Many-valuedness from a universal logic perspective
| Autor: | Jean-Yves Béziau |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Logic 010102 general mathematics 05 social sciences Universality (philosophy) Modal logic Paraconsistent logic Universal logic 01 natural sciences Epistemology Philosophy 0502 economics and business Many-valued logic History of logic Sociology 050207 economics 0101 mathematics Principle of bivalence |
| Zdroj: | Logical Investigations. 26:78-90 |
| ISSN: | 2413-2713 2074-1472 |
| DOI: | 10.21146/2074-1472-2020-26-1-78-90 |
| Popis: | We start by presenting various ways to define and to talk about many-valued logic(s). We make the distinction between on the one hand the class of many-valued logics and on the other hand what we call “many-valuedness”: the meta-theory of many-valued logics and the related meta-theoretical framework that is useful for the study of any logical systems. We point out that universal logic, considered as a general theory of logical systems, can be seen as an extension of many-valuedness. After a short story of many-valuedness, stressing that it is present since the beginning of the history of logic in Ancient Greece, we discuss the distinction between dichotomy and polytomy and the possible reduction to bivalence. We then examine the relations between singularity and universality and the connection of many-valuedness with the universe of logical systems. In particular, we have a look at the interrelationship between modal logic, 3-valued logic and paraconsistent logic. We go on by dealing with philosophical aspects and discussing the applications of many-valuedness. We end with some personal recollections regarding Alexander Karpenko, from our first meeting in Ghent, Belgium in 1997, up to our last meeting in Saint Petersburg, Russia in 2016. |
| Databáze: | OpenAIRE |
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