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L3: Explanations 1 Explanation by subsumption and by specification

SSC: S3 (12-15), S4 (15-18) App 4A/B/C (53-58)

• Explanation by Subsumption– or nomological explanation: – an individual or general fact is subsumed under a

law or theory (and relevant conditions)• Kinds (of relations between premises (explanans) and

conclusion (explanandum)– deductive (DN)– approximative (AN)– probabilistic (PN)

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DN-explanation of an individual fact(1) For all x if Ax then Bx law premise(2) Aa initial condition premise(3) if Aa then Ba from (1) by UI_______________________________________

(4) Ba from (2) and (3) by MP

UI: universal instantiationMP: modus ponensnb: asks for explaining the law

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Ex. Galilei: The law of free fall (LFF)Newton 2: Fp=mp.ap

LawGravitation: Fpq= .mp.mq /(dpq)2

Aux.Hyp no other forcesApplication

ap = mE/(R+h(t))2 , hence

CorrectedLFF: ap is inversely prop. to (R+h(t))2

Aux.Hyp h(t) << R

Approximation

LFF: ap is constant (g)

NB: 2 extra’s: interpretation of g + correcting prediction

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Ex. Ideal gas law

application KTG & AH: elastic collisionsq=2mvw (individuel law)

aggregation AH: statistical hypothesespV=(2/3)N u (collective law)

identificationAH: p P & u (3/2)(R/N)T(transformation) IGL: PV=RT

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Ex: Mendel’s qualitative interbreeding law M0: there are sets of competing factors such that

each individual has one combination of two factorsM1: each descendant gets one factor from each parentAH: only two competing factorsApplication

ff fg ggff ff ff or fg fg

GL: fg ff or fg ff or fg or gg ff or fggg fg fg or gg gg

AH: ffF fg, gf, ggG

Correlation (transformation)

L: FxF F G x G G or F G x F G or F

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(DN/AN) Explanation of laws by theories• Examples: Galilei, ideal gas law, Mendel, Olson• the five-steps-model

– application– aggregation/synthesis– identification– correlation– approximation (AN)

• formal and empirical conditon• with step specific auxiliary hypotheses• as a rule, observational laws!

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Reduction of laws by theories

• ‘Reduction’ if at least one of the steps:

aggregation identification approximation

• Correlation if only: application and correlation

• Discussion about reduction, see L4

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Explanation by Specification• intentional

– actions (and goals) in terms of reasons: – beliefs and desires (DBA-principle)

– only of metaphorical use in natural sciences, esp. biology– has partially generalizable structure

• functional– features in terms of their function, in biology, sociology

and psychology• (specific/abnormal) causal

– events in terms of an abnormal causal factor

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Nomological reconstruction?Ex.: intentional (BDA: belief, desire, action)• to be explained:

– person P performs action A (opening the window)

• premises:– P desires goal G (cooling the room)

– P believes that A is needed for G– LAW: for all P, A, and G holds:

if P desires G and believes that A is needed for G then P performs A

• conclusion: P performs A

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Objections• no clear link with research practice• no role for ‘specific intentional statements’• extreme belief premise• the LAW seems irrelevant• symmetry explanation/ prediction

Von Wright’s alternative: ‘LAW’ is meaning postulate– last two objections disappear– new objection: magical meaning postulate

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Minimal alternative: intentional• Specific intentional statement:

– P performs action A with the intention of approaching goal G• MAIN KEY (first approximation):

– P performs A with the following reasons:– P desires goal G– P believes A to be useful to approach G

• Unspecific intentional statement:– P performs A intentionally

• Corresponding Key: – there is a such that P performs A with the intention of

approaching goal

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Thought process in terms of questions and answers

1) verified fact: P performs A!2) why-question?3) unspecific hypothesis: intentional?4) specific hypothesis: goal G?5) test implications

– falsification, back to 3)– verification, hence, why-answer: goal G!

6) side step conclusion: intentional!7) subsequent questions

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remarks

• process/ product: main product + by-product

• step 6: existential generalization

• objections disappear

• functional/causal– analogous, but with very different keys

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Minimal alternative: functionalex: fanning movement of sticklebacks

• to be explained: species S has trait T• specific functional statement:

– S has T because of the functional consequence C• MAIN KEY (first approximation):

– S has T– T of S is a ‘positive causal factor’ for C– C is a positive causal factor for ‘reproduction and

survival’ of S

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continued

• Unspecific functional statement:– T of S is functional

• Key:– there is a such that S has T because of the

functional consequence

• Thought process analogous to intentional

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Functional thought process

1) verified fact: S has trait T!2) why-question?3) unspecific hypothesis: functional?4) specific hypothesis: functional consequence C?5) test implications

– falsification, back to 3)– verification, hence, why-answer: functional consequence C!

6) side step conclusion: functional!7) subsequent questions

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Minimal alternative: (specific/abnormal) causal

• to be explained: event E occurs in system S• specific causal statement:

– E occurs in S due to specific cause C• MAIN KEY (first approximation)

– E occurs in S– C occurs in S as an abnormal factor– there are normal factors F1….Fn in S such that

(causal law:) if C and F1…..Fn in S then E

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continued

• Unspecific causal statement– E occurs in S due to a specific cause

• Key:– there is a such that E occurs in S due to specific

cause

• Thought process analogous to intentional/functional• Note: only causal specification is kind of subsumption

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Heuristic-methodological principles

• INTENTIONAL– actions are intentionally performed

• FUNCTIONAL– traits of species are functional

• CAUSAL(specific/abnormal)– abnormal events have a specific/abnormal cause

• HM-principles are no law-claims but search principles or default rules

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Causal effectiveness: extra components in the main keys

• Intentional: belief & desire causally effective for action (reasons as causes)

• Functional: 2 cases: the functional consequence and reproduction & survival were evolutionary effective, resp. effective for the retention of the trait

• Causal (specific): the abnormal factor was causally (co-)effective for the event

• Difficult to assess -> (also) default rules

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Varieties of causal explanation

• Causal explanation of events and laws: – by causal specification, which is a kind of:

– DN-/AN-explanation based on a causal law• Causal explanation of actions and goals

– reasons (beliefs and desires) as causes

• Causal explication of functional explanation• Functional explication of intentional explanation

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Styles of Description and Explanation

• Explanation by I/F/C-specification I/F/C-description esp. -classification

• hence : styles of description and explanation– the intentional style– the functional style– the causal or, broader, structural style

• by subsumption under causal laws, e.g. causal specification • by subsumption under other laws/theories

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Choice and number of styles

• Styles are compatible• Choice slogans

– explanation by subsumption, though always possible, not always interesting

– explanation by specification, though not always possible, always interesting when possible

• Question: are there ‘clear and distinct’ subtypes between intentional and functional specification, e.g. in terms of unconscious motives or cultural functions, or is it a continuum?