In this paper, I seek to clarify an aspect of Frege's thought that has been only insufficiently explained in the literature, namely, his notion of logical objects. I adduce some elements of Frege's philosophy that elucidate why he saw extensions as natural candidates for paradigmatic cases of logical objects. Moreover, I argue (against the suggestion of some contemporary scholars, in particular, Wright and Boolos) that Frege could not have taken Hume's Principle instead of Axiom V as a fundamental law of (...) arithmetic. This would be inconsistent with his views on logical objects. Finally, I shall argue that there is a connection between Frege's view on this topic and the famous thesis first formulated in ‘Über Begriff und Gegenstand’ that ‘the concept horse is not a concept’. As far as I know, no due attention has been given to this connection in the scholarly literature so far. (shrink)

Translation of Frege's 'Über Begriff und Gegenstand' (1892). Translation by Peter Geach, revised by Max Black.

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized as the (...) most powerful presentation yet of a neo-Fregean program. (shrink)

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

Die Grundlagen der Arithmetik. Eine Ionisch mathematische UoterciicboDn über den Begriff der Zahl Dr. 0. Frege, ao Profeuor an der Univer»ität Jena. -. ...

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

The dissertation is an inquiry into the ontology and epistemology of numbers. As regards the former, the Fregean conception of numbers as objects and the Russellian conception of numbers as higher-level entities are both critically examined. A conception of numbers as modes of existence , that is, ways or manners in which things exist, is introduced and defended instead. As regards the latter, the basic concepts of arithmetic are explicated in terms of pure logic alone, and all the truths of (...) arithmetic are shown to follow from those explications solely by logical means. A new version of logicism in the philosophy of arithmetic is thereby established. (shrink)

Frege held various views about language and its relation to non-linguistic things. These views led him to the paradoxical-sounding conclusion that "the concept horse is NOT a concept." A key assumption that led him to say this is the assumption that phrases beginning with the definite article "the" denote objects, not concepts. In sections I-III this issue is explained. In sections IV-V Frege's theory is articulated, and it is shown that he was incorrect in thinking that this theory led to (...) the conclusion that "the concept horse is not a concept." Section VI goes on to show that his strict theory about the functioning of ordinary language is inconsistent. Sections VII-VIII investigate Frege's reasons for thinking that "the concept horse" must denote an object; these reasons are not adequate on Frege's own grounds. Section IX sketches a systematic way to allow such phrases to denote concepts (not objects) within the framework of Frege's main views about language. Section X comments briefly on the consequences of this idea for his logistic program. (shrink)