Developments in Logic: Carnap, Gödel, and Tarski

Georg Schiemer (lmu Munich) Semantics in Type Theory

Logical type theory was first introduced in Russell & Whitehead’s Principia Mathematica (1910-1913) and then modified substantially in the 1920s and 30s by Ramsey, Carnap, Gödel, and others. In that period, it was no longer conceived primarily as a foundational system in Russell’s original sense but rather as the “natural” system of logic with several non-foundational applications in mathematic...

- 1 - Carnap and Modern Logic 1 Erich

A distinguishing feature of analytic philosophy, or at least of one central strand in it, is the use of modern logic for the purpose of clarifying and solving philosophical problems. The most prominent figure in this tradition was Bertrand Russell; and second only to Russell was Rudolf Carnap. Directly and strongly influenced by Russell, Carnap passed on this influence to legions of later philo...

Logic in the 1930s: type theory and model theory

In historical discussions of twentieth-century logic, it is typically assumed that model theory emerged within the tradition that adopted first-order logic as the standard framework. Work within the type-theoretic tradition, in the style of Principia Mathematica, tends to be downplayed or ignored in this connection. Indeed, the shift from type theory to first-order logic is sometimes seen as in...

Consequence & Inference

Logic is usually considered to be the study of logical consequence – of the most basic laws governing how a statement’s truth depends on the truth of other statements. Some of the pioneers of modern formal logic, notably Hilbert and Carnap, assumed that the only way to get hold of the relation of consequence was to reconstruct it as a relation of inference within a formal system built upon expl...

First Order Logic and Gödel Incompleteness