Hume's Problem of Induction: Examining the Justification for Inductive Reasoning

1. Lecture 6 • Mental gymnastics to prepare to tackle Hume • The Problem of Induction as Hume argues for it • His question • His possible solutions • His conclusion • Salmon’s illustration of the problem (By the way, do current evolutionary theory and cognitive science “solve” the problem?) • Anticipating the reading by Carl Hempel

2. Logic puzzles Background: Of the majors that score highest on the LSATs and GREs, Philosophy majors and double majors in Philosophy and a science are consistently in the highest group (or are the highest ranking group) Explanation: the particular emphasis Philosophy places on logical reasoning and arguments.

3. Logic puzzles Guidelines for solving logic puzzles: • Take the information given as if written in stone. • Pay attention to the question asked. • Find the beginning of a thread: one thing you can be sure of; this is enables you to unravel the rest. • In general, proceed from the first piece of information provided to the next… • Assume there is a correct answer and that it can be reached given the information provided.

4. A logic puzzle In a mythical (?) community, politicians always lie and non-politicians always tell the truth. An anthropologist meets 3 natives of the community. She asks the first native if she is a politician. The first native answers. The second native reports that the first native denied being a politician. The third native states that the first native is a politician. How many of these natives are politicians?

5. A logic puzzle Ground rule: politicians always lie and non-politicians always tell the truth. The anthropologist asks the first native “Are you a politician?” Can we know what she answered, without relying on what the 2nd and 3rd natives say? What do we know about the 2nd native given what she said? And does she help us to figure out what the 1st native is?

6. A logic puzzle • What can we know given the third native’s claim about whether • What can we know about the first native or the third is a politician? • Recall the question • Can we answer it?

7. A logic puzzle • Yes. The first native, whether a politician or a non-politician, had to deny being one. We don’t know what she is. • We know that the second native is a non-politician because she reported the truth about what the first native said (and had to say). • If the 3rd native is a politician, the first native is not. If the 3rd native is a non-politician, the first native is a politician. • So there is one and only one politician.

8. Part II Hume on the “Problem of Induction”

9. Inductive reasoning • For empiricists such as Hume, all the evidence there is for empirical knowledge (i.e., knowledge concerning “matters of fact,” including scientific knowledge), is sensory experience. • For Hume, we achieve empirical knowledge by reasoning from individual experiences/singular statements to generalizations/universal statements using induction (and we certainly do this a lot).

10. Inductive reasoning • Empirical generalizations (an argument form or type): • On day D1, at time T1, a black raven was observed. • On day D2, at time T2, another black raven was observed. . . • On day Dn, at time Tn, yet anotherblack raven was observed. + A non-black raven has never been observed. ----------------------------------------------------------------------- All ravens are black

11. For some empiricists – including Hume – the only other (respectable) kind of reasoning is deductive • And it involves what Hume calls “relations of ideas” • The intuition here is that some sentences (such as ‘2 + 2 = 4’) are true by definition (if we know what ‘2’ and ‘4’ mean, as well as what ‘+’ and ‘=‘ mean, then we know the sentence is true) or by form (such as ‘A rose is a rose’). • And if a sentence is the conclusion of an argument that is deductively valid and has all true premises, we know its conclusion is true as well (a sound argument). Mathematical theorems, as derived from axioms, are examples. • Hume calls knowledge arrived at in this way “demonstrative knowledge”

12. Hume’s question • What justifies our use of induction? • Recall that for Hume, there are two places to look for a source of such justification: • Experience • Reason • So he proposes we explore each to see if we can discover what justifies inductive reasoning…

13. Experience? • Millions of ravens have been observed and all are black. • A non-black raven has never been observed. --------------------------------------------------------- • All ravens are black • Empirical generalizations, like other forms of inductive arguments, are ampliative – the conclusion goes beyond the premises. So, the truth of the premises does not guarantee the truth of the conclusion. There is a gap. • Can we not say, though, that “induction has worked in the past and currently works – so it is justified”?

14. Hume’s question Can experience justify our use of induction? Say, we argue: Induction has worked in the past and present to allow us to predict events/phenomena. ------------------------------------------------------------------ So, induction will work in the future to allow us to predict events/phenomena and, thus, is justified. If this reasoning doesn’t justify induction, why doesn’t it?

15. Hume’s question Can reason (demonstrative knowledge) provide the justification? No. Because: There is no necessary connection (as there is in ‘2 + 2= 4) between “I’ve always (and so has everyone else) experienced that X causes Y” and “The next X I encounter will cause Y”

16. Hume’s question Can experience justify our use of induction? Maybe if we add a premise: Say, we argue: Induction has worked in the past and present to allow us to predict events/phenomena. Nature is uniform. -------------------------------------------------------------------------- So, induction will work in the future to allow us to predict events/phenomena. This is a deductively valid argument, so why can’t it solve the problem of induction?

17. Hume’s question But what is the justification for this premise?

18. Hume’s conclusions If it’s not justified, then why do we engage in inductive reasoning? And can we avoid engaging in inductive reasoning if Hume is correct about why we do? His conclusion about induction is a skeptical one: but what is the nature of the skepticism? And what are the implications of the problem of induction (which, though many have claimed to “solve it,” has in fact no solution…) for science?

19. Part III Salmon’s poor physics student

20. Salmon’s physics studentwho is also studying Hume! • So this poor student is learning about some laws of nature , and having them demonstrated to him, in his physics class and labs but also • Learning from his Philosophy Prof and TA that these laws (because they are empirical and they are generalizations) not only can’t be proven but it’s irrational (according to Hume) to believe in them

21. Salmon’s physics studentwho is also studying Hume! • Perhaps predictably, the student assumes that Hume’s arguments date to a time when what he (Hume) calls “secret powers” somehow connecting each event A with an event B were not yet known. So it’s simply a historical piece without current relevance (and so he asks, “Why am I asked to read this at all??) • Is he right? Why or why not?

22. Salmon’s physics studentwho is also studying Hume! • Second hypothesis: Hume’s problem is not any longer a problem because since his time, we have discovered many laws of nature: conservation of energy, conservation of momentum, etc. which allow us to predict (correctly) the outcome of any and all relevant experiments and occurrences. • What does he learn from his professors in each discipline about the status of the laws of nature?

23. The physics student’s professors His philosophy TA: did your physics professor say that the laws of conservation of energy and momentum are, by their nature, inviolable, or that there are no known exceptions? His physics professors to whom he asks “Is it possible that any or all of these laws will stop holding tomorrow or on some future date?” Their answer:

24. Part IV Carl Hempel and Sophisticated Inductivism

25. What do to with/about the problem of induction in accounts of science? • Hempel argues against and offers an alternative to what he calls “narrow” inductivism (others of us call this “naïve” inductivism) • Uses a case study to illustrate what he thinks is a model of scientific reasoning • What lessons does he draw from the case? • And be sure to understand what he means by “narrow” and “sophisticated” inductivism