The problem of induction

But I know in advance that none of them is married. The consequence then is that it is not so important, at least for science, if those inferences would lack a rational foundation. The principal role of deduction in science is to derive, logically or mathematically, predictable consequences of the new theory that might be tested by suitable experiments.

As Lange puts it: A matter of fact proposition has the following feature: Clearly, the predicates grue and bleen are not the kinds of predicates we use in everyday life or in science, but the problem is that they apply in just the same way as the predicates green and blue up until some future time t.

Hume, Goodman argues, missed this problem. When is it reasonable to believe what we cannot prove. The Tortoise accepts the premise that p, and the premise that p implies q but he will not accept q. We posit a certain frequency f on the basis of our evidence, and this is like making a wager or bet that the frequency is in fact f.

What Hume is most concerned to point out is that one obvious, natural and attractive way of defending UN cannot work in the end. So there is complete agreement about which regularities hold in your collective experience thus far.

A scientist forms a hypothesis about possible causes for what is observed. Strawson points out that it could be meaningful to ask for a deductive justification of inductive inferences. Okasha suggests that the Bayesian model of belief-updating is an illustration how induction can be characterized in a rule-free way, but this is problematic, since in this model all inductive inferences still share the common rule of Bayesian conditionalisation.

While Hume was interested in causal sequences in time, his justification of induction also applies to modern statistical thinking.

New riddle of induction

For example, if a rider has never fallen off a horse and prepares to try out a new mount, she could say she is unlikely to be thrown, based on her previous experiences, but she should not rule out the possibility altogether. Neither supposition involves any kind of internal contradiction, and so long as he is not allowed to investigate the matter, he cannot rule either proposition out of consideration.

I have in mind the so-called inductive defense of induction: Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever.

Opinions about unobserved matters of fact are somehow derived from experience. Philosophers have responded to the problem of induction in a variety of ways, though none has gained wide acceptance.

The justification of rules of a deductive system depends on our judgements about whether to reject or accept specific deductive inferences. But what exactly is the difference between us and them. But for our purposes it will be useful to work with a somewhat more precise formulation.

For no matter of dispute is to be trusted without judging.

Problem of induction

But that strikes me as totally unwarranted. It is the claim that the regularities that have emerged in my experience are among the regularities that hold throughout nature. Problem of induction, problem of justifying the inductive inference from the observed to the unobserved.

It was given its classic formulation by the Scottish philosopher David Hume (–76), who noted that all such inferences rely, directly or indirectly, on the rationally unfounded premise that the future will resemble the past.

The Problem of Induction. You are hungry and you are about the bite into a hot crusty baguette. But a ‘friend’ stops you and says "Don’t do it. Problem of induction: Problem of induction, problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by the Scottish philosopher David Hume (–76), who noted that all such inferences rely, directly.

Hume’s Problem of Induction 1. We naturally reason inductively: We use experience (or evidence from the senses) to ground beliefs we have about things we haven’t observed.

The "problem of induction" arises when we ask whether this form of reasoning can lead to apodeictic or "metaphysical" certainty about knowledge, as the Scholastics thought. Thomas Aquinas especially thought that certain knowledge can be built upon first principles, axioms.

Thus, for Goodman, the problem of induction dissolves into the same problem as justifying a deductive system and while, according to Goodman, Hume was on the right track with habits of mind, the problem is more complex than Hume realized.

The New Riddle of Induction. Open Court Publishing.

The problem of induction
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Problem of Induction