No, No and No: the negations and their logicsa
DOI:
https://doi.org/10.22370/sst.2020.8.4928Keywords:
Negations, Classical Logic, Non-Classical Logics, Philosophy of LogicAbstract
What are the characteristics of the so-called “classic”, “paraconsistent” and “paracomplete” negations? Can we relate them? What are its syntactic properties? How do they behave semantically? In this paper, we will try to briefly address these discussions. With an introductory character, we will establish and cover some notable aspects of Classical, Paraconsistent and Paracomplete Logics, keeping our attention to the negations that bear the name of these systems. We will also present a fourth system, little known in the specialized field, called “Non-Alethic Calculus”, whose important characteristic is to introduce only one connective of negation (which we will call “non-alethic negation”) that is capable of behaves like classic, paraconsistent or paracomplete negation. In the end, we will present a problem with the possibility of relating these connectors (formally), as is expected to do with Non-Alethic Calculus - and how it is usually done, albeit informally, in the philosophical literature.
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