By Mark van Atten
This quantity tackles Gödel's two-stage undertaking of first utilizing Husserl's transcendental phenomenology to reconstruct and improve Leibniz' monadology, after which founding classical arithmetic at the metaphysics therefore received. the writer analyses the ancient and systematic points of that venture, 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 real systematic matters, Gödel embraced using ancient authors to border his personal philosophical point of view. The philosophies of Leibniz and Husserl outline his undertaking, whereas Brouwer's intuitionism is its central foil: the shut affinities among phenomenology and intuitionism set the bar for Gödel's try and move a long way past intuitionism.
The 4 crucial 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 to justify, by means of an issue from analogy with the monadology, the mirrored image precept in set concept. It additionally offers additional help for Gödel's concept that the monadology has to be reconstructed phenomenologically, via displaying that the unsupplemented monadology isn't really capable of came upon arithmetic at once. the second one reviews Gödel's studying of Husserl, its relation to Leibniz' monadology, and its impact on his released writings. The 3rd discusses how on a variety of events Brouwer's intuitionism really encouraged Gödel's paintings, specifically the Dialectica Interpretation. The fourth addresses the query even if classical arithmetic admits of the phenomenological beginning that Gödel envisaged, and concludes that it does not.
The closing essays offer extra context. The essays gathered the following have been written and released over the past decade. Notes were additional to list additional options, adjustments of brain, connections among the essays, and updates of references.
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Additional resources for Essays on Gödel’s Reception of Leibniz, Husserl, and Brouwer
1986). A précis of a Husserlian philosophical theology. In Hart and Laycock (1986, pp. 89–168). , & Laycock, S. ). (1986). Essays in phenomenological theology. Albany: SUNY Press. Hartimo, M. (2012). Husserl’s pluralistic phenomenology of mathematics. Philosophia Mathematica, 20(1), 86–110. Hauser, K. (2006). Gödel’s program revisited: The turn to phenomenology. Pt. 1. Bulletin of Symbolic Logic, 12(4), 529–590. Hopkins, B. (2010). The philosophy of Husserl. Durham: Acumen. Howard, W. Stories.
Cambridge, MA: MIT. Wang, H. (1996). A logical journey: From Gödel to philosophy. Cambridge, MA: MIT. Yourgrau, P. (1989). Review essay: Reflections on Kurt Gödel. Philosophy and Phenomenological Research, 50(2), 391–408. Yourgrau, P. (1999). Gödel meets Einstein. Chicago: Open Court. Yourgrau, P. (2005). A world without time: The forgotten legacy of Gödel and Einstein. New York: Basic Books. Part I Gödel and Leibniz Chapter 2 A Note on Leibniz’s Argument Against Infinite Wholes Mark van Atten Abstract Leibniz had a well-known argument against the existence of infinite wholes that is based on the part-whole axiom: the whole is greater than the part.
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