Online research in philosophy

Abstract In ?Beyond the Myth of the Myth: A Kantian Theory of Non-Conceptual Content?, Robert Hanna argues for a very strong kind of non-conceptualism, and claims that this kind of non-conceptualism originally has been developed by Kant. But according to ?Kant?s Non-Conceptualism, Rogue Objects and the Gap in the B Deduction?, Kant?s non-conceptualism poses a serious problem for his argument for the objective validity of the categories, namely the problem that there is a gap in the B Deduction. This gap is that the B Deduction goes through only if conceptualism is true, but Kant is a non-conceptualist. In this paper, I will argue, contrary to what Hanna claims, that there is not a gap in the B Deduction.

James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, and it suggests an interesting reason why the rewriting might have been thought necessary.

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian.

(Uncorrected OCR) AB S TRACX Abstract of thesis entitled 'Wittgenstein and the Justification of Deduction' submitted by CHAN Ho Mun for the Degree of Master of Philosophy at the University of Hong Kong in April 1987 The central philosophical problem of this thesis is the justification of deduction. It is argued that the problem is closely related to the nature of rule-following, meaning and understanding, the discussion of which figures prominently in the writings of Ludwig Wittgenstein. The aim is to approach the problem through the writings of Wittgenstein. The present work can also be regarded as an exposition of his ideas on meaning, rules and understanding. It can be shown that Wittgenstein's early solution to the problem is a semantical one. The central thesis of this solution is: the validity of logical inference is justified by the senses of the propositions involved. This leads him to think that an account of the nature of logic requires a theory of sense which serves to explain logical relations (e.g. consequence and i contradiction) between propositions. The appreciation of this line of thought is very crucial for the understanding of Wittgenstein's early work, for it is indeed the historical and theoretical entry point into his early philosophy. It was admitted by Wittgenstein himself that his early philosophy is the best alternative to his later philosophy, and indeed his early solution to the problem is a very good one. However, Wittgenstein came to think, with very good reasons, that it was wrong. His objection to the early solution deserves a detailed examination, and I attempt to provide one here. In his so-called 'transitional period', Wittgenstein begins to reject his early theory of sense, and finally the whole semantical approach is repudiated. This volte face stems from his diagnosis of misconceptions about meaning, rules and understanding, some of which are present in his early work. Yet this does not mean that Wittgenstein has another solution to the problem of deduction. Based on his later ideas on meaning, rules and understanding, and his later philosophy of logic, it can be shown that deduction needs no justification and that the sceptical doubt about the possibility of justification is misplaced. In other words, Wittgenstein does not answer the problem, but shows how it may be eliminated. ii.

Kant wrote two versions of the Transcendental Deduction, the first, “A-”Deduction in 1781, and the second, “B-”Deduction in 1787. Since Henrich's “The Proof Structure of Kant's Transcendental Deduction”, most work on the Transcendental Deduction attempts to make sense of the B-Deduction's two-step argument structure. Though the A-Deduction has suffered comparative neglect, it has received some attention from interpreters who take its extended treatment of the “subjective” side of cognition to amount to a brand of proto-functionalism. Whatever the merits and demerits of these proto-functionalist approaches, they tend to deemphasize the two arguments that constitute the “objective” side of the A-Deduction, the “argument from above” and then the “argument from below”. Since Kant himself refers to this objective side of the A-Deduction as the “Deduction of the Pure Concepts of the Understanding”, it is surprising that the structure of these arguments has not received closer scrutiny. This is doubly true since Kant actually claims that his revisions for the 1787 version of the Deduction impacted only the “presentation” of it. Any lessons learned from the central arguments of the A-Deduction should help clarify the structure of its younger and more closely studied brother.

This book is a foray into the thorny interpretive issue of what to make of Kant's so-called "Metaphysical Deduction" of the categories. As with many of the arguments in the first Critique, the claim of the Metaphysical Deduction is easier to make out than its argument. The claim is that by some or other reference to "general logic," one may obtain a "transcendental logic," i.e., a justification (or "deduction") of the categories (of the understanding) necessary to the (very) possibility of experience. But how? By, Kant says, discerning, in general logic, a "clue" to transcendental logic. But what sort of clue? And then what clue exactly? We need a meta-clue to get a clue.Herein lies the very mixed reception the ..

The author presents a deduction system for Quantum Logic. This system is a combination of a natural deduction system and rules based on the relation of compatibility. This relation is the logical correspondant of the commutativity of observables in Quantum Mechanics or perpendicularity in Hilbert spaces.Contrary to the system proposed by Gibbins and Cutland, the natural deduction part of the system is pure: no algebraic artefact is added. The rules of the system are the rules of Classical Natural Deduction in which is added a control of contexts using the compatibility relation.

Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of the method to a generation of philosophers?with an eye to determining what the ?essential characteristics? of natural deduction are.