Abduction and Inference to the Best Explanation

1. Abduction and Inference to the Best Explanation Philosophy department, Shandong University WANG Huaping

2. 3 3 Abduction & IBE 1 3 Cases Task 4 2 Problems Content

3. Basic Types of Inferences: Deduction • Deduction:Derive a conclusion from given axioms (“knowledge”) and facts (“observations”). • Example: All humans are mortal. (axiom) Socrates is a human. (fact/premise) Therefore, Socrates is mortal. (conclusion) • The conclusion can be derived by applying the modus ponens inference rule (Aristotelian logic). • Theorem proving is based on deductive reasoning techniques. WANG Huaping Shandong University Scientific Research Methodology 2011

4. Basic Types of Inferences: Induction • Induction:Derive a general rule (axiom) from background knowledge and observations. • Example: Socrates is a human (background knowledge) Socrates is mortal (observation/ example) Therefore, I hypothesize that all humans are mortal (generalization) • Remarks: • Induction means to infer generalized knowledge from example observations: Induction is the inference mechanism for learning. WANG Huaping Shandong University Scientific Research Methodology 2011

5. Basic Types of Inferences: Abduction • Abduction:From a known axiom (theory) and some observation, derive a premise. • Example: Socrates is mortal (observation) All humans are mortal (theory) Therefore, Socrates must have been a human (explanation) • Remarks: • Abduction is typical for explanation. • If one has the flue, one has moderate fewer. • Patient X has moderate fewer. • Therefore, he has the flue. • Strong relation to causation WANG Huaping Shandong University Scientific Research Methodology 2011

6. Basic Types of Inferences WANG Huaping Shandong University Scientific Research Methodology 2011

7. Basic Types of Inferences: Abduction • Abduction has the structure, if p then q, q therefore p. This is deductively invalid because it is possible for the conclusion to be false when the premises are both true. The fallacy is called affirming the consequent. • Nevertheless, it is hard to see how we could get by without such abductive inference. For example, we infer that it has rained from the fact that the road is wet. This inference is abduction. WANG Huaping Shandong University Scientific Research Methodology 2011

8. Basic Types of Inferences: Abduction • The term “abduction” was coined by Charles Sanders Peirce in his work on the logic of science. • Abduction can be thought of as consisting of three steps. First, identify a phenomenon that requires explanation. Second, generate theories that would explain the phenomenon. Third, choose the theory that best explains the phenomenon. Abduction, then, involves three main elements: the phenomenon to be explained (i.e. the explanandum), the competing theories qua explanations (i.e. the potential explanans), and the principles for ranking theories. WANG Huaping Shandong University Scientific Research Methodology 2011

9. Basic Types of Inferences: Abduction • Explanans: Explanans are theories. A theory explains a phenomenon by showing why it is as it is. A theory can explain why an event occurs, for example, by subsuming it under a law. Accordingly, a physician can explain why Lindsay catches a cold by theorizing that she was exposed to a virus, which yields a high probability of catching a cold. To see that the physician’s theory explains the phenomenon in an intuitive sense of “explain”, note that the theory should satisfy a parent who asks, “Why did my daughter catch a cold?” WANG Huaping Shandong University Scientific Research Methodology 2011

10. Basic Types of Inferences: Abduction • The ranking. As Harman (1965) suggests, several considerations help to determine the ranking of theories, including, among many others, simplicity and comprehensiveness. Such considerations can be thought of as (non-demonstrative) inferential principles. Although the principles require specification, the idea is banal: ceteris paribus a simple explanation beats a complex explanation, a comprehensive explanation beats a narrow explanation, and so on. WANG Huaping Shandong University Scientific Research Methodology 2011

11. Basic Types of Inferences: Abduction • When the underlying principles converge, the abduction is simple, establishing whichever claim the principles support. When the underlying principles diverge, however, they must be balanced. Abduction, then, can be thought of as a two-step process. First, one determines how each principle ranks competing theories. Second, one balances the principles in order to produce a final ranking. WANG Huaping Shandong University Scientific Research Methodology 2011

12. Inference to the Best Explanation What is IBE? • A pattern of inductive inference • General template: • Evidence e is the case. • h best explains e. • Therefore, h is (probably) true.

13. Inference to the Best Explanation • Facts e1, …, enare in need of explanation. • Among the hypotheses h1, …, hm that potentially explain e1, …, en, hiis the “loveliest”, i.e., optimizes the “theoretical virtues.” • So, hiis (probably) true. • Theoretical virtues = consilience, simplicity, analogy, conservatism, consistency, empirical adequacy, …?

14. Inference to the Best Explanation • IBE is supposed to be a rule of inference according to which, where we have a range of competing hypotheses, and all of which are empirically adequate to the phenomena in some domain, we should infer the truth of the hypothesis that gives us the best explanation of those phenomena. Gilbert Harman introduced the term ‘Inference to the best explanation’ in an article of that name in the Philosophical Review in 1965. • We usually use IBE in everyday life. WANG Huaping Shandong University Scientific Research Methodology 2011

15. Inference to the Best Explanation • For example, you ring your friend’s doorbell and there is no answer. The following hypotheses all predict this: (1) Your friend has become paranoid and thinks that enemy agents are ringing the bell. (2) Your friend has suddenly gone deaf. (3) Your friend has been pretending to live there, but in fact lives somewhere else. (4) Your friend is out. • Normally we would infer (4) was correct because it offers a simple explanation of the data that coheres with our other beliefs. WANG Huaping Shandong University Scientific Research Methodology 2011

16. Case 1 • It was discovered that the orbit of Uranus, one of the seven planets known at the time, departed from the orbit as predicted on the basis of Isaac Newton's theory of universal gravitation and the auxiliary assumption that there were no further planets in the solar system. • One possible explanation was, of course, that Newton’s theory is false. Given its great empirical successes for (then) more than two centuries, that did not appear to be a very good explanation. WANG Huaping Shandong University Scientific Research Methodology 2011

17. Case 1 • Two astronomers, John Couch Adams and Urbain Leverrier, instead suggested (independently of each other but almost simultaneously) that there was an eighth, as yet undiscovered planet in the solar system; that, they thought, provided the best explanation of Uranus' deviating orbit. • Not much later, this planet, which is now known as “Neptune”, was discovered. WANG Huaping Shandong University Scientific Research Methodology 2011

18. Case 2 • Ernest Rutherford (1871-1937) • Learned physics in J. J. Thomson’ lab. WANG Huaping Shandong University Scientific Research Methodology 2011

19. Lead collimator Gold foil a particle source q Case 2 • In 1909 Rutherford undertook a series of experiments • He fired aparticles at a very thin sample of gold foil • According to the Thomson model the a particles would only be slightly deflected • Rutherford discovered that they were deflected through large angles and could even be reflected straight back to the source

20. Case 2 beam of alpha particles radioactive substance circular ZnS - coated fluorescent screen gold foil WANG Huaping Shandong University Scientific Research Methodology 2011

21. Rutherford’s Apparatus beam of alpha particles radioactive substance fluorescent screen circular - ZnS coated gold foil WANG Huaping Shandong University Scientific Research Methodology 2011 Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 120

22. Case 2 Speaker gives “click” for each particle Window Particle path Argon atoms WANG Huaping Shandong University Scientific Research Methodology 2011

23. Case 2 Florescent Screen Lead block Polonium Gold Foil WANG Huaping Shandong University Scientific Research Methodology 2011

24. Case 2 • What Expected • The alpha particles to pass through without changing direction (very much) • Because • The positive charges were spread out evenly. Alone they were not enough to stop the alpha particles WANG Huaping Shandong University Scientific Research Methodology 2011

25. What expected… WANG Huaping Shandong University Scientific Research Methodology 2011

26. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Because the mass was evenly distributed in the atom. WANG Huaping Shandong University Scientific Research Methodology 2011

27. What got… WANG Huaping Shandong University Scientific Research Methodology 2011

28. The Predicted Result: Case 2 expected path expected marks on screen Observed Result: mark on screen likely alpha particle path WANG Huaping Shandong University Scientific Research Methodology 2011

29. . . . . . . . . . . . . . . gold foil Case 2 . beam of alpha particles undeflected particles . . deflected particle WANG Huaping Shandong University Scientific Research Methodology 2011

30. Case 2 Rutherford interpreted this result by suggesting that the a particles interacted with very small and heavy particles Particle bounces off of atom? Case A Case B Particle goes through atom? Particle attracts to atom? Case C . Particle path is altered as it passes through atom? Case D WANG Huaping Shandong University Scientific Research Methodology 2011

31. Case 2 observation hypothesis alpha rays don’t diffract ... alpha radiation is a stream of particles alpha rays deflect towards a negatively charged plate and away from a positively charged plate ... alpha particles have a positive charge alpha rays are deflected only slightly by an electric field; a cathode ray passing through the same field is deflected strongly ... alpha particles either have much lower charge or much greater mass than electrons WANG Huaping Shandong University Scientific Research Methodology 2011

32. Alpha particles + + - - + + - + - + - + - - + - Case 2 Nucleus Plum-pudding atom Nuclear atom Thomson’s model Rutherford’s model WANG Huaping Shandong University Scientific Research Methodology 2011

33. Results of foil experiment if plum-pudding had been correct. Electrons scattered throughout positive charges - + + - + + - + - - + + - + - - WANG Huaping Shandong University Scientific Research Methodology 2011

34. Conclusions:Atom is mostly empty spaceNucleus has (+) chargeElectrons float around nucleus Case 2 WANG Huaping Shandong University Scientific Research Methodology 2011

35. - - - - - - - - - - The Rutherford Atom n + WANG Huaping Shandong University Scientific Research Methodology 2011

36. Case 2 This is the modern atom model. Electrons are in constant motion around the nucleus, protons and neutrons jiggle within the nucleus, and quarks jiggle within the protons and neutrons. This picture is quite distorted. If we drew the atom to scale and made protons and neutrons a centimeter in diameter, then the electrons and quarks would be less than the diameter of a hair and the entire atom's diameter would be greater than the length of thirty football fields! 99.999999999999% of an atom's volume is just empty space! WANG Huaping Shandong University Scientific Research Methodology 2011

37. Problems • What is an explanation? • Are consilience, simplicity, and analogy the only theoretical virtues? • Are a theory’s explanatory abilities the most important criteria? • What about prediction and control? • More to come! WANG Huaping Shandong University Scientific Research Methodology 2011

38. Problems • Noncausal explanations: History of science, nonscientific practice have many noncausal explanations. • Bad Lots: Suppose we infer only from the pool of potential explanations that we take seriously. How will we ever know that the best explanation in this pool isn’t the best of a bad lot? WANG Huaping Shandong University Scientific Research Methodology 2011

39. Problems Psychologically impossible: • Potential explanation of e = any causal account of why e happened; true or otherwise • Thus pool of potential explanations of e = h1,…, hm, then m = ∞. • This would it psychologically intractable to infer the best explanation. WANG Huaping Shandong University Scientific Research Methodology 2011

40. Problems Unborn hypotheses • There are many more explanations that we never think of—”unborn hypotheses”—than that we take seriously. • The best explanation is a random member of this much larger class of explanations. • Therefore, the best explanation is very unlikely. WANG Huaping Shandong University Scientific Research Methodology 2011

41. Task Please give an example of abductive inference in every life or scientific research. WANG Huaping Shandong University Scientific Research Methodology 2011