Twentieth-century philosophy

2. Logical structure and the limits of sense

By the outbreak of World War I, Russell had arrived at a conception of philosophical analysis and overall ontology according to which the world can be articulated into simple, individual constituents which are independent of one another, and which it is the goal of analysis to elicit and clarify. For Russell, at least some of these constituents were simple elements of perceptual experience – so-called “sense data” – while others were universals or general attributes or properties. This conception – what Russell called in a series of lectures during the war “logical atomism” – was decisively influenced by the closely related conception of the young Ludwig Wittgenstein, who had appeared in Cambridge in 1911 to pursue questions of logic with Russell. Wittgenstein’s powerful and terse treatise, the Tractatus Logico-Philosophicus, was composed partly as he served in the war, although it was only published in 1921. The Tractatus saw language and the world as sharing the underlying structure of what Wittgenstein called “logical form.” By means of a symbolism which made logical form perspicuous, sentences and facts could be jointly analyzed into their logically simple constituents.

Despite the reductive and analytic approach of this project, its development was already strongly marked by critical reflection about the totality and limits of language and thought. In the Tractatus, Wittgenstein held that “all philosophy is a ‘critique of language’,” (Wittgenstein 1922, 4.0031), one of its central aims being to trace from within the limits of meaningful language and thereby to clarify the boundaries of possible thought. After 1906 or so, when Husserl developed the new methodology of “epoché” or “bracketing” of the natural attitude to gain access to the contents of experience and thought, he increasingly identified phenomenology as a variety of transcendental idealism, seeing it as, at least in part, an inquiry into the “constitution” or production of sense and meaning by a “transcendental” subjectivity outside the world (see Phenomenology, epistemic issues in). Even earlier, already in 1901, considerations about the limits of the coherently thinkable had led Russell to discover a fundamental paradox which was widely taken to ruin Frege’s project of logicism. This was Russell’s paradox of the set of all sets that are not members of themselves (see Paradoxes of set and property). If, as Russell’s paradox seemed to show, it is impossible for such a set, or indeed a totality of all sets, to exist or be thought of as a coherent whole, then the definitions required for logicism to succeed could not go through without further restrictions, and its hope of clarifying mathematical reality by means of a naïve appeal to logic and set theory would appear to be fundamentally disappointed.