Poincaré vs. Russell on the rôle of logic in mathematicst

Philosophia Mathematica 1 (1):24-49 (1993)
In the early years of this century, Poincaré and Russell engaged in a debate concerning the nature of mathematical reasoning. Siding with Kant, Poincaré argued that mathematical reasoning is characteristically non-logical in character. Russell urged the contrary view, maintaining that (i) the plausibility originally enjoyed by Kant's view was due primarily to the underdeveloped state of logic in his (i.e., Kant's) time, and that (ii) with the aid of recent developments in logic, it is possible to demonstrate its falsity. This refutation of Kant's views consists in showing that every known theorem of mathematics can be proven by purely logical means from a basic set of axioms. In our view, Russell's alleged refutation of Poincaré's Kantian viewpoint is mistaken. Poincaré's aim (as Kant's before him) was not to deny the possibility of finding a logical ‘proof’ for each theorem. Rather, it was to point out that such purely logical derivations fail to preserve certain of the important and distinctive features of mathematical proof. Against such a view, programs such as Russell's, whose main aim was to demonstrate the existence of a logical counterpart for each mathematical proof, can have but little force. For what is at issue is not whether each mathematical theorem can be fitted with a logical ‘proof’, but rather whether the latter has the epistemic features that a genuine mathematical proof has.
Keywords Poincaré  Russell  Kant  proof  role of logical reasoning in proof  intuition  intuitionism  constructivism  non-logical character of mathematical proof
Categories (categorize this paper)
DOI 10.1093/philmat/1.1.24
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,756
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Towards a Theory of Mathematical Argument.Ian J. Dove - 2009 - Foundations of Science 14 (1-2):136-152.
Towards a Theory of Mathematical Argument.Ian J. Dove - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), Foundations of Science. Springer. pp. 291--308.

View all 6 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

48 ( #109,891 of 2,177,988 )

Recent downloads (6 months)

1 ( #317,698 of 2,177,988 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums