This essay argues that the key to understanding Kant's transcendental idealism is to understand the transcendental realism with which he contrasts it. It maintains that the latter is not to be identified with a particular metaphysical thesis, but with the assumption that the proper objects of human cognitions are “objects in general” or “as such,” that is, objects considered simply qua objects of some understanding. Since this appears to conflict with Kant's own characterization of transcendental realism as the view that (...) (mistakenly) regards appearances as if they were things in themselves, the essay explicates the connection between the concepts of an object (or thing) considered as such and a thing considered as it is in itself. In light of this, it maintains that Kant's transcendental idealism is compatible with a robust empirical realism and that many of its critics are tacitly committed to a misguided transcendental realism. (shrink)

The chapter on temporality in Merleau-Ponty’s Phenomenology of Perception , is situated in a section titled, “Being-for-Itself and Being-in-the-World.” As such, Merleau-Ponty’s task in the chapter on temporality is to bring these two positions together, in other words, to articulate the manner in which time links the cogito (Being-for-Itself) with freedom (Being-in-the-World). To accomplish this, Merleau-Ponty proposes a subject located at the junction of the for-itself and the in-itself, a subject which has an exterior that makes it possible for others (...) to have an interior. This analysis will take Merleau-Ponty to an impasse where, on the one hand, there appears to be an objective world and the time of objects in that world, and on the other, there is the subject’s notion of events and the passing of time. Referring to Bergson’s notion of time, this essay proposes that there must be a temporal interval between perception, feeling and action in order for the subject to be “temporal by means of an inner necessity,” as Merleau-Ponty prescribes. (shrink)

The issue is obscured by the fact that the word `space' can be used in four different ways. It can be used, first, as a term of pure mathematics, as when mathematicians talk of an `n-dimensional phase-space', an `n-dimensional vector-space', a `three-dimensional projective space' or a `twodimensional Riemannian space'. In this sense the word `space' means the totality of the abstract entities-the `points'-implicitly defined by the axioms. There is no doubt that there exist, iii this sense, non-Euclidean spaces, because all (...) that is claimed by such an assertion is that sets of non-Euclidean axioms constitute possible implicit definitions of abstract entities, that is to say that some sets of non-Euclidean axioms are consistent. If Kant or any other philosopher had denied this, he would have been wrong; but Kant himself took care not to deny it, 2 and there is little reason to suppose that any philosopher concerned about space has been using the word in this, the pure mathematician's, sense. (shrink)

ABSTRACT I suggest how a broadly Kantian critique of classical logic might spring from reflections on constructibility conditions. According to Kant, mathematics is concerned with objects that are given through ‘arbitrary synthesis,’ in the form of ‘constructions of concepts’ in the medium of ‘pure intuition.’ Logic, by contrast, is narrowly constrained – it has no objects of its own and is fixed by the very forms of thought. That is why there is not much room for developments within logic, as (...) compared to the progress in mathematics. Kant’s view of logic remains critical, though – through considerations that are effectively on the scope and limits of classical logic and which play a part in his transcendental idealism. The most important ones are to be found in his critique of the use of reductio ad absurdum proofs in metaphysics and his solutions to the ‘antinomies of pure reason.’ Arguably, these considerations carry over to mathematics as well – by way of ‘analogues’ to the antinomies – in particular in resolving infinity paradoxes. (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted in the (...) tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (shrink)

This essay investigates the transformation of the faculty of understanding in Kant’s Transition from Metaphysical Foundations of Natural Science to Physics drafts found in Opus postumum. I argue that in fascicles X and XI Kant implicitly reverses the architectonic order of sensibility and understanding. Without an account of this reversal, Kant’s critique of Isaac Newton’s conception of phenomena and the so called Selbstsetzungslehre in fascicle VII fall apart. I argue that what is at stake is a challenge Kant makes to (...) his own presuppositions and a challenge to the Kantian philosopher who wishes to stay with a strictly ‘critical’ Kant. (shrink)