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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."
? "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." o 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. o "A projectible predicate is one that is true of all and only the things of a kind." o "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." o 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."
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