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 (...) two new logical geometries, and develop a formal, well-motivated account of their informativity. This enables us to show that the square is strictly more informative than many of the more complex diagrams. (shrink)

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 (...) oppositions that proceeds with colored diagrams and an increasing set of bitstrings. (shrink)

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)

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 (...) logical forms for quantifying statements, depending on how these ‘thing’s are ordered into a whole predication. Finally, an algebraic semantics is proposed for the finite set of quantifying statements to order these into a (fragmentary) dodecagon of logical relations. The corresponding Sub-Model Semantics (hereafter: $$\mathbb {SMS}$$ ) aims to update the usual theory of opposition whilst leading to a research program for other kinds of statement like categorical and even modal propositions. (shrink)