Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation (...) to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper. (shrink)

Although the notion of logical object plays a key role in Frege's foundational project, it has hardly been analyzed in depth so far. I argue that Marco Ruffino's attempt to fill this gap by establishing a close link between Frege's treatment of expressions of the form ‘the concept F’ and the privileged status Frege assigns to extensions of concepts as logical objects is bound to fail. I argue, in particular, that Frege's principal motive for introducing extensions into his logical theory (...) is not to be able to make in-direct statements about concepts, but rather to define all numbers as logical objects of a fundamental kind in order to ensure that we have the right cognitive access to them qua logical objects via Axiom V. Contrary to what Ruffino claims, reducibility to extensions cannot be the ‘ultimate criterion’ for Frege of what is to be regarded as a logical object. (shrink)

Matthias Schirn has argued on a number of occasions against the interpretation of Frege's ``objects of a quite special kind'' (i.e., the objects referred to by names like `the concept F') as extensions of concepts. According to Schirn, not only are these objects not extensions, but also the idea that `the concept F' refers to objects leads to some conclusions that are counter-intuitive and incompatible with Frege's thought. In this paper, I challenge Schirn's conclusion: I want to try and argue (...) that the assumption that `the concept F' refers to the extension of F is entirely consistent with Frege's broader views on logic and language. I shall examine each of Schirn's main arguments and show that they do not support his claim. (shrink)

In this paper I discuss Frege's distinction between objects and concepts and suggest a solution of Frege's paradox of the concept horse. The expression ''the concept horse'' is not eliminated and the concept is not identified with its extension, but the concept is identified with the sense of the corresponding predicate. This solution fits better into a fregean ontology and philosophy of language than alternative solutions and allows for a general answer to the question why Frege's system is infected with (...) Russell's paradox. Russell's paradox is caused by the reification of a concept. Certain problems of modern set theory seem to have a similar cause.Eine weithin sichtbare Warnungstafel muss aufgerichtet. (shrink)

After describing the philosophical background of Kerry’s work, an account is given of the way Kerry proposed to supplement Bolzano’s conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege’s work and Kerry’s views were then attacked by Frege.The following two issues were central to this controversy: the relation between the content of a concept and the object of a concept; the logical roles of the definite article.Not only did Frege in (...) 1892 offer an unconvincing solution to Kerry’s puzzle concerning “the concept horse” but he also overlooked the many criticisms levelled by Kerry against the notion of an extension on which his own definition of number was based. (shrink)

After describing the philosophical background of Kerry's work, an account is given of the way Kerry proposed to supplement Bolzano's conception of logic with a psychological account of the mental acts underlying mathematical judgements.In his writings Kerry criticized Frege's work and Kerry's views were then attacked by Frege.The following two issues were central to this controversy: (a) the relation between the content of a concept and the object of a concept; (b) the logical roles of the definite article. Not only (...) did Frege in 1892 offer an unconvincing solution to Kerry's puzzle concerning 'the concept horse' but he also overlooked the many criticisms levelled by Kerry against the notion of an (indefinite) extension on which his own definition of number was based. (shrink)

Gottlob Frege sostuvo que las palabras-concepto sólo se refieren a conceptos no a objetos y que los términos singulares se refieren sólo a objetos no a conceptos. Estas tesis dan lugar a la paradoja del concepto, de acuerdo con la cual ‘el concepto F’ no se refiere a ningún concepto. Mark Textor sostiene que su principio del espejar explica el origen del problema. Sin embargo, argumento que su artículo no explica todas las consecuencias de las tesis de Frege y mi (...) supuesto semántico ontológico puede verse como una consecuencia del principio del espejar de Textor. (shrink)

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.