LOGICAL ATOMISM

Although mostly associated with the logical analysis of language, analytic philosophy began in the philosophy of mathematics. Working independently, both Gottlob Frege and Bertrand Russell pursued programs of reducing mathematics to logic, and the philosophical motivations behind these projects were to find broader application. The most important was the rejection of psychologism—the idea that logical objects are reducible to mental activity —and hence the careful distinction between the (objective) semantic content of a proposition and the (subjective) activity of, for example, believing that proposition. Thus, Frege was to distinguish between the sense and reference of a denoting concept—the former being the way in which the latter was “presented” to a competent speaker of the language—which explained how identifying statements (“Hesperus is Phosphorus”) could nevertheless be surprising. Russell proposed that denoting concepts was ultimately reducible to definite descriptions that contained only logical proper names, which explained how statements about non-existing entities (“the present King of France”) could nevertheless be meaningful. This approach culminated in Wittgenstein’s Tractatus Logico-Philosophicus (1921), which argued that every meaningful proposition must have a precise logical structure, and that this structure mirrors the logical structure of the world.