Immanuel Kant claims that transcendental idealism yields a form of realism at the empirical level. Polite silence might best describe the reception this assertion has garnered among even sympathetic interpreters. This book challenges that prejudice, offering a controversial presentation and rehabilitation of Kant's empirical realism that places his realist credentials at the centre of the account of representation he offers in the Critique of Pure Reason. This interpretation ranges over the major themes contained in the Analytic of Principles and relevant (...) portions of the Dialectic. Kant's analysis of the conditions necessary for determinate representation is shown to involve a realist understanding of the relation of mind and world. The realist character of Kant's account of empirical truth, and his commitment to the unity of nature, are defended against competing empiricist, pragmatist, and methodological readings. This title links Kant studies to contemporary philosophical debates, and will appeal to scholars and students of Kant, as well as epistemologists, metaphysicians, and philosophers of science interested in a powerful, experience-sensitive, form of realism. (shrink)

The ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notoriousGrundlagenstreitcentered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, misconstruals which (...) last to our own time: Current literature often portrays popular views of intuitionism as the product of Brouwer's idiosyncratic subjectivism; modern logicians view intuitionism as simply applying a non-standard formal logic to mathematics; and contemporary philosophers see that logic as based upon a pure assertabilist theory of meaning. These pictures stem from the way Hilbert structured the controversy.Even though Brouwer's own work and behavior occasionally reinforce these pictures, they are nevertheless inaccurate accounts of his approach to mathematics. However, the framework provided by the Brouwer-Hilbert debate itself does not supply an adequate correction of these inaccuracies. For, even if we eliminate these mistakes within that framework, Brouwer's position would still appear fragmented and internally inconsistent. I propose a Kantian framework — not from Kant's philosophy of mathematics but from his general metaphysics — which does show the coherence and consistency of Brouwer's views. I also suggest that expanding the context of the controversy in this way will illuminate Hilbert's views as well and will even shed light upon Kant's philosophy. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice. This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued (...) today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.

Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle grounded on a metaphysical principle of determinacy. This article shows (...) that the for the anti-realist, the law of excluded middle entails that humans have wildly implausible abilities. The proposed synthesis between anti-realism and classical mathematics thus fails. (shrink)

There is little doubt that Salomon Maimon was both highly respected by, and highly influential upon, his contemporaries; indeed, Kant himself referred to Maimon as the best of his critics. The appraisal and reformulation of the Kantian project detailed in Maimon’s Essay on Transcendental Philosophy played a significant role in determining the criteria of success for post-Kantian philosophy, and was thus crucial to the early development of German Idealism. Key aspects of Maimon’s transcendental philosophy remain, however, relatively obscure. In particular, (...) it remains unclear to what degree Maimon’s skepticism is internal to the Kantian framework, and how this skepticism is related to Maimon’s so-called dogmatic rationalism. The central aim of this project is to present Maimon’s as a distinct form of post-Kantian skepticism: one which poses significant problems for Kant’s theoretical project and which motivates a reformulation of the critical framework. In Kant’s eyes, pre-Kantian forms of skepticism are insufficiently critical insofar as they involve a commitment to transcendental realism. By contrast, I argue that Maimon’s skepticism does not involve a commitment to transcendental realism and that it strikes at the heart of Kant’s critical project insofar as it constitutes what I term ‘critical’ as opposed to merely ‘empirical’ skepticism. I further argue that Maimon’s rationalism provides the materials for a response to this form of skepticism. This thesis contributes to contemporary debates in the history of philosophy concerning the nature of Maimon’s coalition system and its relation to German Idealism, but also provides an alternative perspective on contemporary problems in the philosophy of perception concerning, in particular, the possibility of non-conceptual intentional content. (shrink)