the myth of reductive extensionalism

8/22/2019 The Myth of Reductive Extensionalism

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DOI 10.1007/s10516-007-9016-x

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ORIGINAL PAPER

The Myth of Reductive Extensionalism

Itay Shani

Received: 7 March 2007 / Accepted: 7 August 2007 / Published online: 1 September 2007 Springer Science+Business Media B.V. 2007

Abstract Extensionalism, as I understand it here, is the view that physical reality consists

exclusively of extensional entities. On this view, intensional entitities must either be elimi-

nated in favor of an ontology of extensional entities, or be reduced to such an ontology, or

otherwise be admitted as non-physical. In this paper I argue that extensionalism is a mis-

guided philosophical doctrine. First, I argue that intensional phenomena are not conWned to

the realm of language and thought. Rather, the ontology of such phenomena is intimately

entwined with the ontology of properties. After providing some evidence to the popularityof extensionalism in contemporary analytic philosophy, I investigate the motivating rea-

sons behind it. Considering several explanations, I argue that the main motivating reason is

rooted in the identiWcation of matter with extension, an identiWcation which is one of the

hallmarks of the mechanistic conception of nature inherited from the founding fathers of

our modern scientiWc outlook. I then argue that such a conception is not only at odds with a

robust ontology of properties but is also at odds with our best contemporary physics. Rather

than vindicating extensionalism contemporary science undermines the position, and the

lesson to be drawn from this surprising fact is that extensionalism needs no longer be

espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the

ontological approach to intensional phenomena advocated throughout the paper also gainssupport from an examination of the historical context within which intension was Wrst

introduced as a semantic notion.

Keywords Extensional entities Extensionalism Intensional entities Mechanistic

philosophy Modes Naturalism Properties

and one part of the thing is matter and the other form

Aristotle, Metaphysics VII, 8

I. Shani (&)

Department of Philosophy, School of Social Sciences, University of the Witwatersrand, Private Bag 3,

Wits, Johannesburg, 2050, South Africa

e-mail: [email protected]


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1 Introduction

One of the most well-entrenched metaphysical presumptions of modern western philoso-

phy is the belief that, deep down, nature is exclusively extensional and, hence, that inten-

sional entities, whatever they may be, cannot be considered rightful citizens of physicalreality properly understood. It is this presumption, I argue below, which motivated the

quest for a purely extensional scientiWc language in the heyday of early analytic philosophy

and of logical positivism, and which, to date, continues to motivate ambitious attempts to

reduce intensional discourse to extensional theoretical vocabulary. Notably, this very self-

same presumption is also reXected in the widely held belief that the intensional character of

mental states, as manifested, for example, in the phenomenon of seeing (hearing, smelling,

etc.) as, depends on the manifestation ofnon-physical properties (see e.g., Fodor and Pyly-

shyn 1981), from which it follows that physical systems, qua physical systems, are strictly

extensional. It is, in short, due to this presumption that we feel justiWed in maintaining that

the intensional realm is conWned to language and thought, while the world at which lan-

guage and thought are directed, and which they strive to comprehend, describe, and trans-

form, is uncontestedly extensional.1

Yet, despite the entrenchment of this presumption, despite its establishment as an

uncontested dogma, we have every reason to view it with suspicion. An inquiry into the

very nature of the distinction between intension and extension, and into the metaphysi-

cal foundations of the bias towards an extensionalist ontology, reveals, I submit, that in the

present theoretical context we have every reason to consider such a bias obsolete and

unfounded. We are neither justiWed in assuming that intensional phenomena are limited to

the conW

nes of language and thought, nor in holding that physical reality is, at its core,exclusively extensional. The bias towards extensionalist ontology has long been a

deWnitive mark of naturalism, yet it is on naturalistic grounds, I argue, that it ought to be

abolished.

In Sect. 2 I discuss the standard contemporary approach to intensional phenomena.

While technically developed, I argue that the standard view is ontologically underdevel-

oped. In particular, I argue that it does not explain, nor even address, important questions

such as what makes the variety of intensional phenomena intensional in the Wrst place

(apart from the trivial fact that they all violate the extensionality principle), or which inten-

sional phenomena are ontologically more basic (in the sense that the intensional character

of most, or all, other intensional phenomena is derivative from their own intensional char-acter). In Sect. 3 I respond to this challenge by identifyingproperties as the quintessential

intensional entities. All other intensional entitiesconcepts, propositions, and so onare

intensional in virtue of their relations to properties.

While the discussion in Sect. 3 points in the direction of an ontologically embedded

approach to the riddle of intensional phenomena there are strong philosophical persuasions

against such an approach. In Sect. 4 I review some of the most prominent examples demon-

strating the bias of modern analytic philosophy towards radical extensionalism and the

overwhelming tendency to either eliminate intensional phenomena, or reduce them to

1 There are, of course, exceptions to this metaphysical bias. For example, Turvey et al. (1981) resist the ten-

dency to delimit intensions to the noetic realm of language and thought and go some way in their attempt to

allocate intensions in physical reality. More generally, the extensionalist bias that occupies us here tends to

dissolve in a process-based metaphysics. However, these are exceptions and their heterodox character only

attests to the grip of extensionalism on mainstream philosophical thought.


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acceptable extensionalist ontology, or to conWne them to an isolated non-physical

realm. I touch on the views of Carnap, Quine, Lewis, and of non-reductive physicalism.

Section 5 addresses the metaphysical foundations of this extensionalist bias. In particu-

lar, I consider some of the principal reasons behind the tendency to endorse a nominalist,

object-centered ontology while denying properties an equal ontological footing. I begin byconsidering Quines contention that properties cannot be properly individuated; I argue that

this charge is, at best, inconclusive. A more signiWcant motivating reason behind the exten-

sionalist bias is the view that, being universals, properties are too spooky to be taken as

primitive constituents of physical reality. I argue that the view that properties are univer-

sals, let alone ante rem universals, is by no means compulsory. In particular, I suggest that

a modes conception of properties, according to which properties are concrete aspects of

concrete individuals, oVers an attractive alternative to the extremes of both nominalism and

Platonism. The most signiWcant single factor behind the extensionalist bias, however, is

traced to the mechanistic legacy of the 17th century scientiWc revolution and, in particular,

to the reduction of matter to a purely extensive substancea res extensa.

In Sect. 6 I argue that once the notion that properties are concrete modes is systemati-

cally pursued it becomes evident that there are categorical ontic diVerences between prop-

erties and objects, diVerences that not only explain why properties are intensional but also

indicate in unequivocal terms that the quest of reducing properties to an object-based ontol-

ogy is ill advised. The discussion in this section also points at the existence of an intrinsic

connection between properties (understood as concrete modes) and dynamic patterns of

organization, patterns that, in many ways, are not unlike the immanent forms of scholastic

philosophy that fell into disrepute with the advent of the mechanistic worldview.

The most persuasive argument against the irreducible reality of such immanent forms,and thereby also against the irreducible reality of quintessentially intensional entities, is

based on the view that in the Wnal analysis such forms must be reduced to formless parti-

clesthe elementary building blocks of nature. Yet, in Sect. 7, I argue that, rather than

making good of such a reduction, contemporary theoretical physics severely undermines it.

Relativity theory, quantum mechanics, quantum Weld theory, and string theory show a

steady alienation from the atomistic notion of a world constituted of formless elementary

building blocks while persistently aYrming the irreducible reality of dynamic patterns of

organization. In short, the driving motivation behind reductive extensionalism, its apparent

consonance with a robust scientiWcally oriented worldview, is undermined by science itself.

Finally, I show that the connection between the semantic notion of intension and themetaphysical notions form and quality is not only conceptually compelling (as argued

throughout the paper) but also historically grounded. Examining the original context in

which the term intension was introduced as a semantic category revealingly shows that

the term was borrowed from an earlier usage in the medieval doctrine of the intension and

remission of forms, where it was deeply entwined with the notions of quality and form.

2 Intensional Phenomena: The Standard Picture

The bias in favor of the view that physical reality, as such, is exclusively extensional is

implicit in our entire philosophical tradition of approaching intensional phenomena. To

appreciate this we need only observe that the terms intension and intensionality are

commonly associated with noetic entities: ideas or concepts in the case of intension,

sentences or propositions in the case of intensionality. Thus intensional phenomena, those

phenomena which are the loci of intensions, or which manifest intensionality, are


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commonly thought of as either features of mental processes, or linguistic features, or, per-

haps, abstract logical features.

What complements this familiar picture is the presumption that in contrast to this inten-

sional realm there is another realm, to which we may refer as the world, or nature, or

physical reality. The latter is a realm of things, hence of extensional entities, in whichintensional phenomena has no foothold. While intensional phenomena are thought to be

aboutthis extensional realm (when they are not about other intensional phenomena, see the

discussion of intensionality below), and while on any reasonably naturalistic account of

mind and its place in nature they are also, in some sense,partof it,2 intensional phenomena

are not considered constitutive of this physical realm per se. While mind and language may

well be intensional, nature, the idea goes, ultimately is not.

Given this sweeping relegation of intensional phenomena to the noetic realm of lan-

guage and thought it seems almost preposterous to suggest that we are missing something

important by doing so; yet, this is precisely what I am about to argue. In order to lay the

ground for the argument, however, we must consider Wrst the relevant notions of inten-

sion, intensionality, and intensional entities. As we shall see, the cognitive abodes of

intensions, and those cognitive entities that manifest intensionality, belong to a broader

class of intensional entities of which cognitive phenomena are but a proper subset. Thus,

even within the standard picture of intensional phenomena, the restriction of all things

intensional to the conWnes of language and thought is rather problematic.

2.1 Intension and Extension

We nowadays speak of intensionality, intensional entities, intensional logics and soon, but we shall do well to begin with the much older notion of intension. The traditional

philosophical distinction between intension and extension can be traced back to 17th cen-

tury logical theory.3 In their famous bookLogic, or the Art of Thinking (see Arnauldt

1662), the Port Royalists Arnauld and Nicole distinguished between the comprehension of

an idea and its extension. Employing the same distinction later on in the century it was

Leibniz (1690) who substituted intension for comprehension, thereby creating an

2 By claiming that on any reasonably naturalistic account of mind and its place in nature intensional phe-

nomena must, in some sense, be an integral part of nature the intensional phenomena I have in mind are con-

crete cognitive and linguistic structures. By contrast, abstract entities, for example Fregean thoughts, cannot

be considered as partaking in physical reality and, on account of that, ought not to be literally endorsed by

naturalists (by contrast, the capacity to construct and to grasp abstractions is, of course, fairly compatible with

naturalism).3 Doubtless, some readers will be inclined to resist this assertion, arguing that the distinction can be traced

further back to medieval philosophy if not to Aristotle himself. While I have no pretensions of being an

authority on such matters, I found little evidence to support it. Aristotles categories are general types of pred-

ication (highest genera, according to some interpretations), and nowhere in the Topics (1987d), or the Cate-

gories (1987a), do we Wnd clear evidence that he understood them to be anything like the early-modern notion

of intensionthe collection of attributes implied by an idea. The medieval notion intentio, rendered as a

translation of the terms mana and maqul which were used in medieval Arabic interpretations of Aristotle,stands, roughly, for a sign in the soul or for whatever it is which stands before the mind in thought (Kneale

and Kneale 1962, p. 229; Crane 2000). As such, it can no more be considered a precursor of intension than of

intentionality. Perhaps the closest we get to genuine precursors of intension and extension are the notions of

signiWcatio and suppositio (respectively) as used in the medieval theory of the properties of terms. Yet, even

here the analogy is far from perfect (see Ashworth 2006; Read 2006). Finally, the term intension was, indeed,

used during the middle ages but in a diVerent context, namely, in discussions concerning the intension and

remission of forms (see Sect. 8).


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elegant terminological antithesis to extension accurately representing the contrast

between the two concepts.

On this view both extension and intension pertain to ideas. The extension of an idea is

the class ofthings over which it extendsthe class of individuals that fall under it, or to

which it applieswhile intension is identiWed with the attributes implied by, or containedin, the idea. For example, the extension of triangle consists of all triangles, while the

intension of the term consists of attributes such as Wgure, three lines, three angles, the

equality of these three angles to two right angles, and so on.

Clearly this early modern distinction already implies the dichotomy that concerns us:

extension is associated with external reality whereas intension is associated with the

inner recesses of the mind. Surely this has been the common way of understanding the dis-

tinction ever since. Consult any contemporary textbook or encyclical entry dealing with

intension and extension and you will Wnd that the intension of a concept (term, expres-

sion) is almost invariably identiWed as the meaning of that concept (term, expression),

where meaning is here understood as an internal non-referential factor.

Understood in this manner, the dualism of intension and extension is a reXection of a

more familiar dualism prominent in 17th century thought, the dualism of mind and matter.

As we shall see, however, such a dualistic way of curving out the distinction is not only

ontologically problematic, as the discussion that follows clearly indicates but also, as I

argue in Sect. 8, too simplistic even from a historical point of view.

At the turn of the 20th century an even more secluded view concerning the domain in

which intensions may roam gained ascendancy. On the early modern conception, the

semantic component identiWed as intension is an intrinsic feature of ideas, and as ideas in

the mind are intentional states it is, ipso facto, an intrinsic characteristic of actual inten-tional states. By contrast, on the inXuential anti-psychological accounts of both Frege

(1892) and Husserl (1913) the semantic notions corresponding to intensionFreges

sense and Husserls noemaare portrayed as designators of abstract entities which,

while capable of occurring in, or of being grasped by, actual intentional states are not con-

crete constitutive aspects of such states.4 Finding such abstract entities hard to digest, natur-

alistically inclined philosophers commonly react either by denying the reality of intensional

meaning factors altogether, or by turning back to a more psychologically embedded

approach. Yet none of these typical responses challenges the basic dualism inherent in

identifying extension with matter, or physical stuV, and the corresponding identiWcation

of intension as belonging to an antithetical mind stuV.

2.2 Intensionality

The reality of intensions gives rise to a related phenomenon known as intensionality. It is

customary to distinguish intensionality from extensionality by distinguishing between

intensional contexts and extensional contexts. An extensional context is one in which

denoting terms whose denotata are co-instantiated (e.g., covalent sentences, co-extensive

predicates, and co-referential singular terms) can be intersubstituted salva veritate; an

intensional contextis one in which such substituitivity cannot be guaranteed. As an exam-ple of an extensional context, consider the sentences below:

4 In interpreting Husserls noema as being an abstract entity on par with Freges sense I follow Follesdal

(1969, 1990).


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S1. All pelicans are feathered.

S2. All pelicans have intertarsal joints.

Given the co-extensiveness of the predicates feathered and possessor of intertarsal joints

S2 may be substituted for S1 (and vice versa) without thereby altering the truth-value of the

original sentence. Hence, sentences such as S1 and S2 deWne an extensional context and are

said to be extensional. By contrast, consider now the following sentences:

S3. Doolittle believes that all pelicans are feathered.

S4. Doolittle believes that all pelicans have intertarsal joints.

In this case, substituting S4 for S3 may fail to preserve the truth-value of the original sen-

tence: co-extension notwithstanding, Doolittles belief that pelicans are feathered does not

entail that he also believes that they have intertarsal joints. So, sentences like S3 and S4deWne an intensional context and are said to be intensional.

What sentences like S3 and S4 illustrate is that contexts in which propositional attitudesare being reported, or described, contexts like x believes that ..., y hopes that ..., z

desires to, u expects that ..., and so on, are intensional. Let us call such cognitive contexts

C-intensional.

Interestingly, not all intensional contexts are C-intensional; in particular, an important

class of intensional contexts are modal-terms contexts. To use a stock example, consider

this pair of sentences:

S5. Necessarily creatures with kidneys have kidneys.

S6. Necessarily creatures with kidneys have hearts.

Despite the fact that all chordates are renates, and although S5 is true, it does not followthat S6 is true. So, modal-terms contexts, too, are intensional and we may label such con-

texts M-intensional. That not all intensional contexts are C-intensional is an important

point which any theory of intensional phenomena with aspirations for completeness

ought to address. But although I believe that the account presented in this paper can, in

principle, be extended so as to subsume M-intensional contexts, I shall leave the explana-

tion of such contexts for another occasion. Providing an ontologically grounded account

of the entire spectrum of intensional phenomena is a magnanimous task whose achieve-

ment in one single paper is, Im afraid, beyond my capacities. This is not only because

the very question what is the ontological basis of intensional phenomena? has rarely

been explored in any systematic fashion before, but also because the connection between

the underlying ontology of C-intensional contexts and that of M-intensional contexts is

by no means obviouswith the implication being that any attempt to argue for the exis-

tence of such a connection requires extra care and deliberation. Therefore, I shall be

entirely content if the present eVort, partial though it may be, succeeds in showing that a

large and important class of intensional entities, including (but not exhausted by) C-

intensional contexts, share a common ontological background and does so in a way

which runs counter to the reductive aspirations of extensionalism. I turn back to C-inten-

sional contexts, then.

An ontological inquiry into the nature of intensional phenomena compels us to gobeyond the dry fact that certain contexts are C-intensional and to ask what, in the nature of

the phenomena, accounts for the intensionality manifested in such contexts. The answer, I

suggest, can be summarized in the following four theses, which I shall present and explain

in order.


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Th1

C-intensional contexts are constituted by higher-order propositional structures

(HOPS), namely, by sentences, utterances, or cognitive representations reporting the con-

tent of other, lower-order, propositional structures (LOPS).5,6

Explication: Consider again S3 and S4. Such sentences are attitude reports (Crane 2001, p.

21); they describe the attitudes taken by a psychological agent (Doolittle) toward an inten-

tional object, or objects (pelicans). Put diVerently, C-intensional contexts are constituted by

propositional structures that take other propositional structures as their intentional objects:

whereas Doolittles belief to the eVect that all pelicans are feathered is about pelicans, S3 is

about Doolittles belief.7

Th2 Failures to substitute one HOPS for another, co-extensive HOPS, salva veritate are

due to failures to preserve the contentof the originally reported LOPS.

Explication: Quite simply, the reason why S3 does not entail S4 is that the two attitude

reports ascribe diVerent contents to the attitude taken by Doolittle vis--vis pelicans: thereis a diVerence in content between the belief that all pelicans are feathered, and the belief

that they are all creatures with intertarsal joints.

Th3

Failures to preserve the content of a LOPS upon substitution of co-extensive HOPS

are due to the fact that intentional content is individuated in part in terms ofintensions and

cannot be speciWed in purely extensional terms.

Explication: Observe, Wrst, that the truth-value of a factual statement, whether intensional

or not, depends on the identity of its intentional object/s. For example, while all pelicans

are feathered is true, all humans are feathered is false. However, when it comes to C-

intensional HOPS like S3 the intentional object is itself an intentional state and, as such, isindividuated in terms of its content. Consequently, sensitivity to the content of Doolittles

belief is crucial for the preservation of the sentences truth-value. But, and here is the major

point, the content of Doolittles belief is notreducible to the identity of the beliefs inten-

tional object. Knowing that Doolittles belief is about pelicans is insuYcient for determin-

ing the identity conditions of the belief. In addition one must know what is Doolittles take

on the big birds, how he represents them to himself, what properties he attributes to them,

in short, what intension is associated with the belief.

Th4 Hence (by Th1 to Th3), C-intensionality, as manifested by certain HOPS, emanates

from the fact that the LOPS being reported by such HOPS are endowed with intensions. In

5 By propositional structure I mean any structure capable of expressing propositional content, whether the

structure is cognitive (a representation) or linguistic (a sentence, an utterance). My reason for not using the

more familiar term proposition is that this term is often associated with Platonic abstract entities, with whose

aYrmation I would hesitate to align myself.

6 It is often maintained that C-intensionality is an exclusively linguistic phenomenon, which has no direct

application to any other sort of representational system. (Dennett 1996, p. 38; see also Crane 2003, p. 34;

Zalta 1988, p. 3). However, as Searle observes (1983, p. 25), while C-intensionality is a feature of HOPS,there is no reason to suppose that such HOPS must be linguisticjust as some higher-order sentences and

utterances are intensional so do some higher-order intentional states.7 One is reminded here of Freges celebrated assertion that [i]n reported speech one talks about the sense,

e.g., of another person's remarks. And that in this way of speaking words do not have their customary ref-

erence but designate what is usually their sense. (1892, p. 25). However, in contrast with Frege, I would say

that it is not senses as such that are being designated in C-intensional contexts but, rather, actual lower-order

representations.


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other words, the intensionality of attitude reports is inherited from the intensional charac-

ter of the attitudes being reported.

Explication: Intensionality, we have seen, is a property of certain HOPS subsuming LOPS

as their intentional objects.8 Such LOPS, however, are atypical intentional objects in that

they themselves are content-bearing intentional states and, as such, possess an irreducible

intensional character and are not fully individuated in terms of their extensions. Therefore,

in interchanging co-extensive LOPS the preservation of semantic identity cannot be guar-

anteed, from which it follows that neither can the corresponding substitution at the meta-

level of the HOPS directed at such LOPS guarantee truth-preservation. In sum, failures to

substitute co-extensive attitude reports salva veritate are due to the fact that the reported

attitudes cannot, in general, be interchanged salva signiWcatum. C-intensionality is rooted

in the fact that intentional states are endowed with an intensional dimension, namely, that

they are veritable loci of intensions.9

2.3 Intensional Entities

In clarifying the connection between intensionality and intensions, we may do well to

appeal to a broader category subsuming both. Such a logical category is the category of

intensional entities. Intensional entities are characterized by the fact that they contravene

the extensionality principle, i.e., the principle that equivalence (as in the case of equivalent

sets), or co-presence (as in the case of co-present individuals), imply identity (cf. Bealer

2000). That is, if F and G are two intensional entities such that F G, or that F and G are

co-instantiated, it does not follow that F = G.

Naturally, this class of entities includes various kinds of noetic entities such as ideas,concepts, propositions and propositional attitudes, precisely those entities which are the

bearers of intentional content (hence of intensions) and which give rise to the phenomenon

of intensionality. Thus, for example, despite being co-extensive, the concepts feathered

and possessor of intertarsal joints are mutually distinguished. Ditto when it comes to

propositions such as expressed by S1 and S2, which diVer from one another in that the Wrst

sentence employs feathered as its grammatical predicate while the second employs pos-

sessor of intertarsal joints. Finally, note that sentences such as S3 and S4, which constitute

an intensional context, are also a subspecies of intensional entities: the potential diVerence

in their truth-value expresses the fact that the co-extensionality of belief reports does notimply their identity.

Intensional entities are contrasted with extensional entities like concrete objects, or sets,

which, unlike the former, abide by the extensionality principle: extensionally equivalent

sets are, ipso facto, identical, and so is the case with co-instantiated concrete individuals.

8 As Crane observes (2001, p. 21), not all reports of intentional states are intensional. Some reports do not

attempt to capture the subjects perspective, and, as a result, their truth-value does not depend on the inten-

sions expressed by the intentional states they describe. For example, the sentence John is thinking of Alaska

does not specify the exact manner under which Alaska is represented in Johns thought; it merely dictates that

it is, indeed, Alaska that John is thinking of. Hence, replacing the singular term Alaska by a co-extensiveexpression such as the largest state of the US will result in a truth-preserving substitution.9 For this reason, it seems to me that Searle is wrong when he insists, with typical verve, that there is no close

connection between intensionality-with-an-s and intentionality-with-a-t, and that the only connection be-

tween them is that some sentences about intentionality-with-a-t are intensional-with-an-s. (Searle 1983, p.

24). Clearly, when it comes to C-intensionality (which seems to be the kind of intensionality he is interested

in) Searles denial of a close connection to intentionality-with-a-t is untenable as it downplays the fact that

the intensionality of attitude reports is a contigenton the intentionality of the reported attitudes.


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Notably, however, not all intensional entities are noetic; properties and relations, for

example, are intensional entities par excellenceneither properties nor relations are such

that when co-instantiated they are necessarily identical (e.g., the property of being feath-

ered and the property of possessing an intertarsal joint are markedly distinct). Clearly, then,

intensional entities are an impressively heterogeneous bunch: some, for example conceptsand propositions, are noetic, while others, notably properties and relations, are not. More-

over, within the class of noetic intensional entities, some entities manifest intensionality

(e.g., C-intensional propositions), while others (lower-order representations), are not.

In the face of such ontological heterogeneity it is only natural to look for a unifying

explanation, an explanation which will properly address the question what binds properties,

psychological attitudes and attitude reports together in virtue of which they all qualify as

intensional entities.

The conventional wisdom reigning at the present oVers precise logical criteria with

which to identify intensional entities but it oVers little insight into the question what makes

such a heterogeneous lot united in contravening the extensionality principle in the Wrst

place. Worse still, it provides little insight into the possibility of ordering the Weld of inten-

sional entities such that it will become clear which, among these, are more fundamental in

the sense that the intensional character of other intensional entities depends on the fact that

they themselves are intensional.10 In short, we seem to lack a sound understanding of the

ontological proWle of intensional entities and of the nature of the divide between intensional

and extensional entities. Nor is this, in any way, surprising. After all, crisp logical criteria

for the demarcation of entities are no substitute for a sound knowledge of their substantive

characteristics.

In the remaining parts of this inquiry I attempt to unveil the ontological basis of thedivide between intensional and extensional entities. Once this is done, I argue, it becomes

clear that the extensionalist bias, the tendency of naturalistic, or otherwise scientiWcally

minded philosophers to give extensional entities ontological priority over intensional enti-

ties, is ill motivated, both conceptually and empirically.

3 Fine-Grained Intensions and Coarse-Grained Intensions: Why Properties are Key

in Explaining Intensional Phenomena

As noticed, it is an interesting and intriguing feature of the typology based on the exten-sionality principle that while some intensional entities, such as concepts, propositions,

ideas, and thoughts, are noetic, others, such as properties and relations, are not. Clearly, an

ontological inquiry must strive to account for this fact and, equally clearly, it must also con-

cern itself with the question: which, among those entities, are explanatorily more funda-

mental in the sense that their own intensional character is instrumental in explaining the

intensional character of other entities. In this section, I argue that the intensional character

of noetic intensional entities consists of the fact that such entities are property-ascriptive.11

In other words, the intensional character of noetic entities can be traced to the intensional

character intrinsic to the properties they ascribe to the things at which they are directed.

10 Thus, even the claim made in Sect. 2.2 to the eVect that C-intensionality follows from the intensional char-

acter of (the having of intensions by) intentional states is rarely represented in the relevant literature.11 To be sure, noetic entities refer to many things beside properties (objects, situations, events, etc.); never-

theless, as I argue below, the intensional aspect of semantic valuation lies inpredication, and the latter con-

sists inproperty ascription.


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Properties, it will be my conclusion, are the quintessential intensional entities.12 Following

familiar terminology, I shall refer to noetic intensional entities as Wne-grained intensions,

and to non-noetic intensional entities as coarse-grained intensions (see Bealer 2000; Lewis

1983, pp. 200201).13

Consider Wrst Wne-grained intensions. As was shown before (Sects. 2.2 and 2.3), suchentities violate the extensionality principle because their identity conditions, qua semanti-

cally laden entities, are not exhausted by a speciWcation of their relevant extensions. In

other words, part of what constitutes the content of content-bearing phenomena is deter-

mined by a meaning factor that seems to be non-amenable to extensional individuation.

Rivers of ink have been poured in attempts to clarify the nature of this intensional meaning

factor and no consensus is in sight but if we ask ourselves what is its most signiWcant trade-

mark the answer, I think, is clear. What makes concepts, propositions, thoughts, and their

ilk intensional is the fact that they are predicative, namely, that in addition to simply be

directed at things external to themselves (hence, be associated with extensions) they also

predicate something about those things.

The intensional character of predication is manifested in the fact that one-and-the-same

entity (or class of entities) may be the object of diVerent predications. To go back to our

stock example, to assert ofx that it is feathered is to predicate it with an attribute quite

diVerent than the one connoted by the assertion that it possesses an intertarsal joint. This

diVerence of predication constitutes a diVerence in semantic identity that is independent of

the question whether or not the things that are feathered are also the very same things that

are endowed with intertarsal joints.14

From this example and countless others possible it can be readily ascertained that predi-

cation consists in none other than the ascription ofproperties (feathered, stable, radio-active, etc.) to the things being predicated. Thus, a solid chain of reasoning traces the

intensional character ofWne-grained intensions to the phenomenon of property ascription.

Naturally, our next question ought to be is there something about properties that entails the

intensional character of property ascription?

It does not take too much eVort to see that the answer to our query is positive. We have

seen before (Sect. 2.3) that properties are a shining example of intensional entities for the

simple reason that the co-instantiation of two properties and does not imply their

12 A complete argument in favor of the claim that properties are the quintessential intensional phenomena re-quires, in addition to the account provided below, a demonstration that the intensionality ofmodal-terms con-

texts can also be traced to the nature of properties. I believe that such an account can be given for causal modal

statements, where the modal force of such statements is analyzed in terms of the dispositional potency of the

properties that sustain the truth makers of such statements (along the lines suggested by Martin and Heil

1999). However, in accordance with my decision not to discuss M-intensionality in any detail here (see Sect.

2.2), I shall not elaborate on this topic any further.

13 As the terms coarse-grained and Wne-grained suggest, the distinction is often taken to imply that two

Wne-grained intensions, say two logically equivalent concepts, may be distinct despite corresponding to, or

expressing, identical properties (Bealer 2000). While this is a controversial point, I shall not pursue the issue

any further. By helping myself into this familiar terminology I assume neither more, nor less, than the fact

that it corresponds to the distinction between noetic and non-noetic intensional entities.14 An alternative way to make the point is this. Intentional states represent their intentional objects under deW-

nite aspects and their aspectual character is deWnitive of their identity qua content bearing intentional states

(cf. Searle 1992, p. 155). A mental state S whose content can be expressed by the proposition all pelicans

are feathered represents pelicans as feathered. Representing under this aspect is constitutive of Ss semantic

identity. A co-extensive mental state S, representing pelicans as possessors of intertarsal joints, shares with

S the same intentional objects but its contentis nevertheless diVerent due to the fact that it represents those

objects under a diVerent aspect.


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identity. Using P and P as predicates standing for and respectively, we can therefore

verify that the inference from x = y to Px = Py is illicit on account of the intensional char-

acter of and . It therefore seems appropriate to conclude that the intensionality of

noetic intensional entities is rooted in this peculiar proclivity of properties to defy the

extensionality principle. Being instrumental in accounting for the intensional character ofconcepts, propositions, attitude reports, and so on, properties suggest themselves as the

quintessential intensional entities and as the key to a more insightful account of the ontol-

ogy of intensional phenomena.15

If intensional character is, indeed, anchored in the ontology of properties our next step

should be to examine this ontology in some more detail. In particular, I shall concentrate on

what sets properties apart from allegedly extensional entities. To put it more precisely, I

shall focus on the question what meaning can be given to the distinction between intension

and extension outside of semantic contexts, namely, what meaning can be given to these

categories as broadly deWned ontological categories.

4 Extensionalism at Work: Some Examples of the Extensionalist Bias

in Contemporary Analytic Philosophy

Our investigation of the intensional character of noetic entities led us to identify its source

with an ontological fact about properties, namely, with the fact that property co-instantia-

tion does not imply property identity. Yet, if our inquiry takes us in the direction of assign-

ing an intensional character to ever more general, and more fundamental features of reality

(from statements about intentional states, to intentional states, to the properties expressedby intentional states), surely we must ask why is the idea that intensional phenomena might

be rightful, irreducible, residents of physical reality so foreign to the dominant literature on

the subject? Why is it almost unanimously accepted that, in the Wnal analysis, intensional

entities must be reduced to non-intensional entities, or that if they cannot be so reduced

then this very fact constitutes a failure of naturalism?

In present day analytic philosophy this metaphysical stance amounts to the persuasion

that intensional entities are incompatible with naturalism, or physicalism. On this pre-

mise, intensional entities must either be eliminated altogether, or they have to be reduced

to, or otherwise accommodated with, an intension-free physical domain (the Wrst option

corresponds to eliminative physicalism, the second to reductive physicalism, and the thirdto non-reductive physicalism). While our ultimate goal is to trace the metaphysical roots of

this incompatibility thesis (see Sect. 5) and to assess its validity (Sects. 67), it is useful to

consider, Wrst, some of its more familiar manifestations.

The association of physicalism with extensionalism is as early as physicalism itself. In

its original formulation by Neurath (1931),physicalism is the thesis that all empirical state-

ments can be expressed in the language of physics (i.e., the language of physics is adequate

for a complete description of the world). It was, however, Carnapwho followed Neu-

raths path in adopting physicalism, as well as the thesis of the unity of sciencewho made

the association of physicalism with extensionalism explicit. The association was made viathe extensionality thesis (not to be confused with the extensionality principle!). According

to the extensionality thesis (Russell, in Whitehead and Russell 1925; Carnap 1937), every

15 From now on I shall use properties in a wide sense, which includes also many-place relations. The claim

advanced in this section, then, is that the intensional character of noetic intensional entities depends on the

intensional character of the properties andrelations they express.


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utterance made in an intensional language can be translated without loss into an extensional

language. The thesis betrays the idea (which, in the more limited context of mathematical

discourse, can be traced to Frege e.g., 1893) that intensional contexts are a reXection of the

imperfection of natural language, and that once our language has been purged of nonsense,

obscurity, and confusion such contexts will be eliminated. In Carnaps adaptation, theextensionality thesis was amalgamated with the doctrine of physicalism to yield the idea

that all expressions utilized by science can be translated into the physical language which

itself can be made extensional (Cornman 1962, p. 57).16 Carnaps ingenious attempts to

construct a language free of intensional idioms did not succeed, but the appeal of reducing

intensional entities to extensional entities has not died out.

A similar sentiment pervades Quines inXuential work in semantics and philosophical

logic. Already in Two Dogmas of Empiricism (1953), Quine declared war on mean-

ings and was heading in the direction of a purely referential semantics. His extensionalist

program is presented in full in Word and Object(1960), where he advocates a Xight from

intension (as one of the chapters of the book is so revealingly called), namely, a systematic

attempt to rid our scientiWc vocabulary of any reference to intensional entities. Conceding

Chisholms (1957, chap. 11) point that there is no way to reduce an intentional vocabulary

to a purely extensional one, Quine settles for eliminativism and announces the baseless-

ness of intentional idioms and the emptiness of a science of intention (1960, p. 221).17 By

the same token, he also rejects coarse-grained intensions, renouncing properties, relations

(in intension), and possibilia as spurious entities, which ought to be dismissed in favor of a

purist ontology of concrete individuals, and classes thereof. Thus, Quines semantics, and

his ontology, are strictly extensionalist.

Yet another important extensionalist program is David Lewiss modal realism (1983,1986). Unlike Quine, Lewis avails himself to possibilia, yet his extensionalist reductionism

is no less austere for that. Lewiss ontology is as extensional as it gets, consisting entirely

of individual objectssome of which are actual (i.e., existing in the actual world), some

are possible (existing in some possible world), some of which are concrete (e.g., the egg

shaped rock I hold in my hand), and some are abstract (e.g., the set containing this rock, my

earphones and your favorite CD).

Lewiss generous appeal to possible worlds enables him to construct an ingenious solu-

tion to the apparent irreconcilability between the reality of properties and the constrictions

imposed by an extensionalist ontology. On Lewiss construal, a property is identiWed with

the set of all its instancesall of them, this- and other-worldly alike. (1986, p. 50). Moretechnically, properties are reconstructed as functions from possible worlds to sets of possi-

ble (sometimes also actual) objects. This enables him to accommodate the problematic fact

about properties noted in Sect. 3, namely, the fact that property co-instantiation does not

imply property identity. On Lewiss account, accidentally coextensive properties, such as

16 As Cornman notes, this is one way to state the thesis of the unity of science. The demand that all predicates

employed by science will be couched in an extensionalist physical language was meant to undermine the

dichotomy between the physical sciences and the sciences of the spirit (the Geisteswissenschaften), presum-

ably the natural abode of intensional entities.17 Lest the reader gets confused with the switch between intentional and intensional, it may be pointed out

that at least some of Chisholms criteria of intentionality are unmistakably criteria of intensionality, i.e., cri-

teria that demonstrate the irreducible intensionality of intentional idioms. In contrasting intentional vocabu-

lary with extensional vocabulary, then, Quine is tacitly presupposing the irreducible intensionality of the

former. Unfortunately, Chisholm himself is not explicit about the fact that his discussion of intentionality is,

to a large degree, a discussion of intensionality, a confusion replicated by other authors as well (e.g., Fodor

and Pylyshyn 1981, p. 188V).


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the property of being a creature with a kidney and the property of being a creature with a

heart, are not coextensive at all. They only appear so when we ignore their other-worldly

instances. (Ibid. p. 51).

There are problems with the technical and conceptual feasibility of Lewiss proposal

(for some objections, see Bealer 2000). Yet, even if a solution along Lewis lines is techni-cally Xawless, I argue below that the ontological motivations underlying it are misguided.

The reduction of properties to an object-based ontology not only ignores the fact that prop-

erties are categorically distinct from objects (as I argue in Sect. 6), it is also premised on an

outdated conception of the fundamental furniture of physical reality (see Sect. 7).18 For

now, however, we need only observe that, like Carnap and Quine, Lewiss working

assumption is that an appropriate ontology, and an appropriate semantics, ought to be

purged of irreducible intensional entities.

What Carnap, Quine, Lewis, and a great many other philosophers seem to believe is that

there is no room for intensional entities in a scientiWcally oriented philosophy. The point is

summarized succinctly by Follesdal, in a review of Quines position: as long as inten-

sional entities are not called for within the theory of nature in order to account for the evi-

dence, there is no reason to believe that there are such entities, nor do we have identity

criteria for them. (1974, p. 29).

Interestingly, this extensionalist bias is also shared by non-reductive physicalists. As a

matter of fact, the belief that physical reality is completely extensional, and can be fully

described in a strictly extensional language, remained invariant throughout the transition

from the reductive positivist ideal of a uniWed science to the more relaxed picture of the

autonomous sciences portrayed by non-reductive physicalists such as Fodor (1974). For,

while on this view there is noX

at denial of the reality of intensional phenomena, it is never-theless denied that such phenomena might be constitutive of physical reality as such.

Token physicalists insist on the reality of an autonomous, irreducible, realm of psycho-

logical (and other special)properties while maintaining that these properties are instanti-

ated by strictly physical realizers. In accordance with this property dualism, the reality of

intensional entities such as concepts, and of intensional phenomena such as the phenome-

non of seeing as (e.g., seeing Venus as the morning star, rather than as the evening star), is

explained by recourse to psychological properties, notably the properties characteristic of

symbolic representations (see, for example, Fodor and Pylyshyn 1981). These properties,

while physically realizable, are not themselves physical. It follows, then, that what consti-

tutes a system as aphysical system has nothing whatsoever to do with intensions.The extensionalist bias of this position consists, then, in the supposition that wherever,

and whenever, physical systems manifest intensional characteristics they do so in virtue of

non-physical properties; physical systems, qua physical systems, are strictly extensional.

Thus, while non-reductive physicalists of the cognitivist creed are more liberal in their

approach towards the reality of intensional entities than reductive and eliminative physical-

ists they nevertheless insist on classifying intensional phenomena as non-physical, thereby

aligning themselves with what I have called the extensionalist bias, namely, the view that

associates physical with extensional, and that denies that intensional entities might play

a constitutive role in the making of physical reality.

18 As explained in Sect. 6, my claim regarding the categorical diVerences between objects and properties per-

tains to the futility of all attempts to reduce properties to a strictly extensionalist ontology. However, it need

not suggest the absurd idea that properties and objects have nothing to do with each other. In other words, we

can still speak meaningfully of objects exemplifying properties and of properties as being, in some sense,

constitutive of objects.


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In light of the overwhelming prevalence of this extensionalist bias it is worthwhile to

examine its metaphysical underpinnings in some detail. I take on this task in the next sec-

tion.

5 Metaphysical Underpinnings of the Extensionalist Bias

There is, then, a solid, if often unspoken, consensus in favor of the view that intensional

entities are not, and cannot be, an integral part of physical reality as such. No doubt, this is

largely due to the association of such entities with mental and linguistic properties. Yet, as

we have seen, even when the reality of intensional entities is associated with non-cognitive

phenomena, such as properties, there is a tendency to deny these phenomena a basic physi-

cal status. Properties are either eliminated in favor of a purely extensionalist ontology (e.g.,

Quine), or they are reduced to entities that conform to such an ontology (e.g., Lewis), or the

bulk of them are declared non-physical (non-reductive physicalism). Thus, the presump-

tion remains that what is truly physical cannot be truly intensional .

In order to assess the validity of this almost unanimous extensionalist bias we must Wrst

attempt to understand its metaphysical background and its historical origins. In particular,

having identiWed properties as the quintessential intensional entities, we need to understand

what lies behind the tendency to deny properties a fundamental physical status, or, what

essentially comes down to the same thing, behind the tendency to reduce them to unequiv-

ocally extensional parameters.

5.1 First Gambit: Properties cannot be Properly Individuated

According to this objection, hailed by Quine (1960, chap. 6; see also Wilson 1955), we

have no clear identity conditions for properties. This means that we have neither clear cut

criteria for judging when two property instances belong to the same type P, nor clear cut

criteria for diVerentiating one member of P from another. While co-instantiation secures

the identity of concrete individuals (physical objects and events), and co-extension secures

the identity of sets, analogous principles for properties, Quine argues, are not available.

There are several lines of argument one could pursue as a rejoinder. First, one may fol-

low Armstrong (1978) in denying that the criteria for solving problems of property individ-

uation must be provided a priori. Causally eVective properties are the domain of scientiWcinquiry and we may learn more about them, including about their identity criteria, as we go.

Second, one may attempt to rise up to the challenge by providing acceptable criteria for

property identity. Thus, for example, one may attempt to account for the identity criteria of

properties in terms of their causal powers or functional roles (for a general overview see

Swoyer 2000). Third, one may observe that since objects, events, and states of aVairs are

individuated in terms of their properties, rather than the other way around (Martin 1996;

Turvey et al. 1981), it is not at all surprising that we Wnd it much more diYcult to individu-

ate properties. It might even be argued that, given the fact that it is in terms of properties

that all other entities are individuated, the individuation of properties cannot be further ana-lyzed without regress, and must be presumed primitive (Heil 2003, chap. 12).

Finally, a particularly appealing rejoinder, in my view, consists of the simple observa-

tion that Quines argument is eVective only insofar as one already suspects that we have no

good independent reasons to believe in the irreducible reality of properties. For, suppose, as

I argue in Sect. 6, that one have good ontological reasons for believing that properties are

irreducibly real physical entities and that they are categorically distinct from extensional


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entities (whether abstract or concrete, actual or possible). In that case, Quines concern is

simply not compelling enough to motivate us to seriously suspect the reality of properties.

Rather, a natural (and, dare I say, healthy) reaction would be to conclude that, while we

ought to take notice of this problem, we simply need to learn more about the ontology of

properties before we could hope to solve it, or perhaps dissolve it. To go back to the citationfrom Follesdal mentioned in Sect. 4, it seems to me that the argument from identity can-

not be separated from the deep seated conviction that intensional entities are simply not

required in order to account for the evidence.

5.2 Second Gambit: Properties are Universals, Hence are Too Spooky to be Taken

as Primitive Constituents of Physical Reality

An ontologically deeper, and certainly historically more inXuential reason behind the reluc-

tance to treat properties as basic ingredients of the physical world has to do with the fact

that throughout the history of philosophy properties have often been considered platonic

universals. The intuition behind thinking of properties as universals is that diVerent particu-

lars (say two spatiotemporally separate white cars) may be the same in certain respects

(e.g., with respect to whiteness). Since properties just are such qualifying respects, and if

being the same as is interpreted as being identical to, it follows that one-and-the-same

property is shared by a plurality of distinct particularshowever causally detached from

one another they may be. Unsurprisingly, this idea is not easily reconcilable with a concep-

tion of physical reality as consisting of concrete systems, all the more so if properties are

understood, as they often have been, as universals ante rem, that is, as general natures, or

platonic forms, whose existence is completely independent of realization in concrete partic-ulars. In reaction to such Platonism, medieval nominalists maintained that reality consists

solely of concrete individuals, taking universals to be nothing more than linguistic labels,

or, at the most, mental abstractions.

No doubt, this nominalist sentiment still looms large in contemporary naturalistic phi-

losophy, as is the supposition that properties are, somehow, shrouded in platonic abstract-

ness.19 Yet, none of this need to be taken for granted. In particular, my intention is to

indicate that there is absolutely no necessity to characterize properties as universals,

let alone ante rem universals, and to intimate that Platonism is by no means the only alter-

native to outright nominalism. The alternative conception of properties I would like to

highlight is that of properties as particular modes of concrete individuals (see Martin andHeil 1999; Heil 2003, chap. 13).20

The modes conception of properties is recognizably similar to trope theory. Williams

(1953) has introduced the term trope to modern philosophical parlance to denote particu-

lar instances of qualities. Thus, two shirts with the same shade of red exemplify two red

tropes, two particular instances of redness. Tropes, however, are not particular instances of

universals. On this account, there is no universal quality such as redness, or the quality of

19

Thus, modulo the admission of sets (whose admission is grounded in their theoretical expediency), bothDavid Lewiss and Quines ontologies are exemplars of nominalism (although, unlike Lewis, Quine believes

that the admission of sets disqualify his ontology from being one). A still more austere nominalism is defend-

ed by Sellars (1967).20 Another important contemporary alternative to either Platonism or nominalism is Armstrongs (e.g., Arm-

strong, 1978, 1989) Aristotelian conception of properties as in rebus universals, i.e., as denizens of spatio-

temporal reality, wholly present in each of their numerically distinct instances. As my sympathies lie

elsewhere, I shall not discuss Armstrongs conception of properties as immanent universals any further.


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being red, of which particular objects partake and in virtue of which they are red. Rather,

what qualiWes our shirts as red is the fact that they possess particular tropes, particular qual-

ity instances, in virtue of which they are perceived as red.

Once properties are interpreted as tropes there is no literal sense in which we can say of

a property that it is shared by distinct physical structures. Describing two objects as shar-ing the same property should be understood as a Wgure of speech, more appropriately

explained as the fact that the objects in case possess exactly similartropes (Martin and Heil

1999).21

As Heil (2003, chap. 13) reminds us, however, trope theorists have often associated their

trope characterization of properties with the thesis that tropes are the building blocks of the

universe and that objects are nothing but bundles of tropes. Heil suggests that if we do not

wish to associate ourselves with this view we might do better by reaYrming the traditional

term mode, and by thinking of properties as modes. The modes terminology has another

advantage, as it directs our attention to the fact that properties are not constitutive parts of

the things in which they inhere but, rather, are constitutive aspects of things; in the familiar

parlance, they are ways things are (Martin 1980; Armstrong 1989), namely, speciWc

qualitative manners, or modes of being, which things exemplify.

I shall have more to say about the modes conception of properties in Sect. 6, since I

believe that understanding properties as modes is pivotal in understanding the categorical

diVerence between things and properties and the futility of the attempt to reduce properties

to a thing-based ontology. Let us turn now to the last and, as I would like to propose, the

most important reason underpinning the extensionalist bias.

5.3 Third Gambit (The Legacy of Mechanism): Reducing Properties to a Basic Set ofExtensional Entities is an Imperative of Good ScientiWc Practice

The most signiWcant single factor behind the prevalence and persistency of radical exten-

sionalism in contemporary philosophical theory can, I believe, be traced directly to the very

metaphysical foundations of modern science. Simply put, the mechanistic outlook of reality

that has emerged with the rise of modern science in the 17th century depicted nature in

almost exclusively extensionalist terms, while denying intensional entities equal footing.

By identifying physical reality with extended matter, it made the bias in favor of an exten-

sionalist ontology, and an extenstionalist semantics, a sine qua non for any scientiWcally

oriented philosophy;22 and while many of the core assumptions of this mechanistic outlookare no longer valid in the present scientiWc context its legacy remains highly inXuential,

extensionalism being only one of its many lasting manifestations. But before we take a

deeper look at the extensionalist foundation of modern science, we must Wrst aYrm the

connection between this metaphysical extensionalism and the semantic extensionalism

with which we began our inquiry, as I suspect that in the current intellectual climate this

connection is far from obvious.

21

Giving up the idea that identical properties might be shared is a potential source of concern insofar as itpresupposes a primitive notion of similarity and deprives us of the ability to explain similarity in terms of the

sharing of universals (I am indebted to Ariel Meirav for turning my attention to this problem.). See Heil (2003,

chap. 14), however, for an argument that no high stakes are involved in the adoption of a primitive notion of

perfect similarity. Be that as it may, I shall not dwell on the issue any further since my intention is not to pro-

vide a systematic argument in favor of trope theory but merely to indicate that there exists a coherent and, in

many respects, attractive alternative to the identiWcation of properties with universals.

22 Notably, Leibnizs philosophical system oVers a rare example of an early alternative to extensionalism.


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As we have seen, the extension of a term (or a concept, or an idea) is the set of things it

picks out, or over which it can be truly predicated. On the semantic conception, then, it is

linguistic and mental entities that have extension, not physical objects per se. Nevertheless,

the links to metaphysical extensionalism cannot be overlooked. Observe, Wrst, that the idea

of a term extending over a class of entities is a metaphorical extension (no pun intended) ofcommonsensical uses of the verb extend, suggesting that the term unfolds, or stretches

out, so as to cover the said entities. Yet, it is from this very same root, extendere, and the

very same idea of being extended, that Descartes notion of spatial extension is also derived

(indeed, it can hardly be a coincidence that the introduction of the semantic notion ofexten-

sion historically coincides with the rise ofextension as a prominent concept in 17th century

physical thought).23 In short, extension in the semantic sense of the term is an apposite

metaphorical extrapolation from extension in the physical, or metaphysical, sense.

Second, extensional entities, those entities that abide by the extensionality principle, are

objectswhether concrete objects (tables, guinea pigs), or abstract objects (numbers,

sets)and this, again, suggests an aYnity to metaphysical extensionalism, i.e., to the doc-

trine that nature,phusis, consists entirely of elementary objects. Now, while it is true that

the objects of semantic, or logical, discourse need not be concrete physical objects it seems

evident that here, again, we have an extension of the idea of an extended physical sub-

stance. This is not the time or place for a meticulous study of how the idea of an abstract

object relates to the idea of a concrete object but it is plain to see that even when our cate-

gory of objects is broadened so as to cover abstract objects we are still dealing with exten-

sional entities, whose identity, like that of the physical objects of Newtonian science but

unlike properties, is determined by their extension.24

Finally, and most signiW

cantly, it can hardly be overemphasized that semantic exten-sionalismpresupposes metaphysical extensionalism. It makes little sense to try to reduce

intensional discourse to extensional discourse unless you believe that extensional entities

are somehow more basic than intensional entities.

In sum, the semantic notion ofextension seems to be rooted in a robustly identiWable

metaphysical background. Overlooking the bond between semantic extensionalism and

metaphysical extensionalism is not only contrived and profoundly ahistorical, but a verita-

ble stumbling block to a sound understanding of the extensionalist bias.

The characterization of physical reality as being essentially extensional can be traced to

the scientiWc revolution of the 17th century, and to the mechanistic conception of the world

to which it gave rise. The most conspicuous expression of this characterization is, ofcourse, due to Descartes. In Descartes dualistic philosophy extension is considered the

essence of material existence, in contrast with cognition, which is the essence of spiritual

existence. Matter in general, res extensa, is a continuum whose only properties are spatial

properties, i.e., the spatial-geometrical dimensions of depth, length, and breadth. It is, in

eVect, a homogenous (hence utterly simple), passive, spatially extended stuV.

The identiWcation of matter with extensive substance has been solidiWed following New-

tons groundbreaking work on the motion of bodies. According to Newton, the material

world consisted ultimately of atoms, namely, of tiny particles considered as the most ele-

mentary building blocks of the universe out of which everything else is composed, and to

23 Both Arnauld and Leibniz, who used extension to refer to a semantic category, were thoroughly familiar

with Descartes notion of matter as res extensa.24 Physical objects are identical when co-extensive (physical sense), and abstract objects, such as sets, are

identical when the objects over which they extend (semantic sense) are co-extensive (in either the physical,

orthe semantic sense).


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which it may be decomposed. Although Newtons conception of matter is, in some impor-

tant respects, quite diVerent from Descartes its implications in terms of the extensionalist

bias are similar, and are no less obvious. As a matter of fact, the diVerence between New-

tons atoms and the extended matter of Descartes is primarily a diVerence of scale. For like

Cartesian extension, the atoms of classical mechanics are homogeneous passive chunks ofmatterin point of fact, they can be thought of as extension reduced to the inWnitesimal

limits of the diVerential calculus.

A skeptic, however, could question the force of my claim that the scientiWc image of the

world bequeathed upon us by the founding fathers of modern science is, indeed, thoroughly

extensional. Recall that, on our account, properties are the quintessential intensional enti-

ties while objects are the paradigmatic extensional entities. It transpires, then, that an exten-

sionally biased ontology is an ontology in which objects are givenpriority over properties.

Yet, the skeptic may argue, it is far from obvious that such a claim can be established vis--

vis the mechanistic worldviews of Galileo, Descartes, Boyle, Newton, and their contempo-

raries. In so arguing, she may point to the fact that some properties, hence some intensional

entities, were absolutely indispensable in either Descartess or Newtons portrayals of the

material world.

Consider Wrst Descartess conception of matter. Even in its most general characteriza-

tion as res extensa, Cartesian matter possesses the geometrical properties of length,

breadth, and depth, and when it comes to particular physical bodies some additional irre-

ducible characteristics (simple natures, in Descartess parlance) must be admitted: impene-

trability, divisibility, Wgure, and, in particular, mobility and Xexibility (the capacity for

conWgurational change due to relative movements of parts). Similarly, Newtons atoms

were predicated with mobility, impenetrability, solidity, and inertia. If such properties wereconsidered indispensable attributes of the most basic material components of the universe,

then what sense can be given to the claim that the mechanistic worldview of the founders of

modern science was disposed towards an ontology of objects, and against an ontology of

properties?

In attempting to answer this question, we must Wrst point to the fact that, taken to its

utmost extreme, extensionalism is simply incoherent: a world which consists of objects

simpliciter is but a phantasm since every object necessarily possess some properties. In the

complete absence of properties, there would be no ground for the diVerentiation of objects

from one another, nor to mutual causal interactions. But although the ideal of a purely

extensional ontology is incoherent when pushed to the limit it may nevertheless be approx-imated to a signiWcant degree. I suggest, then, that we need to think of the extensionalist

bias in relative terms, and that, once we do so, there is solid ground for the claim that the

mechanistic conception of nature presupposed by the founding fathers of modern science

yielded a bias in favor of an overly object-oriented metaphysics. Let us consider now some

of the facts that substantiate the thesis that such a bias was indeed built into the foundations

of modern science.

Note Wrst that, on both the Cartesian and the Newtonian picture, nature is seen as made

out of simple, unorganized objects possessing nothing but a basic set of the most elemen-

tary and indispensable properties, the so-calledprimary qualities

. Note also that the list ofprimary qualities can be divided to two distinct categories. The Wrst category consists of

measurable quanta: for example, geometrical volume, mass, and velocity (in the Newto-

nian sense) are all amounts, or quantities, of matter in motion. The second category consists

of what I shall call underlying qualities. These are qualities, which while not purely quanti-

tative are such that the founding fathers of mechanistic philosophy found them indispens-

able for establishing the coherence and plausibility of the very notion of matter in motion.


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This category includes qualities such as solidity, indestructibility, indivisibility, and iner-

tia.25

In the present context, the class of primary qualities that I identiWed as measurable

quanta deserves some further attention. Consider, Wrst, that not only is it the case that the

mechanistic worldview reduces all qualities to a narrow set of primary qualities but also,that, out of this narrow set, a signiWcant number of qualities are, in fact, quantitiesmagni-

tudes of matter in motion. Interestingly, such magnitudes correspond to what scientists call

extensive magnitudes (see, e.g., Carnap 1966, chap. 7). An extensive magnitude is a mag-

nitude whose value is proportional to the amount of the substance for which it is a measure.

Such a magnitude can be expressed as the additive sum of the separate amounts of the sub-

systems that compose the entire system.26 Thus, for example, Newtonian velocity is an

extensive magnitude in that if bodies A, B, and C move on a straight line in the same direc-

tion, and the velocity of B relative to A is V1, and the velocity of C relative to B is V2, then,

in classical mechanics, the velocity V3 of C relative to A is equal to V1 + V2.

What is worth noticing here is that such magnitudes imply no genuine qualitative nov-

elty: they are merely greater, or lesser extents of matter in motion.27 To put it otherwise,

qualitative novelty, emergence, presupposes non-linearity (Bickhard 2000; Kppers 1992;

Whitehead 1929/1969, p. 41), it does not result from a merely linear summation of micro-

components. Thus, the primary qualities corresponding to extensive magnitudes are more

appropriately thought of as quantitative variabilities of extended matter in its hyolic form

(whatever that may be), rather than as its qualitative modiWers.28 Perhaps this provides for a

partial illumination of what is meant by the frequent, disillusioned, observation that the

mechanistic worldview transformed our image of nature from that of a qualitative realm to

that of a quantitative one (see, e.g, Koyre 1968, pp. 2324).I think that this already gives us a sense of how the ideal of an extensional ontology was

approximated by the mechanistic worldview of the 17th century. On this scientiWc image,

nature is pictured as made out of simple objects, i.e., simple chunks of extended matter.

The only qualities possessed by such elementary objects belong to a narrow set of primary

qualities of which a signiWcant portion of qualities, those that correspond to extensive

magnitudes, are more appropriately conceived as variable quantities of the primitive stuV

out of which elementary objects are made, and the restsolidity, indestructibility, inertia

and so onare minimal qualities without which no coherent, and scientiWcally workable,

sense can be given to the idea of a reality composed of elementary material constituents.

25 Of course, properties such as solidity and impenetrability may come in degrees, hence be measurable, inso-

far as complex bodies (bodies, say, that are made as conWgurations of atoms) may be more or less solid, or

impenetrable. But the point is that the ultimate constituents of nature (e.g., the atoms of Newton, or the cor-

puscles of Boyle) were taken to be solid and impenetrable in an absolute and unvaried sense.

26 Carnap himself is sympathetic to the view that not all extensive magnitudes are additive. For example, rel-

ativistic velocity (in contradistinction with Newtonian velocity) is, on his account, a non-additive extensive

magnitude. However, Carnap also accentuates that (a) the question whether non-additive extensive magni-

tudes are, indeed, extensive is, to a large extent, a matter of convention; (b) that many authors identify exten-

sive magnitudes with additive magnitudes, and that [t]here is no need to criticize such usage (1966, p. 76);

and (c) that, in any case, even on his more liberal approach the vast majority of extensive magnitudes are

additive.27 The point is made by Russell in his discussion of extensive quantities and intensive quantities in On The

Relations of Number and Quantity (1897, pp. 331332). Russell himself attributes this observation to Hegel.28 The essence of this insight was, I believe, captured by Leibniz in asserting that extension expresses nothing

but a simultaneous diVusion or repetition of some particular nature, or what amounts to the same thing, a

multitude of things of this same nature which exist together with some order between them (GP II 269/L536,

quoted in Rutherford 1998, p. 248).


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Yet, the metaphysical picture underlying the rise of modern science can be shown to be

biased in favor of an extensionalist ontology in still another important respect. Such a bias

is manifested in the metaphysical priority given to substances (hence objects) over modes

(hence properties). The gist of this priority can be traced to Aristotles distinction between

substances and accidents. For Aristotle, accidents were things that happen to, and thatdepend upon, an underlying substance without being essential to the existence of that sub-

stance (Met. 1025a14; Top. 102b414). For example Socrates height, or the fact that he

had a snub nose, were thought oVas accidents of the primary substance that is Socrates.

On this picture, then, substances are ontologically fundamental whereas the existence of

accidents is incidental and derivative. Descending to medieval times, the substance-acci-

dent dichotomy was central to scholastic philosophy, providing support, inter alia, to the

doctrine of transubstantiation. Capitalizing on this traditional dichotomy Descartes never-

theless revised it, substituting modes for accidents.29 For Descartes, then, modes were

accidents: while matterres extensapossessed the essential attribute of extension, the

modes, i.e., the qualitative manifold manifested by speciWc bodies, were all accidental.

The presumption that substances are ontologically fundamental is already a reXection of

an extensionalist bias insofar as it suggests the possibility of an independently existent sub-

stance, which, developed to its logical extreme, culminates in the idea of a bare substratum,

to wit, in Lockes infamous unknown something. However, prior to modern times this bias

was eVectively checked by a decisively non-extensional notion of substance. For Aristotle

and the scholastics material substances were in-formedand, hence, richly organized: since

matter was inseparable from substantive form there was never really a room for the view

that, in the Wnal analysis, nature consists of nothing but simple chunks of a homogeneous

extensive stuV

.30

Yet, all this was about to change with the advent of the mechanisticworldview of the 17th century, which purged material substances of their substantive forms

and bequeathed on us the atomistic legacy of an impoverished, unorganized, mattera res

extensawith which nature must ultimately be identiWed if it is to be approached in a sci-

entiWc manner.

In the next section, I argue that an ontological analysis of propertiesthe quintessential

intensional entitiesdemonstrates in unequivocal terms that, insofar as these entities are

understood as concrete modes, or aspects, their reality can be shown to Xy in the face of the

notion of unorganized, homogenous, and passive, elementary material constituents.

6 Why Properties, Understood as Modes, are Categorically Distinct from Objects

Extensionalism is an essentially nominalist position in that it implies the ontological prior-

ity of objects over properties. As we have seen, it is also associated with atomistic reduc-

tionism, namely, with the doctrine that physical reality is ultimately composed of

elementary particles, i.e., of simple, unorganized, independently existent, and inherently

passive, chunks of matter. In what follows, I argue that neither atomism, nor the priority

thesis, are easily reconcilable with a conception of properties as concrete modes.

On the premise that properties are aspects, or concrete modes, it becomes transparentthat they are categorically distinct from objects, from which it follows that it makes little

29 In medieval times the term mode had a variety of diVerent senses none of which corresponded exactly to

the notion of accident.

30 This assertion is, I think, true regardless of the fact that Aristotles conception of substantive forms under-

went some important modiWcations during the Middle-ages (see, e.g., Pasnau 2004).


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sense to attempt to reduce them to the latter, even if such a reduction were technically fea-

sible.31 In addition, it also transpires that the ontology of such modes, or aspects, presup-

poses holistic organization and is, therefore, incompatible with atomism.32 In particular, I

argue that the modes conception of properties implies that the natural systems in which

modes are exempliWed are complexly organized, or to put it more clearly, that such systemsmanifest an intrinsic pattern of organization, an immanentform.

On a modes conception of properties, properties are concrete aspects of things, concrete

qualitative manners, or diVerentiating respects, which things exemplify. Thus, sphericity is

a constitutive aspect of billiard balls, rumination a constitutive aspect of bovines, and so on.

Nominalists, and perhaps more broadly extensionalists, assume that nothing of essence is

lost if we reduce properties to a thing-based ontology. Yet, from the point of view of a

modes conception of properties such reductive attempts seem rather odd.

First, to be an aspect of a concrete thing is not to be another, smaller, thing of which the

former is made. That is, aspects are not constitutive parts of objects; they are not micro-

components from which things are assembled. Sphericity, for example, is not something of

which billiard balls are made, in the sense, say, in which they are made out of molecules.

Rather, spehricity is a way billiard balls are, a mode of being they exemplify (cf. Martin

and Heil 1999).

Second, on a modes conception of properties it becomes clear why properties are inten-

sional entities, viz., why when it comes to properties co-instantiation does not imply iden-

tity. Co-instantiated aspects are complementary dimensions, diVerent faces, of a multi-

faceted whole. Each aspect contributes to the whole in a diVerent way, and is distinguished

in virtue of its unique contribution. Thus, spin angular momentum and orbital angular

momentum are both co-present in planetary bodies; yet, spinning around the center of grav-ity and moving in an orbit are two distinct characteristics of planetary motion, and of what

it takes to be a planet. In short, it is precisely because an object manifests a variety of diVer-

ent faces, causally operative in diVerent ways, that the facesthe aspectsit manifests are

mutually distinguished, co-instantiation notwithstanding.

The fact that to be an aspect of a thing is not to be a thing twice over gives us an alto-

gether good reason for skepticism with regard to the extensionalist enterprise. But a modes

conception of properties also runs counter to the atomism presupposed by extensionalist

reductions.

First, as we have seen, aspects do not come in isolation. Indeed, the fact th

the myth of reductive extensionalism

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