The Problem of Induction

1. The Problem of Induction The Problem of Induction

2. Background: The Scientific Method Observation Hypothesis Test/Experiment Revise Hypothesis Results Evidence supports hypothesis Inconsistent with hypothesis Conclusion/Theory/Law

3. Background: The Scientific Method (cont’d) Science is generally taken to establish theories and laws that apply to all space and time without restriction. • (Though these tend to be ceteris paribus laws.) • The power of science is not in its observation, but in its predictive power. • That gravity and electricity, etc. will continue to operate tomorrow the same as they did yesterday.

4. Hume’s Critique of Induction Central question: How do we acquire knowledge of the unobserved? • How do we know that the laws of science will operate tomorrow the same as they did yesterday? • All science can provide us with is belief about unobserved facts. • “It is one thing to describe how people go about seeking to extend their knowledge; it is quite another to claim that the methods employed actually do yield knowledge.” (252) • Unlike belief, knowledge must be founded upon some evidence. • The scientific method makes inferences from the observed to the unobserved.

5. Hume’s Critique of Induction (cont’d) • Of the observed, we can claim knowledge; but is the inference from knowledge of the observed to the unobserved justified? • Confidence is not justification. • Is there such a thing as inductive evidence?

6. Hume’s Critique of Induction (cont’d) • Do the observed facts constitute sound evidence for the conclusion? • Would we be justified in accepting the conclusion based on the alleged evidence? • Inference does conform to an accepted inductive principle—that observed instances conforming to a generalization constitute evidence for it. • But on what grounds do we accept this inductiveprinciple?

7. Demonstrative & Nondemonstrative Demonstrative Inference: One whose premises necessitate its conclusion. • All valid deductions are demonstrative inferences. Nondemonstrative Inference: One which fails to be demonstrative. • Its conclusion could be false even if the premises are true. Are there inferences whose premises which, while not necessitating its conclusion, lend it support or weight, or make it probable? • Proposal: If so, such inferences would possess a certain strength. • Although not deductive validity, we might call such inferences correct inductive inferences.

8. Ampliative & Nonampliative Nonamliative Inference: One in which the conclusion does not augment the content of the premises. • Ultimately, the conclusion says no more than do the premises; it is simply a reformulation of (part of) the content of the premises. Ampliative Inference: One in which the conclusion adds content not contained in the premises. Question: “Is there any type of inference whose conclusion must, of necessity, be true if the premises are true, but whose conclusion says something not stated by the premises?” (253)

9. Demonstrative & Nondemonstrative; Ampliative & Nonampliative Argument 1: (P1) Some black balls from this urn have been observed. (P2) All observed black balls from this urn are licorice-flavored. (C) All black balls in this urn are licorice-flavored. • Ampliative & Nondemonstrative. Argument 2: (P1) Some black balls from this urn have been observed. (P2) All observed black balls in this urn are licorice-flavored. (P3) Any two balls in this urn that have the same color also have the same flavor. (C) All black balls in this urn are licorice-flavored. • Nonampliative & Demonstrative.

10. Demonstrative & Nondemonstrative; Ampliative & Nonampliative (cont’d) • To prove the argument about the gumballs deductively would require it being nonampliative and demonstrative, and therefore not inductive. • To justify an ampliative inference argument inductively would require nondemonstrative inference, the very thing we are trying to establish. • Hume: We cannot justify any kind of ampliativeinference. • There is no way we can extend our knowledge to the unobserved. • This is, admittedly, repugnant to our common sense and deepest convictions.

11. Attempted Solutions Solution #1: Inductive Justification Claim: The fact is, when it comes to the scientific method, the results speak for themselves. • “If methods are to be judged by their fruits, there is no doubt that the scientific method will come out on top.” (255) Reply: This is an attempt to justify inductive methods inductively, and so is viciously circular, assuming from the premise that science has been successful in the past to the conclusion that it will continue to be successful in the future. • Crystal gazer example

12. Attempted Solutions Solution #2: Complexity of Scientific Inference Claim: Scientific inference is not (or rarely) simple generalization from experience (as in the gumball example). It follows the hypothetico-deductive method, not induction by enumeration. • Following the scientific method, hypotheses are not conclusively proved by any given confirming instance, but it may become highly confirmed. • Such a hypothesis is accepted, at least tentatively. • The only non-deductive part of the scientific method is coming up with the premises.

13. Attempted Solutions Solution #2: Complexity of Scientific Inference Reply: The fallacy with this method is that it attempts to establish a premise (the hypothesis), and not a conclusion: Standard Form: (P1) Observational statements (P2) Hypothesis (C) Predictive statement • But what’s really at stake is the truth of the hypothesis.

14. Attempted Solutions Solution #2: Complexity of Scientific Inference (P1) This feather and this bowling ball are contained in a vacuum. (P2) Objects in a vacuum will fall at an equal rate of acceleration. (C) If dropped, this feather and this bowling ball will fall at an equal rate of acceleration. • If (C) turns out to be true, it serves only to confirm (P2), which is not the conclusion, but a premise. • If we add (C2) “Therefore, objects in a vacuum…” the circularity becomes obvious. • If we reformulate the argument so that (P2) becomes the conclusion, we have a standard (flawed) inductive argument.

15. Attempted Solutions Solution #2: Complexity of Scientific Inference • Moreover, for any body of observational data, there is usually more than one hypothesis compatible with it, but not with each other. Solution #3: Deductivism Claim (Karl Popper): Induction plays no role in science, and there is no such thing as correct inductive inference. • Science depends on falsifiability: it is possible to falsify a generalized hypothesis with one negative instance, but impossible to verify a generalized hypothesis with any number of positive instances. • Such generalized hypothesis (laws, etc.) are never to be regarded as final truths; the attempt to confirm hypotheses plays no part in the aims of science.

16. Attempted Solutions Solution #3: Deductivism • So the scientific method really takes this form: (P1) Hypothesis H holds that if cause C occurs, then effect E will also occur. (P2) If cause C occurs, and effect E does not occur, then hypothesis H is false. (P3) Cause C occurs. (P4) Effect E does not occur. (C) Therefore, hypothesis H is false. • This argument form is deductive, not inductive. Reply: Again, having falsified one hypothesis tends to leave behind several mutually exclusive unfalsified hypotheses. Science isn’t giving us a whole lot here.

17. Attempted Solutions Solution #3: Deductivism Popper: To this we can add corroboration. • The more potentially falsifiable a hypothesis, the greater its content (a hypothesis that isn’t at least potentially falsifiable would be meaningless). • A highly falsifiable hypothesis which, when subjected to testing and remaining unfalsified, becomes highly corroborated. • Although we do not regard any hypotheses as true, degree of corroboration helps us select among mutually exclusive hypotheses. Reply: Popper’s solution doesn’t rid us of induction. Rather, all it does is give us some means of selecting from among multiple hypotheses, each of which contains more content than any of the available basic statements supporting it.

18. Attempted Solutions Solution #7: A Probabilistic Approach Claim: The whole point of induction is not to prove some statement as true, but to establish it as probable. And this is the aim of science. All Hume succeeded in showing is that induction isn’t deduction—but, of course, it was never meant to be. Reply: There are two ways we might treat this; either as: • Frequency Sense: Inductive inferences are not meant to always lead to true conclusions, just usually; or • Rational Belief: To say that an inductive inference is probable is to say one would be rationally justified in believing it.

19. Attempted Solutions Solution #7: A Probabilistic Approach • Option (a): Frequency Sense: Not only can we not say that all inductive inferences with true premises will have true conclusions; we cannot say that any such inductive inferences will have true conclusions. • For all we know, from now on, all inductive inferences with true premises will lead to false conclusions. • Option (b): Rational Belief: A claim that one would be rationally justified in believing some inference must be made on the basis of available evidence, but such a rational justification would thus itself depend on the justifiability of inductive inference.

20. Attempted Solutions Solution #8: Pragmatic Justification Claim: (Hans Reichenbach): Although induction’s powers of prediction cannot be established in advance, it can be shown to be superior to any alternative method of prediction: • Either nature is uniform enough to allow for successful inductive inference from the observed to the unobserved, or it is not. • If it is, induction works; if not, induction fails. • Consider some other method of prediction, say, crystal gazing. • If nature is uniform, crystal gazing may or may not work successfully. • If nature is not uniform, crystal gazing may or may not work successfully.

21. Attempted Solutions Solution #8: Pragmatic Justification • So, if nature is uniform, induction must work, while crystal gazing may or may not. • And, if nature is not uniform, and crystal gazing (along with all other such methods) fails, there is no reliable method of prediction. • But, if nature is not uniform, and crystal gazing works, then crystal gazing is uniform, and can be exploited inductively, and so induction would work. • If any method works, induction works. Reply: The uniformity of nature is not an all-or-nothing affair. • Moreover, as stated, such a method would seem to justify too wide a range of rules for inference.

22. Significance of the Problem No one, including Hume, suggests suspending scientific investigation on the basis that induction presents an apparently insoluble problem. • But given that science as a whole depends on inductive inference, it’s all a bit disquieting. • If the scientific method is so commonsensically superior to other alternatives (such as, say, faith), we should be able to point to why, lest science just becomes one faith among many.