Russell's Paradox and Some Others

(1) In a recent paper (1972 ¹ ) I argue (i) that a language which makes possible the characteristically human form of social life must allow for talk not only about its own sounds, but also about communication by means of those sounds, (ii) that failure to recognise this had led many philosophers into a dangerous confusion between sentences and propositions, (iii) that attempts to formulate logic as a theory of grammatically well-formed sentences involve neglect of the token-reflexive device and misunderstanding of the role of definite descriptions and (iv) that the paradox of the Liar holds no terrors for those who realise how the notion of truth is related to that of a proposition. My reason for concluding with an attempt to solve the old problem by means acceptable to a student of natural languages was, of course, a wish to counter Tarski’s thesis that natural languages are all inconsistent through failure of their users to observe the distinction between language and metalanguage which he considers essential for solution of the Liar paradox. But it may be of interest to show that similar methods are sufficient for solution of Russell’s paradox and some others that were formulated in the early years of this century during debates on the theories of Cantor and Frege.