Russell’s metaphysical logic. (English) Zbl 0981.03004

Linsky, Bernard

CSLI Lecture Notes. 101. Stanford, CA: CSLI Publications. viii, 150 p. (1999).

The author asks about the relation between B. Russell’s logical and metaphysical views. He maintains: “Russell did not view logic as an uninterpreted calculus waiting for many interpretations. Rather, for Russell, logic is a single ‘interpreted’ body of a priori truths, of propositions rather than sentence forms” (pp.5-6). The author’s thesis is “that Russell’s logical and metaphysical views are not only compatible, but that his metaphysics and logic inform each other” (p.6). He argues for this thesis by investigating into several topics, e.g., the role of propositional functions and propositions in Russell’s logical theory, especially in Principia mathematica (chapters 2 and 3), his attempts to avoid paradoxes by proposing a ramified theory of types (chapters 4 and 5), the special nature of the axiom of reducibility and its relation to semantics (ch.6), and several forms of logical constructions (ch.7).

Reviewer: Volker Peckhaus (Erlangen)

MSC:

03-03	History of mathematical logic and foundations
03A05	Philosophical and critical aspects of logic and foundations
01A60	History of mathematics in the 20th century
03-02	Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations

Keywords:

logicism; substitutional theory; type theory; axiom of reducibility; Grelling’s paradox; semantic paradoxes