Freges conception of numbers as objects

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What we do Get involved Shop online Donate. Grows vegetables Fills classrooms Drills wells Empowers women Fights poverty. Thus the second-level concept "existence" applies to the first-level concept "Satellite of Mars", i. Frege's description of number which is a philosophical and not mathematical question, yet essential to mathematics is problematic because it appeals to the relationship "falls under". Yet there is no relationship, at least not a logical one, that is given by "falls under". There is merely a grammatical tradition.

The Foundations of Arithmetic - Wikipedia

We say "objects fall under concepts", but this only expresses the way we casually talk about objects and concepts. It leaves us in the dark regarding both concepts and objects and their relationship. Yet it is their supposed relationship that Frege uses in his definition of number. But the question of what Frege meant by number can be dismissed as secondary to a higher problem.

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The question we should be asking is not what sort of things numbers are, or in what domain they exist, but what are the conditions for the creation of numbers. Frege takes numbers to be independent of any constructional conditions. He takes what is called a trancendentally real line, a posture common to all scientists and mathematicians, and most philosophers. Instead, he should be taking like Wittgenstein a transcendentally ideal line, which shows that there are no independent numbers, nor any domain that supports their existence. Logic and mathematics are unable to distinguish between transcendentally real and transcendentally ideal objects.

The syntax of their expression looks the same in both models, a fact that astonishingly has gone unnoticed throughout the history of science and logic. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. I need help understanding Frege's definition of number Ask Question.

Asked 4 years, 5 months ago. Active 1 year, 1 month ago. Viewed 2k times. Number - The content of a statement of number is an assertion about a concept. Valentino Valentino 1 1 gold badge 7 7 silver badges 18 18 bronze badges. However, one might take care in claiming that this is not a math question since it most definitely involves defining a mathematical object or structure. That being said, I would rather not hold this debate with you.

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Instead, I would like to wait for some positive responses from those who are versed in foundationalism. Thank You.

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  4. Michael D. Stewart Shapiro, "Mill", Section 4. Readings: Gottlob Frege, The Foundations of Arithmetic: a logico-mathematical enquiry into the concept of number , English translation by J.

    Frege's Conception of Numbers as Objects - Scots Philosophical Monographs

    Austin B. Gottlob Frege, "Function and concept" , English translation by P. Gottlob Frege, "On concept and object" , English translation by P. Geach, Geach and Black eds , op. Tyler Burge, "Frege on extensions of concepts ", Philosophical Review 93 , pp. Readings: Gottlob Frege, The Foundations of Arithmetic: a logico-mathematical enquiry into the concept of number ; English translation by J. Austin, , B.