More than two decades ago, Vann McGee presented an alleged counterexample to modus ponens (MP). Despite criticisms, it seems to have survived to date. In this paper, I will defend McGee's counterexample against the criticism by Bernard Katz, as a representative of a type of the defense of MP, which appeals to certain logical principles, or what I call the logical defense of MP. I will argue that his way of criticizing McGee, and therefore of defending MP, actually begs the question. I will conclude that, the logical defense of MP in general will inevitably beg the question, and hence is doomed to fail. (This paper, together with my (2009), constitutes a part of my project on indicative conditionals, which is itself a part of the larger project on the theory of knowledge and belief change.)
Jonathan Bennett, in his (2003), says that for indicative conditionals the unrestricted form of modus ponens (MP) is not valid, but restricted MP is still valid. In this paper I argue that Bennett is wrong, that even the restricted form of MP fails for indicative conditionals. I will show this by constructing, from his own counterexample to other formal properties of indicatives, a counterexample which is immune to the types of criticism that Bennett launches against the famous counterexample to MP by Vann McGee. I will also show that this type of failure of MP can be confirmed visually by a new but natural reading of the Adams-style Venn diagram.
Quantum mechanics is widely believed to be inconsistent with local realism because J.S. Bell proved the contradiction between quantum mechanics and the hidden variable theories based on reality and locality of matter. As described herein, the relation between quantum mechanics and local realism is discussed. This paper presents the question of whether any version of local realism is contradicted by quantum mechanics. The answer is negative. An interpretation is proposed by which the contradiction is explained using physical variables of two types: (1) physical variables of the first type, such as positions and angles (i.e. coordinates), are realistic variables and always possess definite values independently of measurements; (2) those of the second type, such as momenta, angular momenta, and spins (i.e., conserved quantities), are non-realistic variables, which possess no value before measurement. Value definiteness of the first type provides a reliable basis to physical reality of matter, and non-reality of the second type might solve the problem of inconsistency between quantum mechanics and local realism.
In order to deal with Kochen and Specker's no-go result, van Fraassen invoked 'splitting' of non-maximal observable depending on 'context'. In his contextual approach there are different physical quantities corresponding to a non-maximal operator. Such physical quantities are different, so those values are not required to coincide. However, Heywood and Redhead showed the impossibility of local truth-value assignment in contextual approach. Their argument is restricted to finite dimensional and non-relativistic case. In this paper we shall show a similar no-go result in more general framework (von Neumann algebra). Also, our result will be applied to Algebraic quantum field theory.