Synthese 103 (3):421 - 447 (1995)
|Abstract||The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is divided into 5 sections. We first show that already in the set theoretical framework, there are different dimensions to the expression foundations of. We then explore these dimensions more thoroughly. After a very short discussion of the links between these dimensions, we move to some of the arguments presented for and against category theory in the foundational landscape. We end up on a more speculative note by examining the relationships between category theory and set theory.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
M. Kary (2009). (Math, Science, ?). Axiomathes 19 (3):61-86.
Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.
Elaine Landry & Jean-Pierre Marquis (2005). Categories in Context: Historical, Foundational, and Philosophical. Philosophia Mathematica 13 (1):1-43.
Andrei Rodin (2011). Categories Without Structures. Philosophia Mathematica 19 (1):20-46.
Øystein Linnebo & Richard Pettigrew (2011). Category Theory as an Autonomous Foundation. Philosophia Mathematica 19 (3):227-254.
Alan Baker (2003). The Indispensability Argument and Multiple Foundations for Mathematics. Philosophical Quarterly 53 (210):49–67.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
Makmiller Pedroso (2009). On Three Arguments Against Categorical Structuralism. Synthese 170 (1):21 - 31.
Added to index2009-01-28
Total downloads122 ( #4,099 of 549,130 )
Recent downloads (6 months)7 ( #10,444 of 549,130 )
How can I increase my downloads?