Thought: A Journal of Philosophy, EarlyView.

I offer an analysis of the sentence "the concept horse is a concept". It will be argued that the grammatical subject of this sentence, "the concept horse", indeed refers to a concept, and not to an object, as Frege once held. The argument is based on a criterion of proper-namehood according to which an expression is a proper name if it is so rendered in Frege's ideography. The predicate "is a concept", on the other hand, should not be thought of (...) as referring to a function. It will be argued that the analysis of sentences of the form "C is a concept" requires the introduction of a new form of statement. Such statements are not to be thought of as having function--argument form, but rather the structure subject--copula--predicate. (shrink)

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. (shrink)

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. (shrink)

In [Boccuni 2010], a predicative fragment of Frege’s blv augmented with Boolos’ unrestricted plural quantification is shown to interpret pa2. The main disadvantage of that axiomatisation is that it does not recover Frege Arithmetic fa because of the restrictions imposed on the axioms. The aim of the present article is to show how [Boccuni 2010] can be consistently extended so as to interpret fa and consequently pa2 in a way that parallels Frege’s. In that way, the presented system will be (...) compared with the system pe in [Ferreira 2018] and some relevant differences between the two will be highlighted. (shrink)