#10649 - The Problem Of Induction - Epistemology & Metaphysics (Knowledge & Reality)

The problem of Induction

Philosophical Essays – Hume

• “The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with equal distinctness and facility, as if ever so conformable to truth and reality.”

• If you see a new object of which you have no experience you will never be able to discover any of its causes and effects unless you see it in action.

• The mind “can never possibly find the effect in the suppos’d cause, by the most accurate scrutiny and examination. For the effect is totally different from the cause, and consequently can never be discovered in it.”

• “[A]ll arguments concerning existence are founded on the relation of cause and effect;...our knowledge of that relation is deriv’d entirely from experience, and...all our experimental conclusions proceed upon the supposition, that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.”

• Objects’ “secret nature, and consequently, all their effects and influence may change, without any change in their sensible qualities.”

• But:

• “Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever.”

• Inferences from experience are effects of custom rather than reasoning, but it is a useful custom.

‘Induction, Explanation and Natural Necessity’ – Foster (1893)

• Tries to solve the problem of induction by appealing to a notion of objective natural necessity.

• AYER THINKS: “The only way in which this move could be helpful would be if it were somehow easier to discover that all A’s must be B’s than that they merely were so.”

  • But he’s wrong because there’s a form of empirical evidence which is rational but not inductive. We can use inference to the best explanation (that all As must be Bs).

• His solution to the problem of induction (the nomological explanatory solution/NES):

1. The only primitive rational form of empirical inference is inference to the best explanation.

2. When rational, an extrapolative inference can be justified by being recast as the product of two further steps of inference, neither of which is, as such, extrapolative. The first step is an inference to the best explanation – an explanation of the past regularity whose extrapolation is at issue. The second is a deduction from this explanation that the regularity will continue or that it will do so subject to the continued obtaining of certain conditions.

3. A crucial part of the inferred explanation, and sometimes the whole of it, is the postulation of certain laws of nature – laws which are not mere generalizations of fact, but forms of (objective) natural necessity.

• Objection he discusses: How do we know the laws we come up with have global rather than local scope? He says it’s because it’s a better explanation – “dispels the mystery of past regularity without creating the mystery of capricious necessity.”

• “In itself a singular restriction is something which runs counter to the direction of nomological explanation. This is why we serve the purposes of explanation better, if there is a need for explanation at all, by postulating laws without such restrictions, if we can do so compatibly with our data.”

‘Natural Kinds’ – Quine

• “I propose assimilating Hempel’s puzzle to Goodman’s by inferring from Hempel’s that the complement of a projectible predicate need not be projectible.”

• “If we see the matter in this way, we must guard against saying that a statement [all x are y] is lawlike only if x and y are projectible.”

• Quine doesn’t think there’s any projectible predicate whose complement is projectible.

  • “A projectible predicate is one that is true of all and only the things of a kind.”

  • “What makes Goodman’s example a puzzle…is the dubious scientific standing of a general notion of similarity, or of kind.”

• “If properties are to support this line of definition [of similarity] where sets do not, it must be because properties do not, like sets, take things in every random combination.”

  • All kinds are sets but not all sets are kinds.

• If we accept that there is comparative similarity, “[k]inds come to admit now not only of overlapping but also of containment in one another.”

• “[I]t is a mark of maturity of a branch of science that the notion of similarity or kind finally dissolves, so far as it is relevant to that branch of science.”

• “Implicitly the learner of “yellow” is working inductively toward a general law of English verbal behavior, though a law that he will never try to state; he is working up to where he can in general judge when an English speaker would assent to “yellow” and when not.”

• “The brute irrationality of our sense of similarity, its irrelevance to anything in logic and mathematics, offers little reason to expect that this sense is somehow in tune with the world – a world which, unlike language, we never made.”

What is a Law of Nature? – Armstrong

• “[I]f laws are nothing but Humean uniformities, then inductive scepticism is inevitable.”

• Induction is invalid but rational (and it’s a necessary truth that it’s rational).

• “The inference to the laws is a case of inference to the best explanation.”

  • If this isn’t rational then what is? It can still be asked why induction is the ‘best’, but the onus is on the challenger to find something better.

• If ‘induction is rational’ were contingent, it would seem to be the sort of contingent truth for which we would have to have inductive reasons.

  • But this would lead to a vicious regress of justification, so it has to be a necessary truth instead.

• Disagrees with Strawson that it is a necessary truth because it is part of the meaning of ‘rational’ that ordinary inductive inferences are rational.

• He thinks laws are more than just regularities: it is rational to postulate what best explains the phenomena – induction is thus rational > it’s a case of inference to the best explanation.

• Hume overlooked the possibility that observational premises might bestow some logical probability on conclusions about the unobserved, even if they do not entail such conclusions.

• “To infer to the best explanation is part of what it is to be rational. If that is not rational, what is?”

‘The Inference to the Best Explanation’ – Gilbert Harman

• Inductive inference (‘enumerative induction’) is just a special case of inference to the best explanation.

• Induction can’t provide an answer about the conditions under which it is appropriate to employ it.

  • “The answer is that one is warranted in making this inference whenever the hypothesis that all A’s are B’s is (in the light of all the evidence) a better, simpler, more plausible (and so forth) hypothesis than is the hypothesis, say, that someone is biasing the observed sample in order to make us think that all A’s are B’s.”

  • This is inference to the best explanation.

• We actually use certain lemmas when we make these inferences, and the concept of enumerative induction doesn’t do justice to this.

• The lemmas are involved in the justification of belief and thus in our conception of knowledge.

• But I don’t think he provides a general characterization of these lemmas.

P. Strawson (1966)

• “[O]ne statement or set of statements may support another statement, S, which they do not entail, with varying degrees of strength.”

• The question of what grounds there are for thinking that deduction in general is a valid method of argument just doesn’t make sense; a (roughly) analogous thought applies to induction.

  • “[T]o call a particular belief reasonable or unreasonable is to apply inductive standards.”

• “[T]o ask whether it is reasonable to place reliance on inductive procedures is like asking whether it is reasonable to proportion the degree of one’s convictions to the strength of the evidence. Doing this is what ‘being reasonable’ means in such a context.”

  • “Is the law legal?”

• “[A]ny successful method of finding out about the unobserved is necessarily justified by induction.”

Fact, Fiction and Forecast – Goodman

• Before t, all emeralds examined that are green are also grue, but after t, all emeralds examined that are blue are also grue.

  • But green emeralds are not blue emeralds

• “[I]t is clear that if we simply choose an appropriate predicate, then on the basis of these same observations we shall have equal confirmation, by our definition, for any prediction whatever about other emeralds, or indeed about anything else.”

  • Is this because all objects both participate in and fail to participate in an infinite number of sets, and predicates pick out sets?

• “[O]nly the predictions subsumed under law-like hypotheses are genuinely confirmed; but we have no criterion as yet for determining such lawlikeness.”

  • Could you link this to Quine’s observation that our notion of similarity/kinds is anthropomorphic? Lawlikeness depends on having a community of biologically similar individuals!

• “To say that valid predictions are those based on past regularities, without being able to say which regularities, is thus quite pointless. Regularities are where you find them, and you can find them anywhere.”

• “[L]awlike or projective hypotheses cannot be distinguished on any merely syntactical grounds or even on the ground that these hypotheses are somehow purely general in meaning.”

The Problems of Philosophy – Russell

• “[I]f we are to know of the existence of matter, of other people, of the past before our individual memory begins, or of...