Introduction 1. Kant's methods: transcendental and epistemic reflection 2. The metaphysics of Kant's transcendental idealism 3. Transcendental affinity 4. The gap in Kant's Critique of Pure Reason 5. Kant's dynamic misconstructions 6. Kant's metaphysical proof of the law of inertia 7. Three Kantian insights Appendix. Summary of Kant's Transcendental Proof of the Legitimacy of Causal Judgments.

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Kant's Transcendental Proof of Realism

In the Critique of Pure Reason Kant appears to characterize analytic judgments in four distinct ways: once in terms of "containment," a second time in terms of "identity," a third time in terms of the explicative-ampliative contrast, and a fourth time in terms of the notion of "cognizability in accordance with the principle of contradiction." The paper asks which, if any, of these characterizations - or apparent characterizations has the best claim to be Kant's fundamental conception of analyticity in the first Critique. It argues that it is the second. The paper argues, further, that Kant's distinction is intended to apply only to judgments of subject-predicate form, and that the fourth alleged characterization is not properly speaking a characterization at all. These theses are defended in the course of a more general investigation of the distinction's meaning and tenability. Few ideas from the Critique of Pure Reason1 have had a greater impact on the course of analytic philosophy than Kant's celebrated distinction between analytic and synthetic judgments. But despite the distinction's acknowledged importance, and despite a long-running debate over its coherence, many questions about the details of its original formulation remain unsettled. Is Kant attempting to frame a distinction that applies to judgments in general, or only to some privileged sub-class of them? Does he mean to be characterizing analyticity in broadly metaphysical terms - terms, that is, that appeal to a judgment's constituent structure, or does he mean to be appealing (also) to epistemic considerations - for, example, how a judgment could in principle be known? Is it even possible to extract a unified conception of analyticity from Kant's various remarks? The last question arises because in the first Critique alone Kant appears to characterize analytic judgments in no fewer than four distinct ways: once in terms of "containment" (A 6-7/B 11), a second time in terms of "identity" (A 7/B 1 1), a third time in terms of the expliIn translating passages from the first Critique I usually follow the translation of Paul Guyer and Allen Wood. See Kant (1998). In other cases, except where indicated, I have followed the translation in the relevant volume of The Cambridge Edition of the Works of Immanuel Kant. Passages from Kant's other works are cited by volume and page number of the Akademie Ausgabe (Kant, 1968), hereafter "Ak.," which also forms the basis for my own translations.

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Kant's Conception of Analytic Judgment

At the beginning of Die Grundlagen der Arithmetik (§2) (1884), Frege observes that "it is in the nature of mathematics to prefer proof, where proof is possible". This, of course, is true, but thinkers differ on why it is that mathematicians prefer proof. And what of propositions for which no proof is possible? What of axioms? This talk explores various notions of self-evidence, and the role they play in various foundational systems, notably those of Frege and Zermelo. I argue that both programs are undermined at a crucial point, namely when self-evidence is supported by holistic and even pragmatic considerations. At the beginning of Die Grundlagen der Arithmetik (§2) (1884), Gottlob Frege observes that "it is in the nature of mathematics to prefer proof, where proof is possible", noting that "Euclid gives proofs of many things which anyone would concede him without question". Frege sets himself the task of providing proofs of such basic arithmetic propositions as "every natural number has a successor", the induction principle, and "1 + 1 = 2". Frege's observation was true in Euclid's day, and it remains true now. We still admire the achievements of Euclid, Archimedes, Cauchy, Weierstrass, Bolzano, Dedekind, Frege, and a host of others on providing rigorous proofs of "many things that formerly passed as self-evident", as Frege put it (§1). Many of these are propositions that no one in their right mind would doubt—unless it be on skeptical or nominalist grounds (in which case mathematical proof would not settle the issue). Nevertheless, thinkers differ widely on why it is that we prefer proof, and this question goes to the very heart of mathematics. My topic here is closely related to this. It is a commonplace that one cannot provide a nontrivial or noncircular proof of every known proposition. Frege's observation is that mathematics prefers proof, "where proof is possible". What about cases where proof is not possible? What is the epistemic status of the axioms, or basic truths (or inference principles), from which other propositions are derived? If we claim to know the theorems, on the basis of the proofs, then surely we must claim to know the axioms (or inference principles)? How?

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We hold these truths to be self-evident: but what do we mean by that?

We now have naturalistic understandings, at least in principle, of many phenomena that were once mysterious, such as of fire and life. Mental processes and properties, however, so far continue to resist naturalism. In part, this is due to the particular difficulty of naturalizing the normativity of mental phenomena, such as that of the truth and falsity of representation. Normativity is a particularly strong challenge to models of naturalistic emergence. There is a form of representation, however, that is naturally emergent in the organization of interactive systems. Interactive representation has claims to be the fundamental form of representation, from which all others are derivative. Interactivism offers a solution to the problem of the naturalistic normative emergence of representation.

Interaction and Representation

There have been several different and even opposed conceptions of the problem of logical constants, i.e., of the requirements that a good theory of logical constants ought to satisfy. This paper is in the first place a survey of these conceptions and a critique of the theories they have given rise to. A second aim of the paper is to sketch some ideas about what a good theory would look like. A third aim is to draw from these ideas and from the preceding survey the conclusion that most conceptions of the problem of logical constants involve requirements of a philosophically demanding nature which are probably not satisfiable by any minimally adequate theory.

The Problem of Logical Constants

The semantic tradition from Kant to Carnap

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The semantic tradition from Kant to Carnap