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Free logic is one attempt to avoid some of these problems.
However, he thinks that free logic is more apt and convenient to explain the natural language.
Free logics may also allow models that have an empty domain.
This amounts to the contribution which free logic makes to ontology.
Free logics may allow for terms that do not denote any object.
A free logic with the latter property is an inclusive logic.
Reference failures can also be addressed by free logics.
He has written extensively on the subject of free logic, a term which he coined.
Rather, he points out, not only does free logic provide for Quine's criterion-it even proves it!
Lejewski then goes on to offer a description of free logic, which he claims accommodates an answer to the problem.
Free logics: Their foundations, character, and some applications thereof.
He wrote important papers on free logic, general modal logic, and natural deduction systems.
Another problem occurs in free logic.
Lejewski also points out that free logic additionally can handle the problem of the empty set for statements like .
Likewise, if you reject Quine then you must reject free logic.
New essays in free logic.
Furthermore, Jaśkowski was a pioneer in the investigation of both intuitionistic logic and 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.
While Quine called such logics "inclusive" logic they are now referred to as free logic.
Philosophical applications of free logic.
An advantage of this is that formalizing theories of singular existence in free logic brings out their implications for easy analysis.
A free logic is a logic with fewer existential presuppositions than classical logic.
Free logic: Selected essays.
This logic was later developed more fully by Karel Lambert, who called the unrestricted interpretation "free logic".
"In fact, one may regard free logic... literally as a theory about singular existence, in the sense that it lays down certain minimum conditions for that concept."
Wörterbuch der philosophischen Begriffe