Karel Lambert
Encyclopedia
Karel Lambert is a 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.
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.
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
ian at the University of California, Irvine
University of California, Irvine
The University of California, Irvine , founded in 1965, is one of the ten campuses of the University of California, located in Irvine, California, USA...
and the University of Salzburg
University of Salzburg
The University of Salzburg, or Paris Lodron University after its founder, the Prince Archbishop Paris Lodron, is located in the Austrian city of Salzburg, Salzburgerland, home of Mozart. It is divided into 4 faculties: catholic theology, law, humanities and natural science.Founded in 1622, it...
. He has written extensively on the subject of free logic
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 term which he coined.
Lambert's Law
Lambert's Law is the adjustment of a given standard predicate logicPredicate logic
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified...
such as to relieve it of existential assumptions, and so make it a free logic. Taking Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
'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
