What is central to the progression of a sequence is the idea of succession, which is fundamentally a temporal notion. In Kant's ontology numbers are not objects but rules (schemata) for representing the magnitude of a quantum. The magnitude of a discrete quantum 11...11 is determined by a counting procedure, an operation which can be understood as a mapping from the ordinals to the cardinals. All empirical models for numbers isomorphic to 11...11 must conform to the transcendental determination of time-order. (...) Kant's transcendental model for number entails a procedural semantics in which the semantic value of the number-concept is defined in terms of temporal procedures. A number is constructible if and only if it can be schematized in a procedural form. This representability condition explains how an arbitrarily large number is representable and why Kant thinks that arithmetical statements are synthetic and not analytic. (shrink)

The aggregate EIRP of an N-element antenna array is proportional to N 2. This observation illustrates an effective approach for providing deep space networks with very powerful uplinks. The increased aggregate EIRP can be employed in a number of ways, including improved emergency communications, reaching farther into deep space, increased uplink data rates, and the flexibility of simultaneously providing more than one uplink beam with the array. Furthermore, potential for cost savings also exists since the array can be formed using (...) small apertures. (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)

The role of intuition in Kant's theory of mathematics is similar to instantiation rules in first-order logic according to Jaakko Hintikka. This paper is a critical examination of Hintikka's interpretation and reconstruction of Kant's theory. It is argued that Kant's position is question-begging on this interpretation.

In my work on Kant’s Transcendental epistemology, I criticize his three Critiques and show that none of them can solve the problems that Kant endeavored to solve; and he even, in a way, admitted it. In the first Critique, Kant attempts to solve the difficulties of the Cartesian Idealism and Humean Empirism, in combining them mechanically in his own Transcendental formalism and Sensual matter without being able to bridge the gap between them. In the second Critique, Kant endeavored to make (...) his Practical Reason of the a priori pure fact of formal morality into free moral conduct to materialize his ideal commonwealth of ends, but he could not bridge this gap. In his third Critique, Kant attempted to make the aesthetic reflective judgment of beauty objective, including of artworks, but failed to do so. The Peircean pragmaticist method can save the theory of knowledge both from the dogmatism of the metaphysical realists and from the inconsistency of the phenomenalists and holists. Peirce developed his epistemological realism in response to the difficulties of Kant’s transcendental epistemology, especially that of his three Critiques. It seems that in his late research Kant tries to follow Spinoza in the distinction between the causality in nature and the human inner causality as one’s Moral freedom and yet for Kant they operate in different domains to keep human freedom absolute, while the Spinozist conception of human freedom is in Nature and relative to human knowledge of reality and one’s relative power in Nature. Kant’sAnthropology from a Pragmatic Point of Viewis a continuation of his Transcendental critical philosophy, but also his intended empirical epistemology by which to develop a practical deviation from his Copernican Revolution in the direction of the Peircean contra-revolution in Pragmaticist epistemology. (shrink)

Kant's distinction between analytic and synthetic method is connected to the so-called Aristotelian model of science and has to be interpreted in a (broad) directional sense. With the distinction between analytic and synthetic judgments the critical Kant did introduced a new way of using the terms 'analytic'-'synthetic', but one that still lies in line with their directional sense. A careful comparison of the conceptions of the critical Kant with ideas of the precritical Kant as expressed in _Ãœber die Deutlichkeit, leads (...) to the interpretation defended here of Kant's distinction between analytic and synthetic judgments within his philosophy of mathematics. (shrink)

In recent years non-conceptual content theorists have taken Kant as a reference point on account of his notion of intuition (§§ 1-2). The present work aims at exploring several complementary issues intertwined with the notion of non-conceptual content: of these, the first concerns the role of the intuition as an indexical representation (§ 3), whereas the second applies to the presence of a few epistemic features articulated according to the distinction between knowledge by acquaintance and knowledge by description (§ 4). (...) This work intends to dismiss the possibility that intuition may have an autonomous function of de re knowledge in support of an interpretative reading which can be labelled as weak conceptualism. To this end, the exploration will be conducted from a strictly transcendental perspective – i.e., by referring to the so called theory of the “concept of a transcendental object”. (shrink)