145 philosophy of sciencehempel’s deductive-nomological model of explanation difﬁculties of the...

Hempel’s deductive-nomological model of explanationDifficulties of the D-N model

Van Fraasen’s pragmatic approach to explanationKitcher and unification

Scientific explanation

Christian Wüthrich

http://philosophy.ucsd.edu/faculty/wuthrich/

145 Philosophy of Science

Christian Wüthrich Topic 4



Explanation as purpose of science

some believe that science must deliver explanation of whysomething happens—over and above description of whathappens or prediction of what will happenassume we have a theoryproblem of explanation may not be independent from problem ofevidence (What is it to have evidence to believe in a theory?)explanatory inference: inference from set of data to hypothesisthat would explain datageneral goal: give individually necessary and jointly sufficientconditions which a scientific explanation must satisfylogical empiricism: covering-law model of explanation




The basic ideaSome detailsThe big picture

Hempel and Oppenheim (1948)

Carl G Hempel (1905-1997), my academicgrandfather

explanandum: that which is to be explained

explanans: that which explains

“By the explanandum, we understand thesentence describing the phenomenon to beexplained (not that phenomenon itself); bythe explanans, the class of those sentenceswhich are adduced to account for thephenomenon.” (p. 152)

explain = show how to derive by logicalargument

premises (= explanans), conclusion (=explanandum)





D-N (‘deductive-nomological’) model of explanation

‘nomos’ = (Greek) law

(1) L1, ..., Ln (general laws of nature)(2) C1, ..., Cm (particular facts)

(3) E (explanandum)

⇒ not much difference between explanation and prediction!





Conditions of adequacyAn argument of the form of the H-O scheme qualifies as scientificexplanation if (among others) the following conditions are satisfied:

1 The explanandum follows deductively from the propositions inthe explanans.

2 All propositions of the explanans are true.

3 The explanans contains at least one proposition expressing ageneral law of nature.

4 The explanandum does not follow from the non-nomological (=non-lawful) propositions of the explanans alone.

5 The laws in the explanans are not only true, but also in fact lawsof nature according to our best science.

The first two conditions can be seen as the ‘deductive’ part, andconditions 3 through 5 as the ‘nomological’ part of the explanation.





The role of lawsObviously, laws do important explanatory work—but just what is alaw?

first pass: true generalization

need to distinguish those that are accidentally true from ‘laws’

example of accidental truth: ‘All members of the GreensburySchool Board for 1964 are bald’, ‘All fruits in the garden areapples’

example of law: ‘All gases expand when heated under constantpressure’

Hempel: ‘counterfactual support’ is diagnostic of lawhood, butphilosophically hard to capture

⇒ notion of law has proved ‘highly recalcitrant’ (1965, p. 338)second pass: law = true, exceptionless generalization describingregularity PLUS some additional, yet unspecified conditions





The dispensability of a general analysis of laws

DN-model of explanation does not depend upon our ability toformulate a general account of laws of nature, so long as we canagree which statements qualify as laws

⇒ no criteria, condition, explication of lawhood requiredImportant: that there is a law in the explanans, but not why thestatement at stake is a law

Problem: what to do in less clear cases, such as Mendel’s law ofsegregation, which has exceptions

Note: we are not allowed to infer from our intuition that astatement does explanatory work that it is a law, that would beunjustifiedly circular

Problem: according to some philosophers (e.g. Woodward)many generalizations from special sciences may well doexplanatory work, but not qualify as laws





Hempel 1962: ‘Hierarchy of covering laws’

particular fact [this stone dropped just now falls...]⇓

class of particular phenomena [stones dropped fall towards Earth’scenter]⇓

empirical generalization [Galileo’s law of free fall]⇓

comprehensive theories [Newtonian mechanics]⇓

more comprehensive theories [general relativity]





⇒ increase in breadth and depth of scientific understanding

breadth: new principles cover broader range of phenomena

depth: original empirical laws seen as holding only approximately orwithin certain limits

(Often) causal explanations are deductive-nomological in character,but there are D-N explanations which aren’t causal (e.g. subsumptionof Kepler’s laws under Newtonian mechanics, temporal order may bedifferent)

{Causal explanations} ⊂ {D-N explanations}




The D-N model as unnecessaryThe D-N model as insufficient

Difficulties of the D-N model

The difficulties come in two broad categories:

D-N model is not necessary, i.e. there are sets of statementsthat clearly are explanations but do not qualify as explanationsaccording to the D-N model⇒ conditions are too narrow

D-N model is not sufficient, i.e. there are sets of statements thatqualify as explanations according to the D-N model yet onewould not normally think of them as explanatory⇒ conditionsare too broad





The D-N model as unnecessary

1 probabilistic explanations seem important in medicine, genetics,quantum mechanics, statistical physics... yet D-N model can’taccount for them

2 Michael Scriven (1962): statement ‘The impact of my knee onthe desk caused the tipping over of the inkwell’ should count asexplanatory although it does not involve a law





(1) Probabilistic explanation (I-S model)Probabilistic explanations: not deductively valid argument asdemanded by D-N model

⇒ inductive-statistical explanations (I-S model)

Two features:1 laws of probabilistic-statistical form such as ‘Smoking leads to

lung cancer’2 inference is not deductively valid, only ‘inductive’

I-S model is natural extension of D-N model because of

nomic expectability: a phenomenon is explained if it is shownthat it is to be rationally expected, given the particularcircumstances and the relevant laws

deflationist account of causation: Humean regularity theory ofcausation





(1) Fi (in case i, factors F were realized)(2) p(O, F ) is very high (law of probabilistic form)

(3) Oi (instance i under consideration has outcome of typeO)

Important: (1) and (2) make (3) very likely rather than deductivelycertain (indicated by double line)

likelihood: relation (capable of gradation) between statements—notkinds of occurrences as in the probabilistic law; ‘strength of inductivesupport’, ‘degree of rational credibility’





(2) Self-admitted limitation of D-N model

formulation may be incomplete or elliptic (omit mention of certainlaws or facts), but gaps can readily be filled in

partial explanation: complete grounds for expecting that someevent or other of a certain class will occur, but nothing aboutwhich one exactly

actual explanation are always partial in this respect becauseparticular event has infinitely many different aspects, not all ofwhich can be accounted for by finite set of explanatorystatements

explanation sketch: even more cursory





Scriven’s example reconstructed

(from Woodward, 2003, Section 2.4)

1 “Whenever knees impact tables on which an inkwell sits andfurther conditions K are met (where K specifies that the impactis sufficiently forceful, etc.), the inkwell will tip over. (Referenceto K is necessary since the impact of knees on table withinkwells does not always result in tipping.)

2 “My knee impacted a tables on which an inkwell sits and furtherconditions K are met.

3 “The inkwell tips over.”





The D-N model as insufficient: causationIf explanans and explanandum don’t stand in the relevant causalrelation, insufficiency worries arise:

1 Retrodiction: position of planet today and the laws of celestialmechanics don’t explain the plant’s position yesterday

2 Common cause: the falling barometer and the laws ofmeteorology don’t explain the incoming low-pressure front;neither do the yellow fingers and the ‘laws of medicine’ explainthe lung cancer

3 Asymmetry (Sylvain Bromberger 1966): case of flagpole andshadow

General: Problems concerning causal relations point topossibility that explanation and prediction may not be on a par

Hempel’s reply: if D-N model allows explanations to run in twodirections, both directions must really be OK





The D-N model as insufficient: irrelevance

Irrelevance (Wesley Salmon, 1971):

(1) All males who take birth control pills regularly fail to getpregnant.(2) John Jones is a male who has been taking birth controlpills regularly.

(3) John Jones fails to get pregnant.

These arguments indicate that we may need additional conditions, i.e.that the D-N model only offers necessary, but insufficient conditions.





Recent directions in scientific explanation

1 (van Fraassen) pragmatic account of explanation2 (Kitcher, Friedman) explanation in terms of unification:

explanation is matter of connecting diverse set of facts byconnecting them under a set of basic patterns and principles

3 (Nagel) explanation in terms of reduction: explaining a theoryand the phenomena it addresses by ‘reducing’ it to a morefundamental theory

4 (Salmon) explanation in terms of causation: explaining a naturalphenomenon is to state its (necessary and) sufficient causes

5 pluralism about explanation: all of these important types ofexplanatory relations, and possibly more

6 contextualism with respect to explanation: standards for goodexplanations depends on context, particularly on sci disciplineand on historical period




Contrast classesVan Fraassen’s analysis

Bas van Fraasen’s pragmatic approach to explanationAs defended in his The Scientific Image (‘The pragmatics of explantion’)

QuestionWhy did Marge marry Homer?

Explanatory requests are not ex-hausted by their syntactic and seman-tic expression:

(a) Why did Marge marry Homer?

(b) Why did Marge marry Homer?

(c) Why did Marge marry Homer?

What is shared by the three questionsis their ‘topic’.





The relevance of the relevant constrast class

These different explanatory requests can be thought of as requests tobe told why a particular ‘contrast class’ can be excluded:

(a) ⇒ {Maude marries Homer, Luann marries Homer,..., Margemarries Homer,...}

(b) ⇒ {Marge has a fling with Homer, Marge completely disregardsHomer,..., Marge marries Homer,...}

(c) ⇒ {Marge marries Ned, Marge marries Kirk,..., Marge marriesHomer,...}





Van Fraassen’s analysis of explanationCharacterization (Explanation, van Fraassen style)

An explanation consists of a question and an answer. The question isan ordered triple consisting of a topic Fab, a contrast class{Fab, Fac, Fad , ...}, and a ‘relevance relation’ R:

Q (why is it the case that Fab?) = 〈Fab, {Fab, Fac, Fad , ...}, R〉

where Fab expresses that a and b stand in the binary relation F . Thetopic Fab must be true, and the other possibilities in the contrast class(Fac, Fad,...) didn’t in fact occur. An answer A then “explains Q if, inlight of the background knowledge of the inquirer, there is somerelationship between A and the topic, Fab, and the rest of the contrastclass (Fac, Fad, etc.) which excludes or prevents the occurrence ofthe rest of the contrast class, and assures the occurrence of the topic,Fab... van Fraassen calls this relationship between A and the topicand the contrast class ‘the relevance relation’.” (Rosenberg, 55)






An explanation consists of a question and an answer. The question isan ordered triple consisting of a topic Fab, a contrast class{Fab, Fcb, Fdb, ...}, and a ‘relevance relation’ R:

Q (why is it the case that Fab?) = 〈Fab, {Fab, Fcb, Fdb, ...}, R〉

where Fab expresses that a and b stand in the binary relation F . Thetopic Fab must be true, and the other possibilities in the contrast class(Fcb, Fdb,...) didn’t in fact occur. An answer A then “explains Q if, inlight of the background knowledge of the inquirer, there is somerelationship between A and the topic, Fab, and the rest of the contrastclass (Fcb, Fdb, etc.) which excludes or prevents the occurrence ofthe rest of the contrast class, and assures the occurrence of the topic,Fab... van Fraassen calls this relationship between A and the topicand the contrast class ‘the relevance relation’.” (Rosenberg, 55)






An explanation consists of a question and an answer. The question isan ordered triple consisting of a topic Fab, a contrast class{Fab, Gab, Hab, ...}, and a ‘relevance relation’ R:

Q (why is it the case that Fab?) = 〈Fab, {Fab, Gab, Hab, ...}, R〉

where Fab expresses that a and b stand in the binary relation F . Thetopic Fab must be true, and the other possibilities in the contrast class(Gab, Hab,...) didn’t in fact occur. An answer A then “explains Q if, inlight of the background knowledge of the inquirer, there is somerelationship between A and the topic, Fab, and the rest of the contrastclass (Gab, Hab, etc.) which excludes or prevents the occurrence ofthe rest of the contrast class, and assures the occurrence of the topic,Fab... van Fraassen calls this relationship between A and the topicand the contrast class ‘the relevance relation’.” (Rosenberg, 55)





Some comments

An explanation is scientific just in case “it employs a relevancerelation fixed by the theories and experimental methods thatscientists accept at the time the explanation is offered.” (ibid.,55f)

⇒ This pragmatic approach cannot independently identify what isdistinctive of scientific explanations (vis-à-vis non-scientificones).

On the other hand, it can deal with the counterexamples thatafflict the D-N model, and can mark the distinction between trueexplanations (e.g. using QM to explain why square peg doesn’tfit round hole) and good ones (e.g. using Newtonian physics).




Logical empricism’s unofficial story unveiledSome general remarks and a lesson from historyKitcher’s theory of explanationDealing with objections

Philip Kitcher (*1947)

studied mathematics at Cambridge,philosophy/HPS at Princeton, where heobtained his PhDtaught at Vassar College, U of Vermont,U of Minnesota, UCSD, Columbiaphil of mathematics, general phil sci,phil of biologyrecently: “ethical and politicalconstraints on scientific research, theevolution of altruism and morality, andthe apparent conflict between scienceand religion” (from his website)





Logical empricism’s unofficial story unveiled

Philip Kitcher, ‘Explanatory unification’, Philosophy of Science 48 (1981): 507-531.

Philip Kitcher, ‘Explanatory unification and the causal structure of the world’, reprinted in Balashov andRosenberg (eds.), Philosophy of Science: Contemporary Readings, London and New York (2002), 71-91.

Kitcher makes two claims:1 Hempel’s covering law model of explanation is fraught with

difficulties2 but this is only the ‘official’ view of logical empiricism,

there’s another one: the ‘unofficial’ story involvingunification

evidence for the second claim: next slide

Kitcher takes upon himself the task of developing and defendingthis unofficial story





Hempel: (Hempel 1966, p. 83; cf. also Hempel 1965, pp. 345, 444)

“What scientific explanation, especially theoreticalexplanation, aims at is... an objective kind of insight that isachieved by a systematic unification, by exhibiting thephenomena as manifestations of common, underlyingstructures and processes that conform to specific, testable,basic principles.”

Feigl: (Feigl 1970, p. 12)

“The aim of scientific explanation throughout the ages hasbeen unification, i.e. the comprehending of a maximum offacts and regularities in terms of a minimum of theoreticalconcepts and assumptions.”





Two desiderata for an account of scientific explanation

A theory of explanation should...

1 “show how scientific explanation advances our understanding”(508)

2 “enable us to judge the adequacy of the defense” of embryonictheories “by appeal to their explanatory power” (ibid.)

Kitcher claims that the covering law model satisfies neither of thesedesiderata, unlike his model based on unification.





What is an explanation?

Definition (Explanation à la Kitcher)

“[A]n explantion is an ordered pair consisting of a proposition and anact type. The relevance of arguments to explanation resides in thefact that what makes an ordered pair (p, explaining q) an explanationis that a sentence expressing p bears an appropriate relation to aparticular argument.” (509)

“More colloquially, my project will be that of deciding when anargument explains why its conclusion is true.” (510)

One more remark: Kitcher thinks that history of science showsthat explanatory power of a scientific theory must “involverecognition of a virtue over and beyond considerations ofsimplicity and predictive power.” (512)





The general set-up

set of accepted sentences K

“The general problem... is that of specifying E(K ), theexplanatory store over K , which is the set of argumentsacceptable as the basis for acts of explanation by those whosebeliefs are exactly the members of K .” (512)

Answer given by the ‘unofficial view’: “for each K , E(K ) is the setof arguments which best unifies K .” (ibid.)

⇒ articulate this answer!

start by looking at two historical examples: the Newtonianprogram, the reception of Darwin’s theory of evolution





The Newtonian program of dynamic corpuscularianism

Characterization (Dynamic corpuscularianism)

Newton showed how one can infer the motion of bodies from aknowledge of the forces acting upon them, so many C18 Newtoniansattempted to pursue this idea by postulating inter-atomic forces inorder to explain phenomena they believed arose from the motion ofatoms. “In searching for force laws analogous to the law of universalgravitation, Newton’s successors were trying to generalize the patternof argument presented in Principia, so that one ‘kind of reasoning’would suffice to derive all phenomena of motion.” (514)

program remained popular so long as there was promise ofunification





Kitcher’s lessons

From this historic example and from the reception of Darwin’s theoryof evolution, Kitcher draws three morals:

1 certain programs have been favoured not because of theirpredictive power–which they were yet to actualize–, but becauseof their explanatory promise;

2 the explanatory power of these programs is closely tied tounification;

3 there are particular features of the theories/programs that “aretaken to support their claims to unification.” (512)





Kitcher’s theory of explanation: terminology

general argument pattern: roughly, a schematic argument plus fillinginstructions

stringent argument patterns: roughly, patterns containing somenonlogical terms (constrained by rules of substitution) and exhibitingsimilar logical structure (subject to conditions of similarity)

Goal, as stated before: specify, in a principled way, which set ofarguments E(K ) best unifies or systematizes K

lesson from historic examples: unification is achieved by using similararguments in derivation of many sentences of K

Σ is a set of arguments, Π is a set of argument patterns

Σ is generated by Π if each argument in Σ is an instantiation of someargument in Σ

conclusion set C(Σ) of a set of args Σ: set of sentences which occur asconclusions of some argument in Σ





More terminology and a pictureAmong all the set of argumentpatterns Π of Σ, select the onewith the greatest unifying power(this set is called the basis B forΣ.Among all the bases Bi , selectthe one with the greatestunifying power.If Bk is this basis, thenE(K ) = Σk .On first pass: unifying power ofBi with respect to K variesdirectly with size of C(Σ), variesdirectly with stringency ofpatterns in Bi , varies inverselywith size of Bi





Two corollaries

Corollary (A)

“Let Σ, Σ′ be sets of argument which are acceptable relative to K andwhich meet the following conditions: (i) the basis of Σ′ is as good asthe basis of Σ in terms of the criteria of stringency of patterns, paucityof patterns, presence of core patterns, and so forth. (ii) C(Σ) is aproper subset of C(Σ′). Then Σ 6= E(K ).” (522)

Corollary (B)

“Let Σ, Σ′ be sets of argument which are acceptable relative to K andwhich meet the following conditions: (i) C(Σ) = C(Σ′) (ii) the basis ofΣ′ is a proper subset of the basis of Σ. Then Σ 6= E(K ).” (ibid.)





Reminder: two major problems for the D-N model

1 Asymmetry

2 Irrelevance





(a) Solving Asymmetry

Whoever accepts that the specification of the period (together withlaws about pendula) is explanatory of the length of a pendulum, canbe hit with a dilemma:

1 either two patterns of argument must be adopted because adifferent pattern will be needed in the explanation of the length ofnon-swinging bodies

⇒ violation of Corollary B2 or only one pattern is adopted, but the relevant discourse will be

limited to cases of swinging pendula

⇒ violation of Corollary A

⇒ Either way, the candidate explanation does not live up to thestandards as set by the unificationist account and shouldtherefore not be considered an explanation.





(b) Solving Irrelevance

Whoever accepts that the dissolving of the hexed salt is explained byan appeal to its being hexed, can be hit with a dilemma:

1 either two patterns of argument must be adopted because adifferent one will be needed for unhexed salt

⇒ violation of Corollary B2 or only one pattern is adopted, but the relevant discourse will be

limited to cases of hexed salts

⇒ violation of Corollary A

⇒ Either way, the candidate explanation does not live up to thestandards as set by the unificationist account and shouldtherefore not be considered an explanation.





My challenge to Kitcher

Consider once again the case of John’s failure to get pregnantafter having regularly taken birth control pills.

⇒ If it’s the regular taking of birth control pills that explains John’sfailure to get pregnant, then we can use the same argumentpattern (and it should be considered stringent according toKitcher’s conditions).

⇒ more unified explanatory pattern (same in males and females),in concordance with the demands of Corollary B

It seems as if any explanation for males that would differ fromthe ones offered for females would decrease in unifying power.

Or is this a case of spurious explanation?





Spurious unification

Problem: anything can be derived from it conjoined with Boyle’slaw

Answer: this would be a spurious unification

Definition (Spurious unification)

“If the filling instructions associated with a pattern P could bereplaced by different filling instructions, allowing for the substitution ofa class of expressions of the same syntactic category, to yield patternP ′ and if P ′ would allow the derivations of any sentence, then theunification achieved by P is spurious.” (527f)

idea: genuinely unifying patterns should not be able toaccommodate all conclusions


Hempel's deductive-nomological model of explanationThe basic ideaSome detailsThe big picture

Difficulties of the D-N modelThe D-N model as unnecessaryThe D-N model as insufficient

Van Fraasen's pragmatic approach to explanationContrast classesVan Fraassen's analysis

Kitcher and unificationLogical empricism's unofficial story unveiledSome general remarks and a lesson from historyKitcher's theory of explanationDealing with objections

145 philosophy of sciencehempel’s deductive-nomological model of explanation difﬁculties of the...

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