| This work is about logical necessity. Wittgenstein and Quine have claimed, in somewhat different senses, that logical laws are revisable. I examine this claim, and the differences between their views, in the context of more traditional views about the analytic/synthetic distinction and the definition of logical necessity. I support Wittgenstein.;The thesis has three quasi-independent parts, tied together by the following fairly loose pattern: chapter 3, containing original results in Boolean algebra, serves as an important example for the other two; chapter 2, primarily exegesis of Wittgenstein, provides me with some philosophical tools, to motivate chapter 3 and to contrast with the more main stream views in chapter 1; chapter 1 provides a context for the other two, a picture of an important part of the currently dominant form of inquiry, and some suggestions about how things could be different.;The introduction consists of some prefatory remarks which set the stage for the picture developed in chapter 1, and give explicit indications of my own views on the matter, and how I will treat it.;Chapter 1 is focussed around two definitions of logical necessity, a semantic definition and a syntactic or deductive one. Part 1 examines features common to both, when they are considered as dependent on human practices. Part 2 begins with a general discussion of the syntax/semantics distinction, and criticises the sharpness of the usual presentation of it and the associated neglect of pragmatics. It continues with separate discussions of the two definitions, in light of those criticisms. Finally, this is all related to the Wittgenstein/Quine criticism of the analytic/synthetic distinction.;Chapter 2 is devoted to exegesis of some of Wittgenstein's views about contradictions. The example of contradictions serves to focus his larger views about the revisability of logic, the 'motley' of mathematical techniques and the family of language-games.;Chapter 3 contains a development of formal techniques for revising classical propositional deductive structures. The classical calculus is shown to have no special position with respect to the revised structures. And the metatheory of the resulting systems is shown to be incomplete. |
