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Frege's Logic, Theorem, and Foundations for Arithmetic (Stanford Encyclopedia of Philosophy)

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"5a 81 Cite this entry 3 a00 Search the SEP • Advanced Search • Tools • RSS Feed Table of Contents • What's New • Archives • Projected Contents Editorial Information • About the SEP • Editorial Board • How to Cite the SEP • Special Characters Support the SEP • PDFs for SEP Friends • Make a Donation • SEPIA for Libraries Contact the SEP © Metaphysics Research Lab , CSLI , Stanford University b7 2e db Open access to the SEP is made possible by a world-wide funding initiative. Please Read How You Can Help Keep the Encyclopedia Free 27538 Frege's Logic, Theorem, and Foundations for Arithmetic First published Wed Jun 10, 1998; substantive revision Mon Mar 30, 2009 Frege formulated two distinguished formal systems and used these systems in his attempt both to express certain basic concepts of mathematics precisely and to derive certain mathematical laws from the laws of logic. In his Begriffsschrift of 1879, he developed a second-order predicate calculus and used it both to define interesting mathematical concepts and to state and prove mathematically interesting propositions. However, in his Grundgesetze der Arithmetik of 1893/1903, Frege added (as an axiom) what he thought was a distinguished logical proposition (Basic Law V) and tried to derive the fundamental theorems of various mathematical (number) systems from this proposition. Unfortunately, not only did Basic Law V fail to be a logical proposition, but the resulting system proved to be inconsistent, for it was subject to Russell's Paradox. Although the inconsistency in Frege's Grundgesetze is widely known, it is not very well known that a deep theoretical accomplishment can be extracted from his work. The Grundgesetze contains all t"
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http://www.ac-nancy-metz.fr/enseign/philo/textesph /Frege.pdf	die grundlagen der arithmetik	Visit Site
http://arche-wiki.st-and.ac.uk/~ahwiki/bin/view/Ma in/BegriffsschriftLaTeX	begriffsschrift in latex	Visit Site
http://mally.stanford.edu/zalta.html	edward n zalta	Visit Site

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http://plato.stanford.edu/cgi-bin/encyclopedia/arc hinfo.cgi	cite this entry	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../../search/searcher.py	search the sep	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../../search/searcher.py	advanced search	Visit Site
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http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../../board.html	editorial board	Visit Site
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http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../../support/friends.html	pdfs for sep friends	Visit Site
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http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/example.html	a more complex example	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/proof2.html	proof of the law of extensions	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/proof3.html	proof of the principle of extensionality	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/proof1.html	first derivation of the contradiction	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../russell-paradox/	russell s paradox	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/Gl-Hume.html	frege s derivation of hume s principle in the	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/Gg-Hume.html	frege s lsquo derivation rsquo of hume s principle in the	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/WAfact6.html	proof of fact 6 concerning the weak ancestral	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/proof4.html	proof of lemma concerning zero	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/proof5.html	proof of equinumerosity lemma	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/proof6.html	proof of the general principle of induction	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/Q0.html	proof that 0 falls under	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/HerOnQN.html	proof that	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../frege/	frege gottlob	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../frege-hilbert/	frege gottlob controversy with hilbert	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../russell/	russell bertrand	Visit Site
http://plato.stanford.edu/entries/frege-logic/entr ies/frege-logic/../russell-paradox/	russell s paradox	Visit Site