This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

This paper examines the issue of the unity of the critical philosophy in Kant’s Critique of Judgment through a careful consideration of the actual bridge that joins nature and freedom. Kant argues that this bridge is made under the demand for the furtherance of life, and is accordingly to be equated with the demand of freedom. This article specifically focuses on this demand that is, in effect, carried out by the principle of purposiveness. It is argued that this demand is (...) somewhat artificial since it does not fully take into account the real struggle between nature and freedom. (shrink)

In A Theory of Justice (1971), John Rawls introduces the concept of “reflective equilibrium.” Although there are innumerable references to and discussions of this concept in the literature, there is, to the present author's knowledge, no discussion of the most important question: Why reflective equilibrium? In particular, the question arises: Is the method of reflective equilibrium applicable to the choice of this method itself? Rawls's drawing of parallels between Kant's moral theory and his own suggests that his concept of “reflective (...) equilibrium” is on a par with Kant's concept of “transcendental deduction.” Treating these two approaches to justification as paradigmatic, I consider their respective merits in meeting the reflexive challenge, i.e., in offering a justification for choice of mode of justification. My enquiry into this topic comprises three parts. In the first part (Eng 2014a), I raised the issue of the reflexivity of justification and questioned whether the reflexive challenge can be met within the framework of A Theory of Justice. In this second part, I shall outline a Kantian approach that represents a paradigmatic alternative to Rawls. (shrink)

I propose a method of assessing the degree of enlightenment of a society based on its discourses. My hypothesis is that the more objectivity prevails in a society’s spheres of discourse, the more enlightened it is; the more subjectivity dominates, the more unenlightened. This relationship can be made evident through the reconstruction of Kant’s Theory of Prejudice by taking into account the handwritten notes and fragments and the lectures on logic. First, I will discuss some key aspects of Kant’s concept (...) of prejudice. Secondly, I will address the epistemological function of the public sphere in order to show what conditions it must satisfy to fulfil its function. Thirdly, I will argue that not only Selbstdenken but also participatory reason, and therefore the public sphere itself, are both fundamental elements of enlightenment in that they function as counter-maxims against prejudice. (shrink)

This thesis aims to throw an illuminating light on the as yet neglected concept of nothing in Kant’s system, a concept which is taken into consideration, by Kant, in accordance with the guiding thread of the categories of the understanding. My main argument is that Kant has a fourfold division of nothing and each has a transcendental function in his system. This function is basically a limiting one; setting up negative determinations without which Kant’s system would have never been constituted (...) as it is now. It is shown in the thesis that the concept of nothing is divided basically into four: first, nothing as ens rationis that limits and thereby protects knowledge, secondly nothing as nihil privativum that defines the boundaries of phenomenal reality, thirdly nothing as ens imaginarium that makes possible the unity of experience and finally, nothing as nihil negativum that draws the lines of logical thinking. All make, in the last resort and by being the concepts of the opposite, experience possible. The thesis consists of four chapters. The first chapter is an exposition of all four divisions of nothing, the second is the display specifically of the concepts of ens rationis and nihil negativum, and the third is of the concepts of ens imaginarium and nihil privativum. The auxiliary argument of the thesis is that while Hegel makes a strong charge of externality against and thereby severely criticizes the Kantian concept of the thing-in-itself, - the concept of which I propose to be contained under the concept of ens rationis- Kant has equally convincing arguments against such a charge. This is the topic of the fourth and final chapter which has an implicit aim of creating the image of a powerful critical Hegel but on the other hand an equally enduring and war-like Kant. Kant is presented as a philosopher who has powerful responses to institute a balance between himself and his opponent. When Kant’s differing concepts of nothing are taken into account, Hegel’s attack of externality, it is maintained, appears not to have taken into account the full measure of the resources of the Kantian position. Even when it is said that the attack is against one specific concept of the thing-in-itself alone, Kant still seems to have enough resources for toleration and defence indeed. (shrink)