The phenomenon of self-reference combines self-refutation in the case of Plato’s critics of Protagoras in “Theaetetus” and self-predication in the case of a difficulty which Plato himself faces developing the theory of ideas in “Parmenides”. The author of the article asserts that self-predication does not produce a negative impact on Plato’s metaphysics and in no way destroys the integrality of Plato’s philosophy: It is logically correct as are both his criticism of Protagoras’ relativism and the theory of ideas.

In his article, Vsevolod Ladov poses an important question – might paradoxes admit of a uniform solution? As an answer, I propose looking at an approach in which it is argued that we must recognize the truth predicate as merely analogous to a vague predicate. The proponents of this approach (V. McGee, J. Tappenden, H. Field, G. Priest and D. Hyde) insist that there is a structural relation between sorites paradoxes and self-reference paradoxes and that they should have (...) a unified solution. (shrink)

The article contains a critical analysis of Wittgenstein’s theory of logical symbolism. According to an influential interpretation, Wittgenstein presented in the Tractatus a new method of solving paradoxes. This method seems a simple and effective alternative to Russell’s type theory. Wittgenstein’s theory of logical symbolism is based on the requirement of clear notation and the context principle: the type of a symbol only “shows” itself in the way we use the signs of our language. The function sign φ(φx) does not (...) express any paradox, because the syntactic rules for its use, written in clear notation, should “show” us that φ(φx) = ψ(φx). Many researchers (Davant, Ishiguro, Mounce, Ruffino, Friedlander, Jolley, Livingston, Ladov, et al.) follow this interpretation. However, the difficulty of such a view on Wittgenstein’s theory of logical symbolism is that there hides the fallacy of petitio principii. Indeed, in examples of a functional sign of the form φ(φx), we are interested not only in the question of whether the functions φ are different symbols, but also in how this functional sign φ(φx) itself excludes the symbolization of the same object by different ways. This interpretation is contrasted with the idea that Wittgenstein’s theory of logical symbolism is in fact a modified analogue of Russell’s simple theory of types. The reciprocality principle becomes the core of Wittgenstein’s theory: the combinatorial potential of the “prototype” of a functional sign is identical to the combinatorial potential of the “prototype” of an argument. According to Wittgenstein, only describing the combinatorial potential of linguistic expressions (symbols) can vanish the illusion of paradoxes. The function cannot be its argument, because the function sign φ(φx) already contains the “prototype” of its argument, “showing” us that φ(φx) = φx. The correctness of this interpretation does not exclude the possibility that the differences between Russell and Wittgenstein are in fact nothing more than façon de parler. (shrink)