Objectivity and the Duality Principle: Paragraph 26 of Frege’s Foundations of Arithmetic
Belna, Jean-Pierre
Objectivity and the Duality Principle: Paragraph 26 of Frege’s Foundations of Arithmetic - 2006.
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The idea of objectivity is primary in Gottlob Frege’s thought, not only for his conception of logic and mathematics, but also for his philosophy as a whole. He deals with the topic for the first time in 1884, in Grundlagen der Arithmetik, precisely in paragraph 26. He distinguishes the objective from the subjective, of course, but also from the real, what he calls the actual ( wirklich in German). In order to be perfectly understood, he gives as example the colors but, above all, to explain what is objective in geometry and space, he proceeds to a “thought-experiment,” founded on the principle of duality. It is this aspect that I emphasize here, in the general framework of paragraph 26 and in conjunction with Frege’s other works.
Objectivity and the Duality Principle: Paragraph 26 of Frege’s Foundations of Arithmetic - 2006.
18
The idea of objectivity is primary in Gottlob Frege’s thought, not only for his conception of logic and mathematics, but also for his philosophy as a whole. He deals with the topic for the first time in 1884, in Grundlagen der Arithmetik, precisely in paragraph 26. He distinguishes the objective from the subjective, of course, but also from the real, what he calls the actual ( wirklich in German). In order to be perfectly understood, he gives as example the colors but, above all, to explain what is objective in geometry and space, he proceeds to a “thought-experiment,” founded on the principle of duality. It is this aspect that I emphasize here, in the general framework of paragraph 26 and in conjunction with Frege’s other works.
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