Online research in philosophy

In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that Hume’s celebrated “problem of induction” can no longer be set up and is thereby dissolved.

Howson's critique of my essay on Hume's problem of induction levels two main charges. First, Howson claims that I have attributed to him an error that he never made, and in fact which he warned against in the very text that I cite. Secondly, Howson argues that my proposed solution to Hume's problem is flawed on technical and philosophical grounds. In response to the first charge, I explain how Howson's text justifies attributing to him the claim that the principle of induction is shown to be inconsistent by Goodman's riddle. In regards to the second, I show that Howson's objections rest on misunderstandings of formal learning theory and on conflating the problem of induction with the problem of unconceived alternatives.

Hume’s view of reason is notoriously hard to pin down, not least because of the apparently contradictory positions which he appears to adopt in different places. The problem is perhaps most clear in his writings concerning induction - in his famous argument of Treatise I iii 6 and Enquiry IV, on the one hand, he seems to conclude that “probable inference” has no rational basis, while elsewhere, for example in much of his writing on natural theology, he seems happy to acknowledge that such inference is not only reasonable, but is even a paradigm of reasoning against which the theistic arguments must be judged. In the face of this apparent contradiction, many recent commentators have proferred “non-sceptical” interpretations of Hume’s argument concerning induction, but in this paper I sketch an alternative and perhaps less radical method of resolving the problem, by identifying a major threefold ambiguity in Hume’s use of the word “reason”. On this interpretation, Hume indeed sees induction as a paradigm of reasonableness in what is arguably the most important sense, but he nevertheless believes induction to be entirely non-reasonable in another sense, which though less important in common life is nevertheless very significant philosophically. A comparison with Locke can help to illuminate Hume’s position, which though indeed not entirely sceptical about induction, is by no means entirely non-sceptical either.

This article argues that a successful answer to Hume's problem of induction can be developed from a sub-genre of philosophy of science known as formal learning theory. One of the central concepts of formal learning theory is logical reliability: roughly, a method is logically reliable when it is assured of eventually settling on the truth for every sequence of data that is possible given what we know. I show that the principle of induction (PI) is necessary and sufficient for logical reliability in what I call simple enumerative induction. This answer to Hume's problem rests on interpreting PI as a normative claim justified by a non-empirical epistemic means-ends argument. In such an argument, a rule of inference is shown by mathematical or logical proof to promote a specified epistemic end. Since the proof concerning PI and logical reliability is not based on inductive reasoning, this argument avoids the circularity that Hume argued was inherent in any attempt to justify PI.

Hume’s view of reason is notoriously hard to pin down, not least because of the apparently contradictory positions which he appears to adopt in different places. The problem is perhaps most clear in his writings concerning induction - in his famous argument of Treatise I iii 6 and Enquiry IV, on the one hand, he seems to conclude that “probable inference” has no rational basis, while elsewhere, for example in much of his writing on natural theology, he seems happy to acknowledge that such inference is not only reasonable, but is even a paradigm of reasoning against which the theistic arguments must be judged. In the face of this apparent contradiction, many recent commentators have proferred “non-sceptical” interpretations of Hume’s argument concerning induction, but in this paper I sketch an alternative and perhaps less radical method of resolving the problem, by identifying a major threefold ambiguity in Hume’s use of the word “reason”. On this interpretation, Hume indeed sees induction as a paradigm of reasonableness in what is arguably the most important sense, but he nevertheless believes induction to be entirely non-reasonable in another sense, which though less important in common life is nevertheless very significant philosophically. A comparison with Locke can help to illuminate Hume’s position, which though indeed not entirely sceptical about induction, is by no means entirely non-sceptical either.

Popper famously claimed that he had solved the problem of induction, but few agree. This paper explains what Popper's solution was, and defends it. The problem is posed by Hume's argument that any evidence-transcending belief is unreasonable because (1) induction is invalid and (2) it is only reasonable to believe what you can justify. Popper avoids Hume's shocking conclusion by rejecting (2), while accepting (1). The most common objection is that Popper must smuggle in induction somewhere. But this objection smuggles in precisely the justificationist assumption (2) that Popper, as here undestood, rejects. Footnotes1 Invited address at the Karl Popper 2002 Centenary Conference, Vienna, 3–7 July 2002.

In this paper I will argue that Professor Goodman was correct in thinking that there is a problem concerning counterfactual conditionals, but that it is somewhat different from the problem he thought it to be, and is one that is even more basic. I will also try to show that this problem is distinct from Hume's "problem" of induction, and that additional assumptions have to be made for counterfactual induction beyond those required for other kinds of induction.

I develop a critique of Hume’s infamous problem of induction based upon the idea that the principle of induction (PI) is a normative rather than descriptive claim. I argue that Hume’s problem is a false dilemma, since the PI might be neither a “relation of ideas” nor a “matter of fact” but rather what I call a contingent normative statement. In this case, the PI could be justified by a means-ends argument in which the link between means and end is established solely by deductive reasoning. The means-ends argument is an elementary result from formal learning theory that you must be willing to make inductive generalizations if you want to be logically reliable in the types of examples Hume described. This justification of the PI avoids both horns of Hume’s dilemma. Since no contradiction ensues from rejecting logical reliability as an aim, the PI is contingent. Yet since the proof concerning the PI and logical reliability is not based on inductive reasoning, there is no threat of circularity.

R. C. Jeffrey has proposed probabilism as a solution to Hume's problem of justifying induction. This paper shows that the assumptions of his Estimation Theorem, used to justify induction, can be weakened to provide a more satisfactory interpretation. It is also questioned whether the use of probabilism adds significantly to our understanding (or even Hume's understanding) of the problem of induction.

Necessity holds that, if a proposition A supports another B, then it must support B. John Greco contends that one can resolve Hume's Problem of Induction only if she rejects Necessity in favor of reliabilism. If Greco's contention is correct, we would have good reason to reject Necessity and endorse reliabilism about inferential justification. Unfortunately, Greco's contention is mistaken. I argue that there is a plausible reply to Hume's Problem that both endorses Necessity and is at least as good as Greco's alternative. Hence, Greco provides a good reason for neither rejecting Necessity nor endorsing inferential reliabilism.