Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer by Mark van Atten

By Mark van Atten

This quantity tackles Gödel's two-stage undertaking of first utilizing Husserl's transcendental phenomenology to reconstruct and strengthen Leibniz' monadology, after which founding classical arithmetic at the metaphysics therefore acquired. the writer analyses the ancient and systematic facets of that undertaking, after which evaluates it, with an emphasis at the moment stage.

The publication is organised round Gödel's use of Leibniz, Husserl and Brouwer. faraway from contemplating previous philosophers beside the point to genuine systematic matters, Gödel embraced using historic authors to border his personal philosophical point of view. The philosophies of Leibniz and Husserl outline his venture, whereas Brouwer's intuitionism is its critical foil: the shut affinities among phenomenology and intuitionism set the bar for Gödel's try to pass a ways past intuitionism.

The 4 principal essays are `Monads and sets', `On the philosophical improvement of Kurt Gödel', `Gödel and intuitionism', and `Construction and structure in mathematics'. the 1st analyses and criticises Gödel's try and justify, by way of a controversy from analogy with the monadology, the mirrored image precept in set concept. It additionally presents extra aid for Gödel's concept that the monadology should be reconstructed phenomenologically, by way of displaying that the unsupplemented monadology isn't really capable of discovered arithmetic at once. the second one stories Gödel's studying of Husserl, its relation to Leibniz' monadology, and its effect on his publishe

d writings. The 3rd discusses how on quite a few events Brouwer's intuitionism really encouraged Gödel's paintings, specifically the Dialectica Interpretation. The fourth addresses the query no matter if classical arithmetic admits of the phenomenological origin that Gödel envisaged, and concludes that it does not.

The closing essays offer additional context.  The essays accumulated right here have been written and released during the last decade. Notes were extra to list extra recommendations, adjustments of brain, connections among the essays, and updates of references.

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Additional info for Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer (Logic, Epistemology, and the Unity of Science)

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W. (1705) 1882. Nouveaux essais sur l’entendement. In Leibniz (1875–1890, Vol. 5, pp. 39–509). Leibniz, G. W. (1849–1863). Leibnizens mathematische Schriften (7 vols; C. ). Berlin (from vol. 3 Halle): Asher (from vol. 3 Schmidt). Cited according to volume and page(s). Leibniz, G. W. (1875–1890). Die philosophischen Schriften von Gottfried Wilhelm Leibniz (7 vols; C. ). Berlin: Weidmann. Cited according to volume and page(s). Leibniz, G. W. (1903). Opuscules et fragments inédits (L. ). Paris: Presses Universitaires de France.

Gödel carried on these two conversations simultaneously, turning from left to right and back. ) 2 A monograph on the monadology in relation to Cantorian set theory is Osterheld-Koepke (1984). However, the reflection principle is not discussed there. On another note, it is argued there (p. 128) that on monadological grounds we can never decide the Continuum Hypothesis; one may well doubt that Gödel’s understanding of the monadology and its relation to set theory would have had such a consequence.

Nothing is clearer than the absurdity of an actual idea of an infinite number. TH. I agree. But this is not because one couldn’t have the idea of the infinite, but because an infinity cannot be a true whole’ (‘PH. : : : rien n’est plus sensible que l’absurdité d’une idée actuelle d’un nombre infini. TH. Je suis du même avis. Mais ce n’est pas parcequ’on ne sauroit avoir l’idée de l’infini, mais parcequ’un infini ne sauroit estre un vrai tout’, Leibniz (1705) 1882, 146) 7 Although an axiom is a proposition that is evident, Leibniz sees two uses for a demonstration, that is, a reduction to A = A: it contributes to the unification of the sciences and to the analysis of ideas.

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