Generally, the theory, consisting of standard second-order theory and Hume’s Principle, is called Frege Arithmetic. However, Frege Theorem doesn’t amount to the establishment of Frege’s Logicism, because neither Hume’s Principle is considered as analytical truth, nor is second-order logic as logic in strict sense. Most challenges to second-order logic are related with its comprehension axiom, w...

The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of p...

In what follows this assertion will be called the identifiability thesis since it states that two arbitrary but different courses-of-values can be identified with the truthvalues. Frege considers the identifiability thesis a consequence of his previous argumentation ([3], p. 17, lines 23-36) which, following Dummett ([1], p. 408), will be called the permutation argument, because the concept of ...

ion is no patch, for the notion of numerical equivalence onto which it is to converge must presuppose a notion of number such that distinct numbers, given by distinct numerical symbols, can be the same number. This is to be the accomplishment of abstraction, by which, Frege says, “things are supposed to become identical by being equated.” But how can abstraction, a “capability of the human mind...

The name ‘Frege’s principle’ is well known: it is discussed, obeyed or rejected in philosophy, linguistics, logic and computer science (see e.g. [33] and[45]). Surprisingly, two completely different principles which are denoted by that name. In most fields it refers to ‘the principle of compositionality of meaning’: The meaning of a compound expression is a function of the meaning of its parts ...

We investigate the proof complexity of a class of propositional formulas expressing a combinatorial principle known as the KneserLovász Theorem. This is a family of propositional tautologies, indexed by an nonnegative integer parameter k that generalizes the Pigeonhole Principle (obtained for k = 1). We show, for all fixed k, 2Ω(n) lower bounds on resolution complexity and exponential lower bou...

Abstract Hybrid expressivists claim to solve the Frege–Geach problem by offloading explanation of logico-semantic properties moral sentences onto belief-components hybrid states they express. We argue that this strategy is undermined one expressivism's own commitments: That truth belief-component neither necessary nor sufficient for state it composes. articulate a new approach. Instead explaini...

El presente artículo tiene como principal objetivo introducir al lector algunos de los conceptos fundamentales la filosofía Gottlob Frege. Estos son: el binomio sentido/referencia, valor veritativo oraciones con elementos no referenciales, distinción entre pensar, juzgar y aseverar, su concepción indéxicos demostrativos, así defensa existencia un tercer reino. En ellos se mostrarán algunas prob...

By a well-known result of Cook and Reckhow [4, 12], all Frege systems for the Classical Propositional Calculus (CPC ) are polynomially equivalent. Mints and Kojevnikov [11] have recently shown p-equivalence of Frege systems for the Intuitionistic Propositional Calculus (IPC ) in the standard language, building on a description of admissible rules of IPC by Iemhoff [8]. We prove a similar result...