Logical Atomism’s Necessity

Abstract

This chapter highlights Russell’s original conception of logical atomism as a new and boldly scientific method in philosophy that makes Principia’s mathematical logic its essence and applies the logical forms uniquely revealed by Principia to undermine the metaphysician’s arguments for the ineliminability of abstract particulars and their specialized kinds of necessity. Philosophy, Russell explained, is the science of the possible. Wittgenstein expressed agreement in his Notes on Logic and in his Tractatus, proclaiming that the only necessity is logical necessity. I argue that the pristine form of logical atomism is not found in the 1918 lectures, but in Russell’s 1911 “Analytic Realism” and it finds its canonical articulation in his 1914 Our Knowledge of the External World As a Field for Scientific Method in Philosophy. The logical atomism lectures reflect Russell in flux, with his acquaintance epistemology at an impasse. Russell could not imagine how his multiple-relation theory, even amended by acquaintance with logical forms, could find the truth-bearers for general and molecular belief. Russell eventually turned, not to Wittgenstein, but to neutral monism and a tenuous alliance with behaviorism to get over the impasse. I offer hope of returning to Russell’s original acquaintance epistemology and its multiple-relation theory. I argue that modern so-called rival logics, relevant and modal, can be studied within Principia’s logic just as are rival geometries. Principia’s logic is an impredicative (simple) type theory and it studies relational structures by studying the way relations, exemplified or not, order their fields. Rival logics and non-logical necessities are simply distinct structures. Thus, in spite of its hostility to modern non-logical necessities (especially metaphysical necessity de re), Russell’s logical atomism remains the last and best hope for a genuinely scientific philosophy.