Background Hempel s Models of Scientific Explanation 1. Two quick distinctions. 2. Laws. a) Explanations of particular events vs. explanation of general laws. b) Deductive vs. statistical explanations. Deterministic laws. i) General Statements: (x)(px Qx). ii) Universal: all time and space iii) Necessary: not just accidental regularities Statistical laws. P(Q / P) = r
Introduction to Hempel s models Core thesis: Explanations are arguments that the explanandum was to be expected. (p. 685) Formal models: idealizations or rational reconstructions of scientific explanation. Studies in the Logic of Explanation (1948): deterministic explanations (D-N model) Aspects of Scientific Explanation (1962): (probabilistic) explanation (I-S model) statistical Dominated philosophy of science for 20+ years Common features of all models: 1. Arguments: an explanation is an argument from explanans to explanandum. 2. Covering law: an essential part of explanans. 3. Empirical content: explanans must make reference to empirically testable conditions. Classification: Law Explanandum UNIVERSAL STATISTICAL Particular D-N (eclipse) I-S (penicillin recovery) General D-N (Kepler s laws) D-S (Isotope half-life) 2
Particular D-N Explanations (1) Deductively valid argument from explanans to explanandum. (2) General law: explanans makes essential reference to at least one general law. (3) Empirical content: Explanans statements must be verifiable. (4) True: Sentences of the explanans must be true. Formal statement: L 1, L 2, L 3,, L r C 1, C 2,, C k Therefore, E General laws Particular facts Explanandum Example: Dewey s soap bubbles explained by particular conditions and gas laws. Motivating the model: 1. Validity and truth provide expectability. 2. Covering law: breadth and depth of understanding (p. 687) 3. Testability: hallmark of science 4. Truth: without this, we have only a potential explanation. 3
Objections to D-N model 1. Laws 1. No law is needed. Example: Ink stain on carpet Hempel s response: incomplete explanation - elliptical - partial - explanation sketches 2. No clear concept of general laws. Hempel s response: not my problem 2. Causality 1) Asymmetries. Example: Shadow and flagpole 2) Irrelevance. Example: Hexed salt Example: Birth control pills to prevent male pregnancy 3) Mere correlation Example: falling barometer / storm Hempel s response: some explanations are NOT causal. Summary: Necessity and sufficiency Necessity Thesis: each of (1) - (4) is necessary for a good explanation. Main challenge: inkstain examples. Sufficiency Thesis: (1)-(4) are jointly sufficient for a good explanation. Main challenge: asymmetry, irrelevance, mere correlation. 4
D-N Explanation of General Laws Same as particular D-N explanation, except explanandum is a law. Example: Derivation of Kepler s laws from Newton s laws Conjunction problem: Let K = Kepler s laws Let B = Boyle s law Then K can be derived from K B, but this should not count as explanation! Diagnosis: Explanation should be derivation from a true generalization that unifies different areas of science, not a trivial deduction. Kitcher: a theory is explanatory if it is more unified than its rivals. 5
Inductive-Statistical (I-S) Explanation 1. Statistical/ probabilistic laws p(g / F) = r [Hempel: p(g, F) = r] 2. Formal (I-S) model for statistical explanation of particular events p(g/f) = r (where r is close to 1) Fa Ga NOT: a deductive argument concluding that Ga is practically certain Ex: 3. D-S explanation P(R / T S) is high Tj Sj Rj with high probability P(G(n) / F) = f(n) n = k P(G(k) / F) = f(k) 6
1. Modal version (p. 707) fails Analysis of I-S explanations Probabilistic claims are always relational 2. Expectability criterion. Issue: Must explanations be contrastive (show that the explanandum was to be expected rather than some other event)? Objection: Too restrictive: we do explain low-probability events. 3. Difficulties (a) Same problems as for D-N: asymmetries, irrelevance, mere correlation. (b) Statistical explanation of individual events. 4. Ambiguity of I-S explanation. p(g / F) = r (a high value) Fj Gj [r] p( G / F H) = s (a high value) Fa Ha Ga The existence of such pairs of explanations is what Hempel called the problem of epistemic ambiguity. 7
Hempel s solution: Requirement of Maximal Specificity (RMS): If our background knowledge k and premises imply that a belongs to F 1 a subset of F, then this knowledge must also imply a statistical law of form p(g, F 1 ) = r 1, and r 1 = r unless the statement cited is a theorem of probability. Problem: Statistical explanation remains essentially relativized to given knowledge: reference to given knowledge is unavoidable. 8
Explanation/Prediction Symmetry Explanation and prediction are structurally identical. Sub-thesis (A): Every explanation is a potential prediction Sub-thesis (B): Every adequate prediction is potentially an explanation. 1. Sub-thesis (A) Expectability intuition (696): Any rational acceptable answer to the question Why did event X occur? must offer information which shows that X was to be expected, either definitely or with reasonable (high) probability. General Objection: pre-supposes determinism? Specific Objections: 1. Syphilis/paresis example. 2. Explanations in evolutionary biology. 3. Self-evidencing explanations. Hempel s conclusion: sub-thesis (A) is correct. 2. Sub-thesis (B) Ex: Koplik spots/measles Hempel s conclusion: sub-thesis (B) is probably false. 9
Two questions about statistical explanations (Salmon, ch. 4) (1) (Epistemic vs. Ontic) If there are statistical explanations of particular events, why require high probability (= expectability)? a) Arguments in favour of requiring high probability. #1. If a set of facts explains E, those same facts cannot explain the non-occurrence of E. Example: E = death of a weed sprayed with weedkiller [The explanation for E cannot also function as an explanation for the survival of a sprayed weed.] Explanations must be contrastive. #2. If a set of facts explains E, then it is not possible that some other facts would explain the non-occurrence of E. High probability and RMS ensure adherence to #2. b) Arguments against requiring high probability. 1. Pea blossoms: ¾ red, ¼ white; genetic explanation. We understand the white outcome just as well as red so why do we have explanation only if it s red? In general: we understand the improbable outcome exactly as well as the probable one. 2. Electron tunnelling: 0.9 chance of reflection, 0.1 of tunnelling through the barrier. By hypothesis, there is no explanation for why one outcome happens rather than the other. So why do we have explanation only for reflection? 10
(2) (Modal vs. Epistemic/Ontic) Can there be any statistical explanations of particular events? a) Arguments in favour of the modal position ( NO ). OR #1. If under circumstances C, an event of type E sometimes occurs and sometimes not, then C cannot be an adequate explanation for the occurrence of the event of type E. #2. If under circumstances C it is possible for E to fail to occur, then C cannot be an adequate explanation for occurrence of E. Suppose Pr(E / C) = 98%, Pr(~E / C) = 2%. We can t explain E in cases where ~E. But the explanation for E is the same (namely, C). C sometimes explains E, sometimes ~E: violates #1! #3. There are no I-S explanations, but there are D-S explanations of statistical regularities. b) Arguments against the modal position. #1. Large Population argument. Observed frequencies are still particular outcomes. Surely they are explainable! #2. Scientific practice. Scientists want to explain anomalous particular outcomes. (Ex: electron scattering) #3. Applied science. Airplane crashes, individual illnesses, etc. all require individual statistical explanation. 11