This paper will make the case that we can find in Kant’s Second Analogy a substantive response to Hume’s argument on induction. This response is substantive insofar as it does not merely consist in independently arguing for the opposite conclusion, but rather, it identifies and exploits a gap in this argument. More specifically, Hume misses the possibility of justifying the uniformity of nature as a synthetic a priori proposition, which Kant looks to establish in the Second Analogy. Note that the (...) focus on the paper is on Kant’s identification of the form that a solution to Hume’s inductive scepticism must take. In making this point, my paper will look to establish two lemmas: Kant identifies synthetic a priori judgments as a means of justifying metaphysical knowledge in a way that circumvents Hume’s dichotomy between matters of fact and relations of ideas; the Second Analogy looks to establish the uniformity of nature of as a synthetic a priori proposition. However, my paper generally abstains from the question of the tenability of Kant’s argument in the Second Analogy. Doing justice to this latter discussion would require more space than I am able to offer here. My paper therefore has a conditional bearing on the philosophical issue of inductive scepticism. If one believes Kant’s Second Analogy to be philosophically cogent, then Kant offers a successful justification of induction against Hume’s scepticism. If not, then at least one can still admire Kant’s identification of the gap in Hume’s argument, which, to a degree, can be exploited independently of Kant’s system. (shrink)

In this paper, I argue for an interpretation of Hume's Law that sees him as dismissing all possible arguments from is to ought on the basis of a comparison with his famous argument on induction.

This article surveys the state of the literature on Hume’s epistemology, focusing on treatments of what has come to be known as the ‘Kemp Smith problem’, that is, the problem of reconciling Hume’s scepticism with his naturalism. It first surveys the literature on this issue with regard to the Treatise, moving on to briefly compare the Treatise and the Enquiry in virtue of their epistemological frameworks, before finally examining the literature with regard to the first Enquiry.

Much has been written about Kemp Smith's famous problem regarding the tension between Hume's naturalism and his scepticism. However, most commentators have focused their attention on the Treatise; those who address the Enquiry often take it to express essentially the same message as the Treatise. When Hume's scepticism in the Enquiry has been investigated in its own right, commentators have tended to focus on Hume's inductive scepticism in Sections 4 and 5. All in all, it seems that Section 12 has (...) been unduly neglected. This paper seeks to address Kemp Smith's problem from the standpoint of Hume's treatment of scepticism in EHU 12, and finds an interesting internalist account that makes sense both of Hume's discussion in EHU 12, and his aims in the Enquiry as a whole. Moreover, it is one that is of substantive philosophical interest, having intriguing parallels to contemporary epistemological accounts. (shrink)

Hume's epistemological legacy is often perceived as a predominantly negative sceptical one. His infamous problem of induction continues to perplex philosophers to this day, and many of his sceptical worries maintain their interest in contemporary eyes (e.g. with regard to reason, the senses, substance, causation). Yet Hume's positive epistemological contributions also hold significance for philosophy in this day and age. In this paper, I aim to situate Hume's epistemology in a more contemporary context, particularly with regard to the theme of (...) reliabilism that runs throughout this epistemology. This will take the shape of examining correspondences and contrasts between Hume's epistemologies in the Treatise and Enquiry and reliabilism, as well as an examination of how Hume's framework might handle some major challenges for reliabilist epistemologies. In particular, I argue that that while Hume is tempted to an epistemology that is intimately tied to truth in the Treatise, he backs away when confronted with the excesses of scepticism in the conclusion of Book 1, and winds up with an epistemology most similar to the contemporary epistemological frameworks of dogmatism and phenomenal conservatism. Yet, largely because of his reliance on the passions (a respect in which he diverges from these two contemporary frameworks), the epistemology of the Treatise remains crucially dissociated from truth. Meanwhile, in the first Enquiry, he proceeds to develop a two-tiered epistemological framework that first accords all our justification with default authority, and then founds all-things-considered epistemic justification on our evidence for the reliability of our faculties. The first tier most resembles the contemporary epistemological framework of conservatism, while the second tier most closely resembles approved-list reliabilism. In this, a clear reliabilist thread runs through the epistemology of the Enquiry. I will also argue that although Hume did not appear to fully appreciate one of the most significant challenges for reliabilism-that is, the generality problem-his philosophical framework nevertheless contains the beginnings of a response to it. (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...) of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

The Title Principle is seen by a number of commentators as crucial to Hume’s resolution of skeptical doubts in THN 1.4.7, thus providing an answer to Kemp Smith’s (1941) famous worry regarding the tension between Hume’s skepticism and his naturalism. However, I will argue that in the Enquiry, Hume rejects both the Title Principle and the role of the passions in his epistemology. Those who think that neither the Title Principle nor the passions play a significant role in THN 1.4.7 (...) will likely take this as grist for their mills. But for those who endorse such interpretations, my argument presents an interpretive burden to provide some explanation as to why Hume might have become dissatisfied with this epistemic framework, abandoning it in his later work. Having raised this interpretive burden, my paper also seeks to bear it by providing such an explanation. (shrink)