No one doubts that philosophers have discussed at length ‘the problem of induction’, but it would also be generally recognized that there would be disagreement as to precisely what that problem is. Rather than tackle the formulation problem, I will borrow from a popular text:
Our existence as well as science itself is based on the principle of induction that tells us to reason from past frequencies to future likelihoods, from the limited known of the past and present to the unknown of the past, present, and future ... But though inductive probability is psychologically inescapable, we have trouble providing a rational justification for it.
We might say, then, that there is such a practice as induction, and a problem associated with it is that of justifying engaging in it. We engage in reasoning from things we know about the past and present to conclusions about the past, present and future. We can't resist doing this but we have trouble finding a rational justification for doing so. This problem suggests a generalization. We engage in reasoning, reaching new conclusions. It would be hard to resist engaging in this practice. How do we provide a rational justification for it?
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