Phil6334 day#4slidesfeb13

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Mayo slides on Induction, Problem of Induction & some notes on Popper & Problem of Induction.

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Phil6334 day#4slidesfeb13

  1. 1. Traditional Problem of Induction Induction (by enumeration): Infer from past cases where a law or generalization held to future cases. or Induction: (by enumeration): Infer from all (or most) A's have been B's in the past to all (or most) A's will be B's in the future. (A law may be seen to assert a generalization: e.g., all A's are B's — in the past, present and future.) (e.g., Tomatoes have been nourishing in the past, law of gravity has held in the past) How to justify (scientific) induction? A justification takes the form of an argument: ________________________________________ _____________________________________ Conclusion: The inductive method is reliable (it will work in the future): inferring from past to future success is a reliable method. What will the premises be? 1
  2. 2. a. Use an inductive argument to justify induction: Premise: The inductive method has worked, has been reliable, in the past. ______________________________________ Conclusion: The inductive method is reliable (it will work in the future), i.e., inferring from past cases to future cases is a reliable method. Problem: circular. (It uses the method in need of justification to justify that method.) 2
  3. 3. b. Use a deductive argument to justify induction: Premise: If a method has worked (been reliable) in the past, then it will work in the future. Premise: The inductive method has worked, has been reliable, in the past. ______________________________________ Conclusion: the inductive method is reliable (it will work in the future), i.e., inferring from past cases to future cases is a reliable method. Problem: not a sound argument. In order to infer the truth of the conclusion of a deductively valid argument, the premises must be true, i.e., the argument must be sound. But one cannot know the first premise of this argument is true, unless one already knew the very thing which the argument was supposed to justify! Alternatively put in terms of assuming the uniformity of nature Attempts to dissolve the problem It’s asking for justification beyond where it’s appropriate, (i) It’s converting induction to deduction (i.e., it’s asking for a certainly true conclusion from true premises) (ii) That’s just what we mean by rational For (ii), consider my friend the crystalgazer… 3
  4. 4. Counterinductive method: Infer from All A's have been B's in the past to the next A will not be a B. In terms of a method: Infer from the fact that a method M has worked well (been reliable) in the past that M will work poorly in the future. or Infer from the fact that a method M has worked poorly (been unreliable) in the past that M will work well in the future. (The crystal gazer) If a method M has worked poorly (been unreliable) in the past then M will work well in the future. M has worked poorly (been unreliable) in the past Therefore, M will work well in the future. So, unless we allow this justification of counterinduction, we should not allow the following justification of (scientific) induction: If a method M (induction) has worked well in the past then M (induction) will work well in the future. M (induction) has worked well in the past. Therefore, M will work well in the future. 4
  5. 5. You might say, you just can’t argue with someone who accepts counterinduction as rational. It’s like someone who would not accept any argument, thereby rejecting machinery necessary for fruitful discussion. You can’t convince them that induction is superior to counterinduction, but all we care about is showing it’s rational for us to accept scientific induction Leads to the program of building a rational inductive logic: (a) A system of inductive logic is rationally justified if it captures inductive rules of science and common sense that we take as a standard of rationality. (b) A stronger possibility under this umbrella would be to show scientific inductive logic is better suited for accomplishing its goals than any other. This was the hope at least into the 80s and even now in some circles. This was called the New Problem of Induction (confirmation theory, formal epistemology—a bit more general). Every fairly obvious rule winds up with everything confirming everything. 5
  6. 6. Instance confirmation Probabilistic confirmation An instance of All A’s ‘are B’s is an example of an A that is a B. All ravens are black. For all x, if Rx then Bx. Also plausible, if S = S’, then anything that confirms S confirms S’. All ravens are black = All non-black things are non-ravens. So a white shoe confirms all ravens are black. (Armchair ornithology) This was the kind of problem that leads to requiring severity, or something like it. It’s too easy to get confirmations even if the generalization is false. 6
  7. 7. Mayo: Brief Popper Notes Demarcation Criterion: Popper’s problem is how does one determine (demarcate) a scientific theory from a non- or pseudo-scientific theory? This is the problem of Demarcation. The common answer was based on science having a unique “empirical method”. This was essentially inductive proceeding from observation or experiment to theory. But Popper wants to distinguish between empirical methods that are scientific from those that are not, and methods may appeal to observation and experiment (e.g., astrology) but fail to come up to scientific standards. The theories that got him involved: Marx’s theory of history, Freud and Adler’s theories of psychology, and Einstein’s theory of General Relativity. His friends were impressed with these theories’ “explanatory power”: once your eyes were opened, they seemed to explain everything, studying them caused one to undergo a psychological conversion. He presented Adler with a case that seemed to go against Adler’s theory, but Adler explained it even though he had never met the child! Popper asked him how he could be so sure, Adler replies, “Due to my thousand fold experience.” Popper thought to himself (or said aloud), and now the experience is thousand and one fold! 7
  8. 8. The upshot is that all Adler’s observations were interpreted in light of his theory. In fact, one can use the theory to explain human actions that are exactly opposite, e.g., (a) a man drowns a child, (b) a man sacrifices his life to save a drowning child. Both may be explained using the resources of either theory (e.g., inferiority complex or Oedipal complex.) Freud: In case (a), Freud might say the man suffered from repression, while in (b) man had achieved sublimation. Adler: In case (a), the person suffered from an inferiority complex, needs to show he can commit a crime; in (b), the behavior is due to an inferiority complex, as the need to show that he died to rescue the child. There was no behavior that couldn’t be interpreted in terms of either theory. In contrast, Einstein’s theory was impressive because it had a risky prediction: if the predicted light deflection effect was observed to be absent, the theory would be refuted. 8
  9. 9. Popper concluded (36): 1. It is easy to obtain confirmations, if we look for them. 2. Confirmations should only count if they are the result of risky predictions, if without the theory, we should have expected an event incompatible with the theory. 3. Every good theory is a prohibition, the more it forbids, the better it is. 4. A theory that is not refutable by any conceivable event is not scientific. Irrefutability is not a virtue. 5. Every genuine test of a theory is an attempt to falsify it or refute it. There are degrees of testability. 6. Confirming evidence should not count except when it is the result of a genuine test of the theory—it must be able to be presented as a serious but unsuccessful attempt to falsify it (corroborating evidence). 7. Some testable theories when found false are upheld by their admirers, e.g., by introducing ad hoc some auxiliary assumptions or reinterpreting it ad hoc so that it escapes refutation. The price paid is to destroy or lower the scientific status of the theory. #6 (weakest form): An accordance between data* and theory or hypothesis H does not count as evidence for H if such a "passing result" is guaranteed (or practically guaranteed), even if H is false. *Data x does not falsify H, x fits H, H passes the test, etc. Why? The upshot is “The criterion of the scientific status of a theory is its FALSIFIABILITY.” 9
  10. 10. (Note Popper is not talking about meaningfulness, only that unfalsifiable theories are unscientific.) But #2, and #6 are stronger…..they include a positive side….how can Popper argue for them? Before pondering this….let's look at the big picture of how Popper claims to deal with Hume… Side note: Popper always puts the weight on the theory to be scientific and testable; whereas, I think he should put it on the method or test. 10
  11. 11. Popper’s attitude toward Hume’s Problem of Induction: Hume was right. We can’t infer from Constant Conjunction to the next case—we get an infinite regress when we try to justify induction by appeal to experience. (See induction handout.) Popper criticizes Hume on psychological (e.g., the puppies) and logical grounds, p 43-44. His logical criticism of Hume: *Hume’s theory is that of repetition based on similarity. * All we really have is repetition-for-us based on similarity-forus, we must respond to situations as if they were equivalent, take them as similar, and interpret them as repetitions. *Repetition can never be perfect, they are only similar, so they are repetitions only form a certain point of view * That means there must always be a point of view, a system of expectations, anticipation, and interests BEFORE there can be repetition. We can’t explain recognizing cases as similar as due to earlier repetitions because these earlier ones must also have been recognized as repetitions. 11
  12. 12. Two Options or Stances Given Hume’s Problem: p. 45 1. We obtain knowledge non-inductively. 2. We obtain knowledge by induction and thus by a logically invalid and rationally unjustifiable procedure. Hume chooses option 2 and concludes that knowledge is just belief based on habit. Popper wants to take the first option instead, top p. 46. Instead of explaining our propensity to expect regularities as the result of repetition, Popper proposes to explain repetition for us as the result of our propensity to expect regularities and to search for them. We actively try to impose regularities upon the world: Theory of trial and error, of conjectures and refutations. (p.46—the idea that science proceeds from observation to theory is so widely held that many thought Popper was crazy to deny it. But as he says, one cannot “simply observe”.) p. 51 Hume said our beliefs in regularities are irrational—he’s right if he means we can’t prove them true or probable; however, if belief includes our critical acceptance of scientific theories, a tentative acceptance combined with an eagerness to revise the theory if we design a test it cannot pass, then (according to Popper) Hume was wrong, there’s nothing irrational in accepting such a theory, in preferring it or in relying on it for practical purposes. Why? (assumed premise) 12
  13. 13. Because no more rational course of action is open to us. p. 51 “Assume we have made it our task to live in this unknown world of ours; …” nothing "safer" than accepting the "best tested" theory. (Question: is this convincing? What’s so good about a hypothesis that has passed a severe test, as Popper defines it? How can Popper even know a test is severe given especially that he thinks there are always infinitely many hypotheses?) Another way Popperians like to put this (Popper's way of avoiding the problem of induction): Although the truth or approximate truth of H is unjustifiable, it may be rational to (tentatively) accept H. "One should be careful not to confuse the problem of the reasonableness of the scientific procedure and the (tentative) acceptance of the result of this procedure, i.e., the theory or hypothesis—with the problem of the rationality…of the belief that this procedure will succeed." According to Popper: Although it is not reasonable to believe that the method of conjecture and refutation will succeed, or is likely to succeed (i.e., that it is reliable), the method of conjecture and refutation is nevertheless, a reasonable procedure. Again, why? 13
  14. 14. No better than the amoeba p. 52: the critical attitude may be described as the conscious attempt to make our theories, our conjectures, suffer in our stead in the struggle for the survival of the fittest…a more dogmatic attitude would eliminate theories by eliminating us. Summary of Popper’s conclusions: p. 53-4 Since the problem of induction is viewed by Popper as a facet of the problem of demarcation, the solution to the latter must provide a solution to the former. Because of the problem of induction a, b, c seem to clash— some give up on empiricism, but Popper says there is no clash if accepting a law or theory is only tentative. We can preserve the principle of empiricism: the fate of a theory is decided by observation and experiment, by the result of tests. So long as a theory stands up to the severest tests we can design, it is accepted if it does not, it is rejected; but it is never inferred from the evidence, only the falsity of the theory can be inferred, and this inference is purely deductive. (Question: Is it? To infer the conclusion one needs true premises and determining truth demands other inductive reasonings, not mere deduction.) 14
  15. 15. Conjectures and refutations includes falsification (in case of a failed prediction, although even Popper notes that we shouldn’t give up the hypothesis too easily, a bit of dogmatism may be good), and corroboration (tentatively accepting a hypothesis or theory that has passed a stringent test). Critical rationalists: We may justify the rationality of accepting, or preferring, or believing the “best tested” theory T, without justifying T itself (as true, probably true) Probabilism: Justifying claim H is showing it is true or probable. Popper rejects probabilism. The Popperian suggestion is that it’s a matter of showing it grew out of a rational method—(you couldn’t say it was a reliable method, but at most that the method had stood up to testing). 15
  16. 16. Falsifiability is both too strong and too weak. Too weak because H being logically falsifiable hardly means you’ve done a good job probing its errors. Too strong in that most interesting scientific theories aren’t logically falsifiable: -There are background assumptions and theories required to arrive at any prediction (Duhem’s problem). -Most testable predictions are statistical. Popper: Neyman-Pearson Fisher statistics Carnap: Bayesian statistics Popper knew all this, that doesn’t mean they weren’t problems. I have been reading the older Popper in writing my current book, and there he explicitly refers to Fisherian rules of rejection for statistical claims (buried in Popper’s LSD). Want to be able to say: Pr(d(x) > observed; H is false)= very low For d some difference between x and what is expected were H true. Essentially a p-value or statistical significance level 16
  17. 17. What about corroboration? Popper sets out those “confirmation measures” alongside Carnap. But he declares that none of them measures corroboration unless they may be seen as the result of severe testing Doubts that severity can be formalized any more than the rule of “total relevant evidence” among inductivists (i.e., probabilists) Popper in a letter to me: I regret not having learned statistics In looking to statistics to solve induction, Bayes theory philosophers generally looked to a Bayesian confirmation theory (logic or subjective) We saw last time: If H entails x, P(x |H) > P(x). So x “confirms” H to a degree (non-subjectivists embrace the Bayes-boost view, rather than a high posterior). Chapter 4 of EGEK, Wesley Salmon’s approach: P(H|x)/P(J| x) = P(H)/P(J) In the case where H entails x and J entails x [P(x |H)P(H)]/P(x) [P(x |J)P(J)]/P(x) and since P(x |H) = P(x |J) = 1 P(H| x)/P(J| x) = P(H)/P(J) 17
  18. 18. Along with any background needed to get the entailments Unfortunately, H and J are not exhaustive. Salmon (a Reichenbach student) rejected subjective accounts. They were reluctant to appeal to statistical methods because of their empirical assumptions. Salmon changed his mind once I showed him simple tests of assumptions. 18

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