Explanation by Subsumption or nomological explanation:

1. L3: Explanations 1 Explanation by subsumption and by specificationSSC: 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)

2. 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 instantiation MP: modus ponens nb: asks for explaining the law

3. Ex. Galilei: The law of free fall (LFF) Newton 2: Fp=mp.ap LawGravitation: Fpq= .mp.mq /(dpq)2 Aux.Hyp no other forces Application 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

4. Ex. Ideal gas law applicationKTG & AH: elastic collisions q=2mvw (individuel law) aggregationAH: statistical hypotheses pV=(2/3)N u (collective law) identificationAH: p P & u (3/2)(R/N)T (transformation) IGL: PV=RT

5. Ex: Mendel’s qualitative interbreeding law M0: there are sets of competing factors such that each individual has one combination of two factors M1: each descendant gets one factor from each parent AH: only two competing factors Application fffggg ffffff or fgfg GL: fgff or fgff or fg or ggff or fg ggfgfg or gggg AH: ffF fg, gf, ggG Correlation (transformation) L: FxF  FG x G  G or FG x F  G or F

6. (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!

7. 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

8. 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

9. 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

10. 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

11. 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 

12. 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

13. remarks • process/ product: main product + by-product • step 6: existential generalization • objections disappear • functional/causal • analogous, but with very different keys

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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?