Intuition, iteration, induction - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2015

Intuition, iteration, induction

Mark van Atten

Résumé

In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge ; Brouwer disagrees on both counts. I will compare Parsons' argument with Brouwer's and defend the latter. I will not argue that Parsons is wrong once his own conception of intuition is granted, as I do not think that that is the case. But I will try to make two points: (1) Using elements from Husserl and from Brouwer, Brouwer's claims can be justified in more detail than he has done; (2) There are certain elements in Parsons' discussion that, when developed further, would lead to Brouwer's notion thus analysed, or at least something relevantly similar to it. (This version contains a postscript of May, 2015.)

Domaines

Philosophie
Fichier principal
Vignette du fichier
iii-arxiv.pdf (554.29 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01475608 , version 1 (23-02-2017)

Licence

Identifiants

  • HAL Id : hal-01475608 , version 1

Citer

Mark van Atten. Intuition, iteration, induction. 2015. ⟨hal-01475608⟩
145 Consultations
296 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More