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Topic: Axiomatization


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 Axiomatization: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-11-06)
(axiomatization is the process of defining the basic axiomatic system axiomatic system quick summary:
In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems....
Giuseppe peano (august 27, 1858 - april 20, 1932) was an italian mathematician and philosopher best known for his contributions to set...
www.absoluteastronomy.com /encyclopedia/a/ax/axiomatization.htm   (850 words)

  
 Gottlob Frege [Internet Encyclopedia of Philosophy]
He invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic.
In the philosophy of mathematics, he was one of the most ardent proponents of logicism, the thesis that mathematical truths are logical truths, and presented influential criticisms of rival views such as psychologism and formalism.
It represented the first axiomatization of logic, and was complete in its treatment of both propositional logic and first-order quantified logic.
www.iep.utm.edu /f/frege.htm   (9562 words)

  
 Russell's Paradox
Yet a fourth response was embodied in Ernst Zermelo's 1908 axiomatization of set theory.
Zermelo's axioms were designed to resolve Russell's paradox by again restricting the Comprehension axiom in a manner not dissimilar to that proposed by Russell.
ZF and ZFC (i.e., ZF supplemented by the Axiom of Choice), the two axiomatizations generally used today, are modifications of Zermelo's theory developed primarily by Abraham Fraenkel.
plato.stanford.edu /entries/russell-paradox   (1415 words)

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