Metalogic, Schopenhauer and Universal Logic

Béziau, Jean-Yves

doi:10.1007/978-3-030-33090-3_13

Cited by 4 publications

(2 citation statements)

References 41 publications

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“…Vivaldi naturally promoted quadritomy with his masterpiece The Four Seasons. Schopenhauer was also found of a fourfold approach, that he developed at different levels (see [Béziau, 2020]). On the other hand Peirce was very found of trichotomy as well as Robert Blanché, who duplicated it as a colorful hexatomy (see [Blanché, 1966] and [Béziau, 2012d]).…”

Section: Dichotomy and Polytomymentioning

confidence: 99%

Many-valuedness from a universal logic perspective

Béziau

2020

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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.

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Section: Dichotomy and Polytomymentioning

confidence: 99%

Many-valuedness from a universal logic perspective

Béziau

2020

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“…Universal logic can be considered as synonymous to metalogic, a word successively and independently promoted in different ways by Arthur Schopenhauer (1788-1860), Nicolai Vasiliev (1880-1940), and Mordchaj Wajsberg (1902-194?) [52]. Universal logic uses as tools the four main metalogic theories that have been developed in modern logic, in order of appearance: set theory, proof theory, recursion theory, and model theory.…”

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confidence: 99%

Why Logics?

Béziau

2023

Logics

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In this paper we explain the different meanings of the word “logic” and the circumstances in which it makes sense to use its singular or plural form. We discuss the multiplicity of logical systems and the possibility of developing a unifying theory about them, not itself a logical system. We undertake some comparisons with other sciences, such as biology, physics, mathematics, and linguistics. We conclude by delineating the origin, scope, and future of the journal Logics.

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Is Logic Exceptional?

Béziau

2022

Studies in Universal Logic

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Metalogic, Schopenhauer and Universal Logic

Cited by 4 publications

References 41 publications

Many-valuedness from a universal logic perspective

Many-valuedness from a universal logic perspective

Why Logics?

Is Logic Exceptional?

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