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{{BLP primary sources|date=November 2008}} | |||
'''Karel Lambert''' (born 1928) is a [[philosophy|philosopher]] and [[logic]]ian at the [[University of California, Irvine]] and the [[University of Salzburg]]. He has written extensively on the subject of [[free logic]], a term which he coined.<ref>{{Cite journal | |||
| last = Lambert | |||
| first = Karel | |||
| authorlink = Karel Lambert | |||
| title = The Definition of E! in Free Logic | |||
| journal = Abstracts: The International Congress for Logic, Methodology and Philosophy of Science | |||
| publisher = Stanford University Press | |||
| location = Palo Alto, CA | |||
| year = 1960}}</ref> | |||
==Lambert's Law== | |||
Lambert's Law is the major principle in any free definite description theory that says: For all x, x = the y (A) if and only if (A(x/y) & for all y (if A then y = x)). Free logic itself is an adjustment of a given standard [[predicate logic]] such as to relieve it of existential assumptions, and so make it a free logic. Taking [[Bertrand Russell]]'s predicate logic in his ''Principia Mathematica'' as standard, one replaces universal instantiation, <math>\forall x \,\phi x \rightarrow \phi y</math>, with universal specification <math>(\forall x \,\phi x \and E!y \,\phi y) \rightarrow \phi z</math>. Thus universal statements, like "All men are mortal," or "Everything is a unicorn," do not presuppose that there are men or that there is anything. These would be symbolized, with the appropriate predicates, as <math>\forall x\,(Mx \rightarrow Lx)</math> and <math>\forall x\, Ux</math>, which in ''Principia Mathematica'' entail <math>\exists x\,(Mx \and Lx)</math> and <math>\exists x\,Ux</math>, but not in free logic. The truth of these last statements, when used in a free logic, depend on the [[Domain of discourse|domain of quantification]], which may be the null set. | |||
==Published works== | |||
* ''Philosophical Applications of Free Logic'' "A Theory of Definite Descriptions" (1991) details an account of Russell's Theory of Descriptions in free logic. In the process, he demonstrates how a formulation from Hintikka allows for a contradiction by a correlate in logic to Russell's Paradox. He introduces the predicate <math>(\lambda x)(\phi x \and \neg \phi x)</math> | |||
==External links== | |||
* [http://web.archive.org/web/20071222170016/www.flogik.com/home.htm Official Personal Page at Internet Archive] | |||
==References== | |||
<references/> | |||
{{Authority control|VIAF=108460828}} | |||
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME = Lambert, Karel | |||
| ALTERNATIVE NAMES = | |||
| SHORT DESCRIPTION = | |||
| DATE OF BIRTH = 1928 | |||
| PLACE OF BIRTH = | |||
| DATE OF DEATH = | |||
| PLACE OF DEATH = | |||
}} | |||
{{DEFAULTSORT:Lambert, Karel}} | |||
[[Category:1928 births]] | |||
[[Category:Logicians]] | |||
[[Category:21st-century philosophers]] | |||
[[Category:University of Salzburg faculty]] | |||
[[Category:University of California, Irvine faculty]] | |||
[[Category:Living people]] | |||
{{US-philosopher-stub}} | |||
Revision as of 16:19, 26 February 2013
Template:BLP primary sources Karel Lambert (born 1928) is a philosopher and logician at the University of California, Irvine and the University of Salzburg. He has written extensively on the subject of free logic, a term which he coined.[1]
Lambert's Law
Lambert's Law is the major principle in any free definite description theory that says: For all x, x = the y (A) if and only if (A(x/y) & for all y (if A then y = x)). Free logic itself is an adjustment of a given standard predicate logic such as to relieve it of existential assumptions, and so make it a free logic. Taking Bertrand Russell's predicate logic in his Principia Mathematica as standard, one replaces universal instantiation, , with universal specification . Thus universal statements, like "All men are mortal," or "Everything is a unicorn," do not presuppose that there are men or that there is anything. These would be symbolized, with the appropriate predicates, as and , which in Principia Mathematica entail and , but not in free logic. The truth of these last statements, when used in a free logic, depend on the domain of quantification, which may be the null set.
Published works
- Philosophical Applications of Free Logic "A Theory of Definite Descriptions" (1991) details an account of Russell's Theory of Descriptions in free logic. In the process, he demonstrates how a formulation from Hintikka allows for a contradiction by a correlate in logic to Russell's Paradox. He introduces the predicate
External links
References
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