Frege. Jena, Forstweg To the Volunteer. Ludwig Wittgenstein 10 Frege is referring here to his essay “Der Gedanke, ein Logische Untersuchung”. show how this theory developed between the early Grundlagen der. Arithtnetik and the late essay Der Gedanke. This much is of merely exegetical interest, but it . PDF | Michael Dummett has advanced, very influentially, the view that Frege. expresses this in his most important paper,. 'Der Gedanke'.
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PDF | The founder of modern logic and grandfather of analytic philosophy was 70 years old when he published his paper 'Der Gedanke' (The Thought) in Back to Entry · Entry Contents · Entry Bibliography · Academic Tools · Friends PDF Preview · Author and Citation Info; Back to Top Complete Chronological Catalog of Frege's Work; Locations of English Gall and E. Winter, Die analytische Geometrie des Punktes und der Geraden und ihre .. [a] 'Der Gedanke. Der Gedanke kann also nicht die Be- deutung des Satzes sein, vielmehr werden wir ihn als den Sinn aufzufassen haben. Wie ist es nun aber mit der Bedeutung.
Translated in part in Geach and Black.
Chronological Catalog of Frege's Work
Translated by A Quinton and M. Quinton, , in Mind 65, — Hermes et al.
Hermes et al, pp. Google Scholar Geach, P. Google Scholar Hermes, H. Long and R. White, University of Chicago Press, Chicago.
Google Scholar Husserl, E. Reprinted in , Philosophie der Arithmetik, Husserliana Vol. The latter volume contains additional texts from — References in this paper are to the translation of the second edition of this work by J. The second German edition was published in two parts in and Translated by Q.
The Philosophy of Arithmetic: Frege and Husserl
Translated by F. Translated by D. References are to the translation. Landgrebe, Claassen, Hamburg. Translated by J.
Churchill, and K. Google Scholar Kreisel, G.
Lakatos ed. Google Scholar Mohanty, J. Google Scholar Resnik, M. Google Scholar Sluga, H.
Google Scholar Tieszen, R. The Begriffsschrift broke new ground, including a rigorous treatment of the ideas of functions and variables.
Frege's goal was to show that mathematics grows out of logic , and in so doing, he devised techniques that took him far beyond the Aristotelian syllogistic and Stoic propositional logic that had come down to him in the logical tradition. Title page to Begriffsschrift In effect, Frege invented axiomatic predicate logic , in large part thanks to his invention of quantified variables , which eventually became ubiquitous in mathematics and logic, and which solved the problem of multiple generality.
Previous logic had dealt with the logical constants and, or, if A frequently noted example is that Aristotle's logic is unable to represent mathematical statements like Euclid's theorem , a fundamental statement of number theory that there are an infinite number of prime numbers.
Frege's "conceptual notation", however, can represent such inferences.
One of Frege's stated purposes was to isolate genuinely logical principles of inference, so that in the proper representation of mathematical proof, one would at no point appeal to "intuition". If there was an intuitive element, it was to be isolated and represented separately as an axiom: from there on, the proof was to be purely logical and without gaps.
Having exhibited this possibility, Frege's larger purpose was to defend the view that arithmetic is a branch of logic, a view known as logicism : unlike geometry, arithmetic was to be shown to have no basis in "intuition", and no need for non-logical axioms. Already in the Begriffsschrift important preliminary theorems, for example a generalized form of law of trichotomy , were derived within what Frege understood to be pure logic.
This idea was formulated in non-symbolic terms in his The Foundations of Arithmetic Later, in his Basic Laws of Arithmetic vol. Most of these axioms were carried over from his Begriffsschrift , though not without some significant changes.
The crucial case of the law may be formulated in modern notation as follows. The case is special because what is here being called the extension of a predicate, or a set, is only one type of "value-range" of a function.
In a famous episode, Bertrand Russell wrote to Frege, just as Vol. It is easy to define the relation of membership of a set or extension in Frege's system; Russell then drew attention to "the set of things x that are such that x is not a member of x". The system of the Grundgesetze entails that the set thus characterised both is and is not a member of itself, and is thus inconsistent.
Frege wrote a hasty, last-minute Appendix to Vol. Frege opened the Appendix with the exceptionally honest comment: "Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished.
This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion.
Frege's proposed remedy was subsequently shown to imply that there is but one object in the universe of discourse , and hence is worthless indeed, this would make for a contradiction in Frege's system if he had axiomatized the idea, fundamental to his discussion, that the True and the False are distinct objects; see, for example, Dummett , but recent work has shown that much of the program of the Grundgesetze might be salvaged in other ways: Basic Law V can be weakened in other ways.Childhood —69 [ edit ] Frege was born in in Wismar , Mecklenburg-Schwerin today part of Mecklenburg-Vorpommern.
Marcus, ; reprinted Darmstadt: Wissenschaftliche Buchgesellschaft and Hildesheim: Olms, ; reprinted in Thiel  The Foundations of Arithmetic: A logico-mathematical enquiry into the concept of number Complete translation by J.
Jacquette in Jacquette . This principle, too, is consistent if second-order arithmetic is, and suffices to prove the axioms of second-order arithmetic.
This grasping in turn leads us to action; Thoughts as such have an indirect causal impact on the world. Translated in part by R.
Bauer-Mengelberg in van Heijenoort  pp. Gall and E.
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