals with

a necessary condition in the antecedent from which a reverse conditional can be

inferred. I will show that ’if and only if’-sentences are not fundamentally different

from ’normal’ conditionals, they merely represent a way of stating the relationship

between antecedent and consequent clearly.

Let us begin by taking a closer look at such sentences. Byrne et al. (1999) use

sentences beginning with ’if and only if’ in the suppression task:

1Cf Byrne et al. (1999) or Johnson-Laird and Byrne (2002).

94

Chapter 9. Biconditionals 95

If Elisa had an essay to write then she studied in the library all evening.If and only if the library stayed open then she studied in the library allevening. (p. 371)

They claim that in such statements the second sentence is interpreted as a biconditional,

which they define as a sentence where the antecedent is a necessary and sufficient

condition for the consequent to be true. The authors hold that more suppression of

inferences can be observed because biconditionals are represented by fewer models.

They conclude that “saliency or strength of antecedents can also be manipulated

independently of content” (p. 361). But I think changing the form of the sentences

in such a way is not independent of the content, it rather disambiguates the meaning

because the interpretation depends less on the involvement of world knowledge.

The words ’if and only if’ make clear that the second condition is necessary, so

the interpretation of the two conditions as separate alternatives is excluded.2 This

hypothesis is supported by the interviews, although the following excerpts can only

give a coarse idea because the statements were not designed to test these claims. In

the first two examples, I rather wanted to test whether interpretations can be enforced

by certain formulations, which indeed seemed to be the case. Yet, to get more secure

results, more systematic testing of these effects would be necessary.

Subject 1A: If John practises a lot then he will become a good pianist.Of course only if he is musically gifted.John practises a lot. What follows?S: He will be good in playing the piano. If he practises a lot ... if he is justgifted he will be good in it anyway, but he still has to practise.A: What if he only practises?S: Um, if he is not gifted? # he still could if he practises a lot.A: (reading sentences again)S: Okay, yeah, he can only be a good pianist if he is musically gifted,and practises a lot. So, John practises a lot, but it doesn’t tell us if he ismusically gifted or not. So, he might not be a good piano player.

2In the same way, we can argue that an additional requirement is not stronger if it is introduced by’if and only if’, it is only more obvious that the antecedent contains an additional requirement. The wayByrne et al. (1999) try to express the strength of an additional by the number of mental models is notvery compelling. They say that the weak requirement ”if Steven knows the host well then he attends thedance party” leads to models in which it does not make a difference whether he knows the host or not,as long as he is invited. But in this case, the second condition is not an additional requirement. So, theydo not really represent degrees of necessity, what matters is whether a condition is necessary or not.


Subject 2S: (reading) If John practises a lot, then he will become a good pianist.Of course only if he is musically gifted.John practises a lot.A: What follows here?S: So, he might become a good pianist.A: What could prevent him from becoming a good pianist?S: Because he might not be musically gifted. So, maybe, no matter howmuch he practises, he just can’t understand rhythms and, or dynamics, andso no matter how *much* he practises, it *just* sounds crappy.

Subject 10A: Imagine you are sitting in a bus, and there are some people sitting at theback of the bus, and they are having a discussion. And you try to find outwhat they are talking about. And you hear them saying these sentences.Can you read them aloud.S: If Mary has an essay deadline, she studies late in the library. If thelibrary stays open, she studies late in the library.(...)S: Because one would say: if she’s got a deadline, then she studies late.The other one would say: Yes, but only if the library is open. And theother one is saying: she does have an essay deadline. So, that applies.

According to Johnson-Laird and Byrne (2002) “the biconditional: If, and only if,

A then C, is synonymous with the conjunction: If A then C, and if not A then not C”

and “can also be paraphrased as: If A then C, and if C then A”.

Thus, mental model theorists correctly state that in ’if and only if’-sentences the

antecedent is a necessary condition for the consequent to obtain, but they fail to realise

that starting a sentence with ’if and only if’ is only a way of making clear that this

relationship holds. They also fail to explain how a biconditional connection is derived

from the necessity and sufficiency of the antecedent.

A different account of biconditionals can be found in the literature on ’conditional

perfection’. This term, introduced by Geis and Zwicky (1971) stands for the

interpretation of a conditional as a biconditional, or more precisely, for the “invited

inference” of an ’if and only if’-sentence from an ’if’-sentence. They claim that a

conditional if A then B can entail only if A then B, which corresponds to the sentence

if not A then not B. Taken together these sentences yield the biconditional if and only

if A then B. Again, it is taken for granted (without mentioning involvement of further


reasoning) that If A then B and If not A then not B are equivalent to a conditional

in both directions, and that this on its part is equivalent to If and only if A then B.

Without further explanations, papers like Geis and Zwicky (1971) or Horn (2000)

represent these sentences by means of the material implication and try to account for

the inference of ’if and only if’-sentences from ’if’-sentences in terms of scalar Gricean

implicatures. But they do not give a clear account of the meaning of ’only if’ and ’if

and only if’.

A more elaborate analysis is presented in van der Auwera (1997a) and van der

Auwera (1997b). Van der Auwera also analyses this inference by means of scalar

implicatures, but in his approach ’only if’ is not treated as a basic concept. According

to him

the analysis of the only if meaning, which is the conditional perfectionimplicature, is compatible with independently held hypotheses on themeaning of the components if and only (van der Auwera, 1997a, p. 177)

Thus, he describes the meaning of ’only if’ in the sentence “Only if you mow the lawn

will I give you five dollars” as:

(i) your mowing the lawn is a ceteris paribus sufficient condition formy giving you five dollars, and (ii) it is not the case that there are twoconditions each ceteris paribus sufficient for my giving you five dollars.This means, in other words, that, ceteris paribus, the mowing of the lawnis not only sufficient, but also necessary (van der Auwera, 1997a, p. 181)

Van der Auwera demonstrates that no separate concept for ’only if’-sentences is

necessary. Thus, he explains the inference from ’if’- to ’only if’-sentences, but he

does not state clearly how this relates to ’if and only if’-sentences and what his idea

of biconditionals is, he just seems to accept the assumptions of previous papers like

Geis and Zwicky (1971). Yet, his work is useful in investigating the meaning of ’if and

only if’, suggesting that it is also composed by the meaning of its parts. Thus, there is

no reason to assume that more than an emphasis on the necessity of the antecedent

is added to the meaning of ’only if’. As stated above, the meaning of sentences

starting with ’if and only if’ is not entirely different from the meaning of simple

conditionals, the added words have rather the function of making the relationship

between antecedent and consequent clearer.


As these approaches have failed to account for the bidirectionality of conditionals,

it can be asked whether there is really a bidirectional conditional relationship. Previous

studies might not have explained the relationship between form and representation in

the right way, but the fact that bidirectionality can sometimes be found in reasoning

from conditionals cannot be denied. Our interviews illustrate this phenomenon.

Subject 22A: You have these three sentences: If the red light is on, the rat is in thecage. If the door is closed, the rat is in the cage. And the red light is on.S: Okay, yeah, the red light is on, the rat is in the cage, and the door isclosed.A: Okay.L: # the door necessarily has to be closed?S: # I’m not, if the red light is on, the rat is in the cage. Yeah, I reckon, ifthe door is closed, the rat is in the cage. Then, it depends how you thinkabout it, how you listen to the sentence, whether you think there’s a reverselogic as well. How do you think: because the door is closed, the rat’s inthe cage. And then, if the rat is in the cage, the door has to be closed. Idon’t know whether that follows. I think, the door is closed, the rat is inthe cage, yeah, no, it follows both ways. So, yeah, the door is closed.L: #S: The sentence can be reversed, and it means the same, exactly the same.A: What do you mean by the sentence can be reversed?S: Well, if the door is closed the rat is in the cage, it means the same as, Ithink it means the same as: if the rat is in the cage, the door is closed.

This subject says that the sentence can be reversed, i.e. there is a conditional

relation in both directions. It seems, however, that this is not his original interpretation

of the sentence. He rather derives the reverse conditional from the meaning of the

normal conditional (i.e. the sufficiency of the antecedent) and the necessity of the

antecedent. This suggests that the relationship between antecedent and consequent

allows one in some situations to infer a reverse conditional, which is then added to

the meaning of the sentence. Although this phenomenon can be captured in terms

of ordinary conditionals and is not another type of conditional, it can be labelled as

’biconditional’.

Let us compare these claims with Sanford (2003), who rejects the symmetry of


biconditionals.3 Like many others, he equates biconditionals with ’if and only if’-

sentences, which he correctly analyses as having a necessary and sufficient condition

in the antecedent. From the fact that “Necessary and sufficient condition of is a non-

symmetric relation” (p. 203) he concludes that biconditionals are not symmetric. But

as we have seen, bidirectionality is inferred from the necessity of the antecedent.

Another problem is the way he illustrates his analysis with examples. He claims that

“The cactus flowers if and only if it rains” is not equivalent to “It rains if and only if

the cactus flowers”. It may be true that there is not the same kind of connection in both

directions. In the first sentence, there is a causal relationship between antecedent and

consequent, which does not exist in the second sentence. Thus, the second sentence is

not as obvious as the first.4 But if one adopts a closed world assumption and reasons

only based on the content of the sentences, it is definitely possible to infer that the

cactus necessarily flowers in all situations where it rains, and that if the cactus flowers,

then it has rained. It is important to note that this is the notion of necessity we need

in analysing conditionals. We do not define necessity by concepts like causality or

temporal consequence, but as the simple co-occurrence of events in all considered

situations.

Although we have showed that there are bidirectional conditionals, we have

not described the processes leading from the interpretation of a conditional with a

necessary and sufficient condition in the antecedent to a biconditional, i.e. the existence

of an additional conditional in the reverse direction. The interviews do not allow one

to draw a conclusion as to where in the interpretation and reasoning process the reverse

conditional appears and what its representation is like, i.e. whether it is of the same

nature as ’normal’ mental conditionals.

As affirmation of the consequent inferences correspond to the form of reverse

conditionals, analysing them might shed more light on biconditionals. Rader and

Sloutsky (2002) test modus ponens and affirmation of the consequent inferences

from stories, and claim that both occur during comprehension and not during

3It is not clear why he keeps the term ’biconditional’ if he rejects the bidirectionality of theconditional relationship.

4Reversed conditional sentences also often seem to be ungrammatical or not to make sense becausetenses or anaphora do not fit. But the symmetry of biconditionals is not a matter of surface forms. If onewants to use reverse conditionals in discussions about this symmetry, these aspects have to be adapted.


reasoning without realising that interpretation and reasoning processes are inextricably

intertwined. Moreover, they show that their subjects do not retrieve the reverse

conditional from memory, and take both as evidence against the hypothesis that

conditionals are in these cases represented as biconditionals. This shows the need of

further research on biconditionals in order to find out more about the processes leading

to biconditional interpretations and the way they are mentally represented.

Chapter 10

Conclusion

10.1 The suppression effect

As we saw in the introduction, there have been various attempts to account for what

Byrne (1989) called ’suppression of valid inferences’. One of my goals was to show

how knowledge of the interpretation process can help to explain this effect. The

following sections summarise my findings concerning this issue.

In contrast to the majority of studies on the suppression effect, I did not use a

quantitative method, which means that it is not possible to compare my results directly

to those of other experiments. Yet, in order to use the findings about the interpretation

process to explain previous data, it is important to know whether a similar tendency to

’suppress’ inferences could be observed in our interviews, i.e. whether we observed a

similar pattern of responses.

There were only a few people who totally refused to draw a conclusion. But

many participants qualified their conclusions as a result of the second conditional,

by adding modal operators or stating additional conditions. Most experimenters did

not offer their subjects the opportunity to formulate their own conclusions, but made

them choose from a range of possible conclusions. Participants probably answered

that nothing followed or that they were not sure what followed if they did not find an

option matching their own conclusion. Thus, these qualified conclusions can also be

regarded as suppression in Byrne’s sense.

101

Chapter 10. Conclusion 102

Although we could find suppression effects, more subjects than in previous

studies seemed to draw conclusions that Byrne et al. (1999) classify as “categorical

endorsements”. Therefore, the first question I want to go further into is what the

reasons for different patterns of answers in our study might be. Then, I want to show

why there is such a wide range of different answers at all. Finally, I will examine

whether it is legitimate to speak of suppression of inferences.

10.1.1 Why did we observe less suppression?

As our method differed significantly from those deployed in previous studies, it

is likely that most of the differences in response patterns can be assigned to the

experimental settings. In previous experiments, conclusions were result of a long

and thorough thinking process where subjects tried to find the right solution to a

problem. Our participants, however, gave more spontaneous or intuitive answers

because they were engaged in a conversation. In such situations, people assume

that discourse participants are cooperative and treat the statement as coherent and

consistent. Thus, many of them willingly endorsed the suggested inferences. We

could, however, observe that they often retracted or changed these answers when our

questions made them rethink their conclusions. Perhaps, the resulting more sceptical

responses can be taken as counterparts of the answers given in others’ experiments (in

which intermediate conclusions were usually not recorded).

10.1.2 Why was there such a wide range of different conclusions?

The differences in understanding the task represent one answer to this question. Some

subjects treat the presented statements in a similar way to everyday discourse, others

regard them as some kind of logical task. These different stances determine which

assumptions people make and what they consider to be a valid conclusion.

Another reason for the great variety of answers are the many different ways of

interpreting one statement. Previous studies assumed that all subjects adopted the same

interpretation, but our interviews showed that this is not true. There are more possible

interpretations than has been presumed by other scholars, and people do not always


interpret the material in the way they are expected to do. Many subjects interpreted the

second sentence as introducing an alternative condition in cases where it was meant

to add another necessary condition. And even if they interpreted it as an additional

requirement, they often made modus ponens inferences because they assumed that the

second condition held.

Differences in subjects’ world knowledge and the degree to which they deployed

it were another source of divergence. Involvement of world knowledge influenced

how subjects interpreted sentences, and which conclusions they endorsed. Even if

they made the suggested modus ponens inference, they often rejected the conclusion

because it contradicted their world knowledge.

The dissertation showed that many of these differences in interpreting the presented

material and drawing inferences can be explained by individual differences in person-

ality or mental abilities.

10.1.3 Is there really suppression?

To answer this question, we have to state again what ’suppression’ means in the original

paper on the suppression effect. Byrne (1989) claims that

in certain contexts subjects reject instances of the valid modus ponens andmodus tollens inference form in conditional arguments. (p. 61)

What this actually means is that subjects do not always draw the conclusions that would

follow in classical logic if one translated the statements into first order logic formulae.

Thus, her findings contradict mental rule theorists claiming that mental inference rules

operate on such mental translations of natural language sentences. She concludes that

there are either no mental rules, or that the sentences are represented in such a way

that the rules cannot be applied to them any more. She does not pursue further the

second possibility, but rejects it because she deems the mental model theory more

plausible. Her final conclusion is that there are no mental inference rules which could

be suppressed. Instead, she explains inferences in terms of mental models representing

possibilities. In her approach, no reasoning mechanisms are suppressed because all

conclusions are derived by a “general semantic procedure” (Byrne, 1989, p. 77).


Although many scholars support the theory of mental models, I have shown

that there are well-founded objections against this approach and that it is not the

only or most plausible possibility to account for the suppression effect. Therefore,

it seems appropriate to go back to Byrne’s intermediate conclusion, which is in

principle right, but only pays attention to one particular theory of mental inference

rules. Putting it in a slightly different way, we can say that there are either: (1)

no mental inference mechanisms corresponding to modus ponens; or (2) that surface

conditionals are translated into mental conditionals in a less straightforward way than

assumed by syntactic approaches to human reasoning. Our underlying assumption in

studying human reasoning is that humans reason in a regular, predictable way and

that the reasoning processes are based on general, non-arbitrary mechanisms.1 This

assumption and the ease with which people perform modus ponens inferences from

simple conditionals make us reject the option (1). In contrast, option (2) is supported

by the interviews analysed in this dissertation. We saw that not all natural language

conditionals are interpreted as conditionals allowing modus ponens inferences from

their surface antecedent. Yet, such inferences can always be made from an antecedent

that is in the present context sufficient for the consequent to be true. The representation

of a conditional can change if another conditional sentence is added to the discourse.

The second conditional can elaborate or correct the first conditional, and thus modify

the antecedent of the mental conditional. In the case of correction, this prevents

modus ponens inferences from the original antecedent. But if the new antecedent is

known to be true, these inferences are still possible. It is also important to note that

conditions are only sufficient for inferring the truth of the consequent within a certain

context. If subjects do not have enough information about the truth of the antecedent,

including necessary background conditions, and do not assume that it holds, they

express uncertainty about the conclusion or do not draw any conclusion at all. This

corresponds to the phenomenon Byrne refers to as ’suppression’.

My account provides a plausible explanation of the suppression effect without

rejecting the idea of an inference mechanism corresponding to modus ponens. It does

not specify what exactly this mechanism and the underlying mental representations

1Of course, there can be individual differences, but these divergences are still fairly regular.


look like. But it presents some factors which have to be considered in modelling the

suppression effect.

10.2 General findings

The findings of this dissertation are not only interesting in studying the suppression

effect, they are also relevant for the general exploration of conditionals in psychology,

linguistics, and philosophy. Psychologists often focus on reasoning from conditionals

and deploy only a very coarse analysis of linguistic phenomena. My work shows

how a rather fine-grained analysis of different interpretations and the consultation of

linguistic theories can point to new aspects in studying conditional reasoning.

In contrast to psychological research, most of the linguistic and philosophical

literature on conditionals is based on scholars’ intuitions and not on empirical studies.

The analysis of my interviews provides a more firmly grounded examination of how

people really understand conditionals. The difficulty distinguishing between interpre-

tation and reasoning in analysing conditionals with true antecedents or biconditionals

shows that the role of conditionals in reasoning has to be considered in studying their

meaning. It also questions the common distinction between implicatures, as pragmatic

inferences, and inferences in reasoning.

The fact that some antecedents were assumed to be true, or meant to correct or

elaborate another antecedent, also shows that the meaning of conditionals cannot be

stated out of context. As with other kinds of sentences, we have to examine how

conditionals change the current context rather than what their meaning in isolation is.

Moreover, antecedents are only a sufficient condition for the truth of the consequent

within a certain context, i.e. if certain background conditions hold. In our case, this

context was often provided by the antecedent of another conditional.

This means that similar surface conditionals can have different abnormality

or complementary necessary conditions, depending on the context in which they

are uttered. It is unclear whether these differences are reflected in the mental

representations of conditionals, i.e. whether similar surface conditionals can have

different mental representations. Another possibility would be that they all have the


same basic representation, and it is determined at another level of processing what the

abnormality conditions for the present context are. The relationship between surface

and mental conditionals is clearer if conditionals are interpreted as ellipses, as in the

presented analysis of the second antecedent correcting or elaborating the first. There is

no direct mapping between surface and mental conditionals because not every surface

antecedent is interpreted as a sufficient condition.

This leads to the subject of homogeneity versus heterogeneity of conditionals. On

the one hand, conditionals seem to be a simple concept and reasoning from them is a

very straightforward task. The sufficiency of the antecedent for inferring the truth of

the consequent seems to be a common feature of all types of conditionals. On the other

hand, we saw that there are different ways of interpreting conditionals and reasoning

from them. One way of explaining this apparent contradiction is to assume various

levels of processing. We identified several factors influencing people’s interpretation

of conditionals and the way they reasoned from them. Uniform representations at an

intermediate level might be modified when these parameters, like the involvement of

world knowledge or assumptions about coherence and consistency of the statements,

are set. It would be interesting to investigate whether this distinction is also relevant

for other sentence types.

My account also questions probabilistic approaches to human reasoning. It

explains uncertain conclusions by the uncertainty of the antecedent or uncertainty

related to a particular domain or utterance type. Moreover, it is shown that probabilistic

terms are often used to make conclusions agree with the speaker’s world knowledge.

10.3 Future work

This work shows that interviewing people about their interpretation of conditionals

and the conclusions they can draw is a promising way of investigating the meaning

and function of if-sentences. Therefore, I think that exploiting the possibilities of this

method further is definitely worthwhile. In the following, I want to present suggestions

for future work in this field. Some points needing further examination became apparent

while analysing the data, others are new ideas that might provide deeper insight into


the nature of conditionals.

The interviews indicate that cases where the second conditional introduces a

necessary condition are particularly interesting because people often seem to assume

that the antecedent is true. As I did not expect this kind of interpretation, the interviews

were not designed to test this aspect systematically. Thus, further work is needed to get

more empirical evidence. The material used and the questions of the interviewers have

to be tailored to the purpose of distinguishing between correction and the assumption

that one antecedent is true. My discussion of correction also raised the question

whether making an implicit assumption explicit is really perceived as a contradiction or

correction. Answering this question could be another goal, although it may be difficult

to elicit the necessary information because the topic cannot be addressed by direct

questions. Following the example of previous studies, we only used such statements

where an implicit assumption is made explicit. These are, however, special cases

of the more general phenomenon of introducing another necessary condition. Thus,

it would be interesting to use statements where the second conditional adds a less

obvious necessary condition. To ensure that the second antecedent is not interpreted

as an alternative condition, it could be commenced by ’only if’. This yields statements

like the following ones.

If she has an essay to write, she will be at home.(Only) if the library is closed, she will be at home.

If Rosa meets up with her friends, they will go to the opera.(Only) if the cinema is closed, they will go to the opera.

They could be followed by questions like: “Why do you think the second speaker

is saying that? Does he agree with the first speaker? Is the first sentence still true?

Do you think the first speaker knew about this condition? Does the second condition

hold?”

This dissertation has only examined modus ponens inferences. It would be

interesting to see whether the investigation of modus tollens and the fallacies supports

the results of this study. As others often used the fallacies as a basis for claiming the

existence of other types of conditionals, like reversed conditionals or biconditionals,

this would enable us to test their hypotheses about the mental representation of


conditionals. In this context, paying more attention to the relationship between

form and representation could also be helpful. Although I presented some sentences

starting with ’only if’, this aspect could be investigated more systematically, involving

sentences starting with ’if and only if’.

When trying to pin down the differences between conditionals referring to habits

and those referring to particular events, I noticed that most of the statements used in

the interviews allowed both types of interpretation. To examine the implications of

this distinction for the reasoning process, it would be necessary to present sentences

for which only one interpretation is possible.

All the studies on reasoning with uncertain premises gave subjects a scale of

conclusions expressing probabilities or frequencies of events. An interesting question

is whether answers contain the same indicators of uncertainty if subjects can formulate

their own conclusions. As I only deployed one such statement in my interviews, I

cannot provide enough empirical evidence to answer this question. Further research,

maybe in form of a conventional experiment where subjects can produce their own

answers, is needed to find out more about the role of uncertainty in reasoning. This

could also test my hypotheses that uncertainty or conditional probabilities are not

part of the basic meaning of conditionals. As in previous studies, conditional and

categorical premises would have to contain different degrees of certainty. One would

have to check whether the same degrees of uncertainty can be found in subjects’

answers. It might also be useful to manipulate the degree of certainty in a less

explicit or obvious way than previous studies. Instead of using words like ’probably’

or ’sometimes’, one could take examples from domains with different degrees of

predictability.

Another idea that could be exploited further is the combination of conditionals with

the same antecedent but different consequents. Again, there can be different kinds

of relationship between the first and the second conditional. The second sentence

can elaborate or correct the first, or just add another consequence, thus changing the

representation of the first conditional and the range of possible inferences. Therefore,

examining these cases further is another way of investigating the interpretation and

reasoning process connected with conditional sentences. Considering some examples,


I want to exhibit briefly which different interpretations of such statements are possible.

In the following sentences, the second conditional introduces an additional conse-

quence of Mary having an essay to write. This phenomenon could be described by the

discourse relation parallel.

If Mary has an essay to write, she will be in the library.If she has an essay to write, she will need lots of coffee.

In contrast, the next statement contains a contradiction, and the second sentence

can be understood as a correction of the first. Her being in the library is only one

possible consequence, thus the antecedent is not a sufficient condition.

If Mary has an essay to write, she will be in the library.If she has an essay to write, she will be somewhere at university.

The following statement also contains a correction, but here the truth of the

antecedent even implies the negation of the first consequent. Mary’s being in the library

will never be a consequence of her having an essay to write.

If Mary has an essay to write, she will be in the library.If she has an essay to write, she will be at home.

Again, elaboration is another possible discourse relation connecting the two

conditionals. This is illustrated in the next example.

If Mary has an essay to write, she will be in the library.If she has an essay to write, she will be in the medicine library.

In case of consistent, parallel sentences it would be interesting to see whether the

two conditionals are represented separately or as one joined conditional (e.g. ’If she

has an essay to write, she will be in the library AND she will need lots of coffee’). If

the two consequents contradict each other, we have a real inconsistency, i.e. there is

no other way to interpret the sentences. But there is the possibility of rephrasing the

sentences as a disjunction, thus leaving open whether the correction is accepted (e.g.

’If she has an essay to write, she will be in the library OR at home’). The inferences

people make could shed more light on their interpretations of these conditionals.

Finally, there is of course the possibility of using more natural material. Correction

or elaboration of conditional sentences are common phenomena in natural language


usage, but the statements of the suppression task do not represent typical ways of

doing this. Thus, one could think of more natural ways of adding another condition to

the interpretation of a conditional sentence.

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