This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...) program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (shrink)

From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...) in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (shrink)

Presented in the “Critique of Pure Reason” transcendental philosophy is the first theory of science,which seeks to identify and study the conditions of the possibility of cognition. Thus, Kant carries out a shift to the study of ‘mode of our cognition’ and TP is a method, where transcendental argumentation acts as its essential basis. The article is devoted to the analysis of the transcendental arguments. In § 2 the background of ТА — transcendental method of Antiquity and Leibniz’s Principle of (...) Sufficient Reason — are analyzed and their comparison with ТА is given. § 3 is devoted to the analysis of TA in the broad and narrow senses; a formal propositional and presupposition models are proposed. In § 4 I discuss the difference between TA and metaphysics’ modes of reasoning. It analyzes the Kant’s main limitations of the use TA shows its connection with the Modern Age and contemporary science. (shrink)