Karel Lambert Explained
| Karel Lambert |
| Nationality: | American |
| Known For: | Coining the term free logic |
Karel Lambert (born 1928) is an American 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] [2]
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
(\forallx\phix\landE!y\phiy) → \phiz
. 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
- "Free Logic and the Concept of Existence", Notre Dame Journal of Formal Logic, VIII, numbers 1 and 2, April 1967.
- Philosophical Applications of Free Logic, New York: Oxford University Press, 1991, "A Theory of Definite Descriptions", pp. 17–27, 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
(λx)(\phix\land\neg\phix)
.
- Free Logic. Selected Essays, Cambridge University Press, 2003.
References
- Lambert . Karel . Karel Lambert . The Definition of E! in Free Logic . Abstracts: The International Congress for Logic, Methodology and Philosophy of Science . Stanford University Press . Palo Alto, CA . 1960.
- News: Bengel. Erick. Everyday People: Hammond resident is a major figure in logic. 14 April 2016. Daily Astorian. 6 Apr 2016.
External links
