Showing papers on "Paraconsistent logic published in 1979"

The logic of paradox

Abstract: The purpose of the present paper is to suggest a new way of handling the logical paradoxes. Instead of trying to dissolve them, or explain what has gone wrong, we should accept them and learn to come to live with them. This is argued in Sections I and II. For obvious reasons this will require the abandonment, or at least modification, of 'classical' logic. A way to do this is suggested in Section III. Sections IV and V discuss some implications of this approach to paradoxes.

Information-seeking dialogues: Some of their logical properties

Abstract: The dialogical games introduced in Jaakko Hintikka, “Information-Seeking Dialogues: A Model,” (Erkenntnis, vol. 14, 1979) are studied here to answer the question as to what the “natural logic” or the logic of natural language is. In a natural language certain epistemic elements are not explicitly indicated, but they determine which inference rules are valid. By means of dialogical games, the question is answered: all classical first-order rules have to be modified in the same way in which some of them are modified in the transition to intuitionistic logic. (Furthermore, in some cases quantificational rules have to be modified further.) The rules that are left unmodified by intuitionists are applicable only to the output of certain game rules, but not to others. In. this sense, neither classical nor yet intuitionistic logic is the logic of natural language. We need a new type of nonclassical logic, justified by our information-seeking dialogues.

The Logic of Hegel's Logic

Abstract: ONE OF THE PROBLEMS involved in doing the history of philosophy is reinterpreting past philosophers in such a way that the relevance of their work to contemporary discussion can become clear. In doing so one often finds that certain doctrines to which a philosopher himself attached great significance may not be central to a particular line of his argument. Recent efforts at interpreting Kant have attempted, for example, to disentangle the objectionable part of the Kantian metaphysics from the \"object ive\" argument contained therein. The whole doctrine of transcendental psychology in Kant's first Critique, for example, may perhaps be shelved without injuring the rational core of the argument. With Hegel, however, the case seems prima facie more difficult, since Hegel's whole system is seemingly tied down to a very obscure metaphysics, that of the \"Wor ld Spirit .\" However, just as not all of Kant's doctrine is necessary to his philosophy, perhaps not all of Hegel's philosophy is inextricably bound up with commitment to such shadowy entities. In this paper I would like to try to draw out the central argumentative core of Hegel's Science oj Logic. To do this, I will first sketch briefly what Hegel takes to be the goal of such a theory. Second, I will outline the basic logical structure of the work. The result will be, it is hoped, a presentation of Hegel's philosophy that will make it not the obscure confidant of World Spirit, but rather one not far from contemporary concerns.

A new classical relevance logic

Abstract: The system C of Pottinger (1974) has as primitive logical constants = (entailment), -9 (S4 strict implication), -, (relevant implication), D (intuitionist implication), & (intuitionist conjunction), v (intuitionist disjunction), and A (absurdity). In Section 8 of Pottinger (1974) it was pointed out that the addition of either 2-A A or 2B 2A .A B2 to C collapses -* into material implication and that the addition of either 21A * A or