**Topic:**

**PARACONSISTENCY**

## Paraconsistent Logics and Paraconsistency:

Technical and Philosophical Developments

by Newton C. A. da Costa, D?cio Krause & Ot?vio Bueno

Saying in a few words, paraconsistent logics (PL) are the logics that can be the logics of inconsistent but non-trivial theories. A deductive theory is paraconsistent if its underlying logic is paraconsistent. A theory is inconsistent if there is a formula (a grammatically well formed expression of its language) such that the formula and its negation are both theorems of the theory; otherwise, the theory is called consistent. A theory is trivial if all formulas of its language are theorems. Roughly speaking, in a trivial theory 'everything' (expressed in its language) can be proved. If the underlying logic of a theory is classical logic, or even any of the standard logical systems like intuitionistic logic, inconsistency entails triviality, and conversely. So, how can we speak of inconsistent but non trivial theories? Of course by exchanging the underlying logic to one which may admit inconsistency without making the system trivial. Paraconsistent logics do the job.

Let us remark that our use of terms like 'consistency', 'inconsistency', 'contradictory' and similar ones is syntactical, what is in accord with the original metamathematical terminology of Hilbert and his school. On the other hand, in order to treat such terms from the semantical point of view, in the field of paraconsistency, one must be able to build, for instance, a paraconsistent set theory beforehand. This is possible, as we shall see, although most semantics for paraconsistent logics are classical, i.e., constructed inside classical set theories. So, the best, to begin with, is to employ the above terms syntactically.

Source: CLE

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See also:## Science and Partial Truth - A Unitary Approach to Models and Scientific Reasoning

by Newton C. A. da Costa & Steven French

Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.

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Posted by Tony Marmo
at 01:01 BST

Updated: Sunday, 5 September 2004 13:56 BST