Philosophia Mathematica 2 (1):16-35 (1994)
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)|
References found in this work BETA
No references found.
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.
Identity in Homotopy Type Theory, Part I: The Justification of Path Induction.James Ladyman & Stuart Presnell - 2015 - Philosophia Mathematica 23 (3):386-406.
The Importance of Developing a Foundation for Naive Category Theory.Marcoen J. T. F. Cabbolet - 2015 - Thought: A Journal of Philosophy 4 (4):237-242.
Similar books and articles
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.
The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise.Mary Tiles - 1989 - Dover Publications.
The Indispensability Argument and Multiple Foundations for Mathematics.Alan Baker - 2003 - Philosophical Quarterly 53 (210):49–67.
Category Theory as an Autonomous Foundation.Øystein Linnebo & Richard Pettigrew - 2011 - Philosophia Mathematica 19 (3):227-254.
Foundations of Mathematics: Metaphysics, Epistemology, Structure.Stewart Shapiro - 2004 - Philosophical Quarterly 54 (214):16 - 37.
Added to index2009-01-28
Total downloads66 ( #75,637 of 2,143,472 )
Recent downloads (6 months)12 ( #56,382 of 2,143,472 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.