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Logic in Opposition

Fabien Schang

Studia Humana 2 (3):31-45 (2013)

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Epistemic Pluralism.Fabien Schang - 2017 - Logique Et Analyse 239 (60):337-353.details The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and (...) semi-negations. (shrink) Download Export citation Bookmark 4 citations
An Arithmetization of Logical Oppositions.Fabien Schang - 2016 - In Jean-Yves Béziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Basel, Switzerland: Birkhäuser. pp. 215-237.details An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers. Download Export citation Bookmark 3 citations
Logical Geometries and Information in the Square of Oppositions.Hans Smessaert & Lorenz Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.details The Aristotelian square of oppositions is a well-known diagram in logic and linguistics. In recent years, several extensions of the square have been discovered. However, these extensions have failed to become as widely known as the square. In this paper we argue that there is indeed a fundamental difference between the square and its extensions, viz., a difference in informativity. To do this, we distinguish between concrete Aristotelian diagrams and, on a more abstract level, the Aristotelian geometry. We then introduce (...) Download Export citation Bookmark 24 citations
Quantifying Statements (Why ‘Every Thing’ is Not ‘Everything’, Among Other ‘Thing’s).Fabien Schang - 2024 - Logica Universalis 18 (1):185-207.details The present paper wants to develop a formal semantics about a special class of formulas: quantifying statements, which are a kind of predicative statements where both subject- and predicate terms are quantifier expressions like ‘everything’, ‘something’, and ‘nothing’. After showing how talking about nothingness makes sense despite philosophical objections, I contend that there are two sorts of meaning in phrases including ‘thing’, viz. as an individual (e.g. ‘some thing’) or as a property (e.g. ‘something’). Then I display two kinds of (...) Download Export citation Bookmark 1 citation
End of the square?Fabien Schang - 2018 - South American Journal of Logic 4 (2):485-505.details It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and unique pattern of (...) Download Export citation Bookmark 5 citations

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