Russell's second paradox: a dialectical analysis of 'On denoting'

Abstract

Analytical philosophers are used to assume, as a matter of course, that any sound analysis must be un-dialectical. This tenet is based on the axiom of absolute identity or external difference: nothing can differ from itself; nothing can assume different forms. Eventually, this axiom leads to the belief that any real opposition or irreducible two-sidedness is logically impossible. This thesis is an attempt to prove the fertility of a “dialectical” analysis, i.e. an analysis based on paying due attention to the universal, i.e., logical, existential and historical importance of oppositions.

This approach is applied to a much-discussed and vexed issue in the history of early analytic philosophy, namely Russell’s famous article On Denoting and more in particular the so-called Gray’s Elegy Argument (GEA) contained in it.

This leads to the following results: 1) Both the kernel of truth contained in Russell’s “official story” about the genesis of the Theory of Descriptions (ToD) can be made intelligible and its ideological distortion of the historical facts revealed by the manuscript On Fundamentals. The GEA’s problem occasioned the ToD’s conception, but thwarted its adoption. That is why it had to be “forgotten”. 2) In the GEA, the point of view subjected to criticism is neither purely Russellian, nor purely Fregean, but quasi-Fregean. 3) Without taking into account the axiom of external difference, the GEA cannot be understood. For it proves that meaningful denoting is incompatible with the said axiom. If the latter is taken for granted, the GEA seems to disprove the logical possibility of denoting. But it can and must be construed in a different way: as disproving the validity of the axiom of external difference. This perspective reveals an unsuspected kinship between Russell’s paradox and the problem of denoting. The latter deserves to be called Russell’s second paradox.