Bulletin of Symbolic Logic 7 (4):504-520 (2001)
|Abstract||We discuss the differences between first-order set theory and second-order logic as a foundation for mathematics. We analyse these languages in terms of two levels of formalization. The analysis shows that if second-order logic is understood in its full semantics capable of characterizing categorically central mathematical concepts, it relies entirely on informal reasoning. On the other hand, if it is given a weak semantics, it loses its power in expressing concepts categorically. First-order set theory and second-order logic are not radically different: the latter is a major fragment of the former|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
J. Michael Dunn (1980). Quantum Mathematics. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Richard Kaye (2007). The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications. Cambridge University Press.
Gregory H. Moore (1980). Beyond First-Order Logic: The Historical Interplay Between Mathematical Logic and Axiomatic Set Theory. History and Philosophy of Logic 1 (1-2):95-137.
P. T. Johnstone (1987). Notes on Logic and Set Theory. Cambridge University Press.
Jaakko Hintikka (1996). The Principles of Mathematics Revisited. Cambridge University Press.
Jouko Väänänen (2012). Second Order Logic or Set Theory? Bulletin of Symbolic Logic 18 (1):91-121.
Ignacio Jané (1993). A Critical Appraisal of Second-Order Logic. History and Philosophy of Logic 14 (1):67-86.
Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
Added to index2009-01-28
Total downloads41 ( #27,837 of 548,984 )
Recent downloads (6 months)3 ( #25,729 of 548,984 )
How can I increase my downloads?