The Russell-Wittgenstein Theory of Symbolism

In his article “Criticism of the Theory of Types in the Early Wittgenstein's Philosophy”, Vsevolod Ladov attributes the following two claims, inter alia, to Russell: (1) Some sentences of natural language, such as “This sentence is false”, are paradoxical. (2) The existence of paradoxical sentences is a flaw of natural language that should be fixed. According to Ladov, these claims motivated the development of the theory of types by Whitehead and Russell, so this theory was worked out as a tool for improving natural language. Ladov contrasts this position with the early Wittgenstein's theory of symbolism according to which paradoxes cannot be formulated in natural language because the intrinsic logical syntax of natural language makes this impossible. Ladov concludes that Wittgenstein's theory of symbolism is a more radical version of hierarchical approach to paradoxes than Whitehead and Russell's theory of types. I challenge attribution of (1) and (2) to Russell and show that the type theory by Whitehead and Russell, on the one hand, and Wittgenstein's theory of symbolism, on the other hand, share the following claims: 1) The hierarchical logical syntax preventing self-referential expressions is intrinsic to natural language. 2) Since self-reference is a necessary condition of paradoxes like the Liar paradox, they cannot be formulated in natural language. 3) The paradoxical character of sentences like “This sentence is false” is an illusion. The conjunction of these claims can be named the “Russell-Wittgenstein theory of symbolism”. So I also challenge Ladov's claim that there is a deep difference between these theories with respect to the problem of paradoxes. Finally, I challenge two tenets from Wittgenstein's Tractatus that are frequently reproduced in literature: the tenet that the theory of types depends on semantics and the tenet that the theory of types is confined to the prevention of self-reference.

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