Karel Lambert (born 1928) is an American

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

and

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

ian at the

University of California, Irvine The University of California, Irvine (UCI or UC Irvine) is a public land-grant research university in Irvine, California. One of the ten campuses of the University of California system, UCI offers 87 undergraduate degrees and 129 graduate and pr ...

and the

University of Salzburg The University of Salzburg (german: Universität Salzburg), also known as the Paris Lodron University of Salzburg (''Paris-Lodron-Universität Salzburg'', PLUS), is an Austrian public university A public university or public college is a univ ...

. He has written extensively on the subject of

free logic A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter propert ...

, a term which he coined.

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 First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantifie ...

such as to relieve it of existential assumptions, and so make it a free logic. Taking

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...

's predicate logic in his ''

Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...

'' as standard, one replaces universal instantiation,

\forall x \,\phi x \rightarrow \phi y

, with universal specification

(\forall x \,\phi x \land E!y \,\phi y) \rightarrow \phi z

. 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

\forall x\,(Mx \rightarrow Lx)

and

\forall x\, Ux

, which in ''Principia Mathematica'' entail

\exists x\,(Mx \land Lx)

and

\exists x\,Ux

, 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 In mathematical analysis, a null set N \subset \mathbb is a measurable set that has measure zero. This can be characterized as a set that can be covered by a countable union of intervals of arbitrarily small total length. The notion of null s ...

Published works

* "Free Logic and the Concept of Existence", ''

Notre Dame Journal of Formal Logic The ''Notre Dame Journal of Formal Logic'' is a quarterly peer-reviewed scientific journal covering the foundations of mathematics and related fields of mathematical logic, as well as philosophy of mathematics. It was established in 1960 and is p ...

'', 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 Kaarlo Jaakko Juhani Hintikka (12 January 1929 – 12 August 2015) was a Finnish philosopher and logician. Life and career Hintikka was born in Helsingin maalaiskunta (now Vantaa). In 1953, he received his doctorate from the University of Hels ...

allows for a contradiction by a correlate in logic to

Russell's paradox In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains a ...

. He introduces the predicate

(\lambda x)(\phi x \land \neg \phi x)

. * ''Free Logic. Selected Essays'', Cambridge University Press, 2003.

References

External links

Official personal page at Internet Archive
1928 births American logicians 21st-century American philosophers Academic staff of the University of Salzburg University of California, Irvine faculty Living people {{US-philosopher-stub