The Problem of Induction

1. The Problem of Induction Reading: ‘The Problem of Induction’ by W. Salmon

2. Hume’s dilemma • Horn 1: There can be no inductive justification of induction (e.g. via (PUN)) because such justifications presuppose that some inductions are justified. • Horn 2: There can be no deductive justification of induction because deductive inferences are non-ampliative, but inductive inferences are ampliative.

3. Solutions? • Solution 1—the “success of science” solution: The reason we are justified in using inductive methods is that they work. Science, which utilizes such methods, has been massively successful in predicting the course of the future and providing us with an understanding of the natural world. To doubt its methodology is ridiculously irrational.

4. Solutions? • The problem with solution 1: It appears to be another instance of the inductive justification of induction, which, as we have seen, is circular.

5. Solutions? • Premise: Observed cases of the application of the scientific method have yielded successful predictions. • Conclusion: Unobserved cases of the application of the scientific method will yield successful predictions. • The argument is clearly another inductive, ampliative inference: precisely the sort whose justification is in question.

6. Solutions? • The success of science solution and the crystal gazer. • Ah ha! The crystal ball reveals that crystal gazing will yield predictive success in the future! • The proponent of the success of science solution is behaving exactly as the crystal gazer is. • Using her method in the justification of that method.

7. Solutions? • A possible reply to the circularity objection to inductive justifications of induction: • A circular argument assumes its conclusion as a premise. • “God exists because it says so in the bible and the bible is the word of God.”—circular.

8. Solutions? • Hume asks me to show: Induction is justified. • I then argue that nature is uniform or that the success of past inductions supports the hypothesis that induction will be successful in the future. • In neither case do I assume as a premise that induction is justified in order to argue that it is. Instead I use an inductive pattern in support of the claim that such patterns are sometimes justified.

9. Solutions? • So in order for the charge of circularity to stick, it must be that one can never use a certain rule or pattern of inference in justifying that very rule or pattern. There can be no “self-supporting” rules. • Does the skeptic have an argument for this? • But what about the analogy with the crystal gazer? • If crystal gazing had the track record that science does, would the analogy be as effective-seeming?

10. Solutions? • Solution 2: the complexity of science solution: Scientific inference is vastly more complicated than the examples involving simple enumerative induction suggest. • The sun will rise tomorrow. • Scientists understand the functioning of the solar system in terms of the laws of physics. Predictions about astronomical events are derived from these laws and statements of initial or standing conditions.

11. Solutions? • Laws and theories are general statements (All Fs are Gs), but they are rarely simple generalizations from experience. • Newton’s gravitational theory: Bodies attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. • The law is not established by observing instances—by enumerative induction.

12. Solutions? • Instead, it is accepted as a hypothesis/conjecture and then subjected to testing. • The hypothesis deductively entails certain consequences (the behavior, e.g., of the planets, the tides, falling bodies, the pendulum, etc.)—the more of these, and the more diverse they are, the better. • If any of the consequences are false the theory is rejected (here again the method is deductive).

13. Solutions? • If a consequence is true then the hypothesis acquires some degree of confirmation—lots of true consequences = high confirmation and acceptance. • As for the formulation of the hypothesis itself, that is not a deductive procedure, nor is it an inductive one; it’s a nonlogical procedure involving the ingenuity of the scientist. • This picture of the functioning of science = “the hypothetico-deductive method”.

14. The hypothetico-deductive method (HDM) P1 H P2 P3 Any P false, reject H. Any P true, H is confirmed.

15. 3 Problems with HDM • 1. Hypothesis formulation is not simply a matter of ingenuity. Some observational evidence is used in the initial construction of the hypothesis. The connection between this evidence and the hypothesis is ampliative/inductive.

16. 3 Problems with HDM • 2. True consequences of a theory are said by HDM to confirm it. Lots of true consequences = acceptability. But this inference from the true consequences of the theory to the (acceptability of the) theory itself is inductive/ampliative. The predictions of a theory are, at once, both deductive consequences of the theory and, if true, inductive evidence for it.

17. 3 Problems with HDM • 3. The general problem: If there really are no ampliative inferences used in the scientific method, then science can’t take us from what we know about observed matters of fact to knowledge of unobserved matters of fact.

18. The scientific method O1 P1 H P2 O2 P3 O3

19. Solutions? • Solution 3: The “it’s a pseudo-problem” solution: Hume apparently does not know what it means to be reasonable or have a justified belief in something. To be reasonable/to have a justified belief in something is simply to base that belief on evidence, either deductive or inductive.

20. Solutions? • When he asks whether it’s reasonable to use induction what he’s asking is whether it’s reasonable to be reasonable. But of course it’s reasonable to be reasonable! • When he asks whether induction is justified, he’s asking whether beliefs based on inductive evidence are justified, which they are by definition!

21. Solutions? • Problems with Solution 3: • 1. Confuses the descriptive problem with the normative one? Yes we use inductive methods. Yes we call those methods acceptable/justified. But are they really? • 2. There is an answer to the question of how deductive inferences are justified—shouldn’t there be an answer to the same question asked of induction?

22. Solutions? • 3. Justified belief = inductively arrived at belief? Seems wrong. How/why are such beliefs the ones we count as justified? • Solution 4: The probability solution: Inductive inferences don’t, and aren’t meant, to generate certain conclusions. The best we can hope for using induction is conclusions that are probable.

23. Solutions? • Problems with solution 4: • 1. When we say that inductive conclusions are probable not certain, we might mean that sometimes such inferences fail. This is obvious. Hume’s problem: Are we justified in believing the conclusions of any of our future inductions? • 2. Probability as frequency. The problem: Projecting the frequencies to the future/unobserved

24. Solutions? • Solution 5: The pragmatic solution: • We can’t justify induction, but we can show that it is the best method for making predictions about the future/unobserved. • We can’t justify induction because we can’t know in advance whether nature is uniform. • But we do know: If nature is uniform, induction will work—and—if nature is not uniform, then induction will fail.

25. Solutions? • Now compare induction to some alternative method, say crystal gazing. • If nature is uniform, crystal gazing may or may not work. So if nature is uniform, induction is to be preferred. • If nature is not uniform, then induction will fail, but so will any alternative method.

26. Solutions? • Because if the alternative method did not fail, if it consistently yielded true predictions, the success of that alternative would constitute a uniformity that could be exploited by the inductive method. • We could inductively infer the future success of the crystal gazer from her past successes! • Hence, the inductive method will succeed if any alternative method could.