History and Philosophy of Logic 18 (2):79-93 (1997)
|Abstract||Frege?s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such as arithmetic and set theory. As such, it was seen to fail by Gödel?s incompleteness theorem of 1931. It is argued, however, that this is to impose a later interpretation on the word ?complete? it is clear from Dedekind?s writings that at least as good as interpretation of completeness is categoricity. Whereas few interesting first-order mathematical theories are categorical or complete, there are logical extensions of these theories into second-order and by the addition of generalized quantifiers which are categorical. Frege?s project really found success through Gödel?s completeness theorem of 1930 and the subsequent development of first- and higher-order model theory|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
James H. Schmerl (1980). Decidability and ℵ0-Categoricity of Theories of Partially Ordered Sets. Journal of Symbolic Logic 45 (3):585 - 611.
Richard Kaye (2007). The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications. Cambridge University Press.
Nikolaj Jang Lee Linding Pedersen & Marcus Rossberg (2010). Open-Endedness, Schemas and Ontological Commitment. Noûs 44 (2):329-339.
Enrico Moriconi (2003). On the Meaning of Hilbert's Consistency Problem (Paris, 1900). Synthese 137 (1-2):129 - 139.
Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
William Demopoulus & William Bell (1993). Frege's Theory of Concepts and Objects and the Interpretation of Second-Order Logict. Philosophia Mathematica 1 (2):139-156.
S. Awodey & A. W. Carus (2001). Carnap, Completeness, and Categoricity:The Gabelbarkeitssatz OF 1928. Erkenntnis 54 (2):145-172.
Jean Van Heijenoort (1879/1970). Frege and Gödel. Cambridge, Mass.,Harvard University Press.
Added to index2010-08-10
Total downloads22 ( #56,280 of 549,754 )
Recent downloads (6 months)1 ( #63,425 of 549,754 )
How can I increase my downloads?