Ludovica Conti

This paper focuses on a lesser known version of abstractionism — called Arbitrary Logicism — which combines a deflationist account of abstraction and recent proposals about arbitrary reference. It makes explicit the relation of this proposal to canonical versions of Fregean abstractionist programs. In particular, Arbitrary Logicism will be tested against the epistemological claims of the abstractionist tradition, within which it emerges as an interesting alternative to Neologism and a direct heir to Frege’s Logicism.

The notion of isomorphism provides an important key to understand the picture theory of language, as given in Tractatus logico-philosophicus. This paper discusses the thesis of isomorphism between language and world, surveying a particular issue of Wittgenstein’s proposal, that is the issue about the notion of identity: if we accept an interpretation of the picture-theory as based on the isomorphism between the world and the language, the refusal of identity’s sign have to correspond to a parallel metaphisical rejection. This paper argues that this metaphysical rejection concern Leibniz’s law about the identity of indiscernibles.

I present the traditional debate about the so called explanation of Russell’s paradox and propose a new way to solve the contradiction that arises in Frege’s system. I briefly examine two alternative explanatory proposals—the Predicativist explanation and the Cantorian one—presupposed by almost all the proposed solutions of Russell’s Paradox. From the discussion about these proposals a controversial conclusion emerges. Then, I examine some particular zig zag solutions and I propose a third explanation, presupposed by them, in which I emphasise the role of an implicit premise in the derivation of the paradox. In conclusion, I propose a different zig zag solution obtained by the adoption of a negative free logic.