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Are there synthetic a priori propositions ? The paradigmatic case of mathematics, from Kant to Frege and Peirce
Leclercq, Bruno
2016In Petrov, Vesselin; Beets, François; Anderson, Katie (Eds.) Mathematics in Philosophy
Peer reviewed
 

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Keywords :
Immanuel Kant; Bernard Bolzano; Charles Sanders Peirce; diagrams; schema; formal intuition; icons; ampliative; synthetic apriori
Abstract :
[en] Bernard Bolzano notoriously rejected Immanuel Kant’s claim that arithmetic and geometry were grounded on synthetic a priori judgements based on pure intuition. According to Bolzano, only analysis of concepts could ground the generality of mathematical statements and proofs; such a stand would later lead to logicism (from Frege to Carnap). Far from going in this way, however, Charles Sanders Peirce, who was one of the fathers of formal logic but also a great admirer of Kant, provided semiotic reasons to believe that diagrams do have a general meaning and that they can provide a knowledge which is both general and “ampliative”. Unlike mere logical analysis, diagrams (the analogon of Kant’s schemas) help to explore concepts by going somehow “outside of them” in such a way that new knowledge is gained. This provides new support to Kant’s notion of intuitive construction, which is supposed to be both deductive and inventive
Research center :
MéThéor - Métaphysique et Théorie de la Connaissance - ULiège
Disciplines :
Philosophy & ethics
Author, co-author :
Leclercq, Bruno  ;  Université de Liège > Département de philosophie > Philosophie analytique et de la logique
Language :
English
Title :
Are there synthetic a priori propositions ? The paradigmatic case of mathematics, from Kant to Frege and Peirce
Publication date :
2016
Main work title :
Mathematics in Philosophy
Editor :
Petrov, Vesselin
Beets, François ;  Université de Liège - ULiège > Département de philosophie
Anderson, Katie
Publisher :
Chromatika
ISBN/EAN :
978-2-930517-50-6
Pages :
31-56
Peer reviewed :
Peer reviewed
Available on ORBi :
since 29 June 2015

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