- Author
- Year
- 2012
- host editors
-
P. Dybjer
S. Lindström
E. Palmgren
G. Sundholm - Title
- Second order logic, set theory and foundations of mathematics
- Book title
- Epistemology versus Ontology
- Book subtitle
- Essays of the Philosophy and Foundations of Mathematics in Honor of Per Martin-Löf
- Pages (from-to)
- 371-380
- Publisher
- Dordrecht: Springer
- ISBN
- 9789400744349
- ISBN (electronic)
- 9789400744356
- Series
- Logic, Epistemology, and the Unity of Science, 27
- Document type
- Chapter
- Faculty
- Interfacultary Research
- Institute
- Institute for Logic, Language and Computation (ILLC)
- Abstract
-
The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the power sets. It is argued that in many ways this difference is illusory. More importantly, it is argued that the often stated difference, that second order logic has categorical characterizations of relevant mathematical structures, while set theory has non-standard models, amounts to no difference at all. Second order logic and set theory permit quite similar categoricity results on one hand, and similar non-standard models on the other hand.
- URL
- go to publisher's site
- Language
- English
- Persistent Identifier
- https://hdl.handle.net/11245/1.374373
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