A selection of the writings of Wittgenstein in the philosophy of logic and mathematics written in the years 1937-1944. There is no concern with the foundations of mathematics in the sense of metamathematics nor in the sense of investigation of the possibility of providing secure axiomatic foundations for such notions as that of "set." Indeed, the original motives for these latter investigations are rejected; instead, a clarification of the grammar of mathematical propositions is sought. The author discusses the notions of (...) mathematical proof at length and attacks both the Russellian view that mathematics is an appendage of logic and Hilbert's program of proof-theory.--W. T. (shrink)

Elaborates a system of logic designed to provide an adequate framework for the extreme empiricist principles of Logical Positivism--a task which, the author argues, klassische Logistik is incapable of fulfilling. Interesting features of this system include its lack of type distinctions and its departure from the usual theory of propositional functions and quantifiers--there is, in particular, no negation, and no analogue either of material implication or of universal quantification, though, in certain cases, the effect of the universal quantification of an (...) implication can be obtained.--W. T. (shrink)

The first volume of a projected two-volume work in mathematical logic. Along with an introduction containing brief but careful and remarkably compact discussions of such topics as the kinds of expressions occurring in formalized language, the logistic method, syntax, and semantics, the book comprises clean and precise treatments of the propositional calculus, and first- and second-order functional calculi, including parenthetical remarks about the intended semantical interpretations of these calculi, some development of the calculi themselves, and discussions of completeness and consistency. (...) A great number of exercises are included, ranging from elementary exercises in technique to brief sketches of theories not treated in the text.--W. T. (shrink)

A selection of the published papers of Russell on the subjects of logic and epistemology. Included are "The Philosophy of Logical Atomism," "On Denoting," and "Mathematical Logic as Based on the Theory of Types." Each essay is preceeded by some remarks by the editor on the context and history of the essay.--W. T.

Translations, from French, German, and Polish originals, of most of Tarski's prewar papers on the subjects mentioned in the title, including the well-known "Der Wahrheitsbegriff in den formalisierten Sprachen." Tarski has provided, for this volume, a number of cross-references among the papers included, and some footnotes indicating later developments in the subjects treated. In two of the papers, the text itself has been added to.--W. T.

A number of systems of logic, including formulations of the two-valued propositional logic, alethic modal propositional logics and deontic modal propositional logics, are described and discussed with the aim of utilizing some of these systems for the sociological analysis of normative structures. Evidence is adduced that certain normative concepts are explicated or partially explicated in these systems.--W.T.