What is required of a foundation for mathematics?

Philosophia Mathematica 2 (1):16-35 (1994)
Abstract
The business of mathematics is definition and proof, and its foundations comprise the principles which govern them. Modern mathematics is founded upon set theory. In particular, both the axiomatic method and mathematical logic belong, by their very natures, to the theory of sets. Accordingly, foundational set theory is not, and cannot logically be, an axiomatic theory. Failure to grasp this point leads obly to confusion. The idea of a set is that of an extensional plurality, limited and definite in size, composed of well defined objects.It is the extension of Greek notion of 'number' (arithmos) into Cantor's 'transfinite'.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/2.1.16
Options
 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: 25,645
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - forthcoming - British Journal for the Philosophy of Science:axw006.

Add more citations

Similar books and articles
Arithmetical Set Theory.Paul Strauss - 1991 - Studia Logica 50 (2):343 - 350.
Mengenlehre—Vom Himmel Cantors Zur Theoria Prima Inter Pares.Peter Schreiber - 1996 - NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 4 (1):129-143.
Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
Wittgenstein and the Real Numbers.Daesuk Han - 2010 - History and Philosophy of Logic 31 (3):219-245.
Notes on Logic and Set Theory.P. T. Johnstone - 1987 - Cambridge University Press.
Category Theory as an Autonomous Foundation.Øystein Linnebo & Richard Pettigrew - 2011 - Philosophia Mathematica 19 (3):227-254.

Monthly downloads

Added to index

2009-01-28

Total downloads

66 ( #75,637 of 2,143,472 )

Recent downloads (6 months)

12 ( #56,382 of 2,143,472 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums