Fabien Schang

The Cube, the Square and the Problem of Existential Import

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotles system appears then as a fragment of a broader system which can be developed by using FOL.

Abstract logic of oppositions

A general theory of logical oppositions is proposed by abstracting these from the Aristotelian background of quantified sentences. Opposition is a relation that goes beyond incompatibility (not being true together), and a question-answer semantics is devised to investigate the features of oppositions and opposites within a functional calculus. Finally, several theoretical problems about its applicability are considered.

Oppositions and Opposites

A formal theory of oppositions and opposites is proposed on the basis of a non-Fregean semantics, where opposites are negation-forming operators that shed some new light on the connection between opposition and negation. The paper proceeds as follows.

Eastern Proto-Logics

An alternative semantic framework is proposed in the following to reconstruct and make sense of “Eastern logics”: a Question-Answer Semantics (thereafter: QAS), including a set of questions-answers and a finite number of ensuing non-Fregean logical values. Thus, meaning is provided by yes-no answers to corresponding questions about relevant properties. These logical values help to show that the saptabhaṅgī (and its dual, viz., the Buddhist Mādhyamaka catuṣkoṭi) is not a many-valued paraconsistent logic but, rather, a one-valued proto-logic: a constructive machinery that serves as a formal theory of judgment, rather than a Tarskian-like theory of consequence. Such an explanatory model of contradiction assumes a deep redefinition of logical values.

An Arithmetization of Logical Oppositions

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. To finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.

Non-Epicurean Desires

In this paper, it is argued that there can be necessary and non-natural desires. After a discussion about what seems wrong with such desires, Epicurus’ classification of desires is treated similarly to Kripke’s treatment of the Kantian table of judgments. A sample of three cases is suggested to make this point. Keywords: desire, Epicurus, judgment, nature, necessitation.

On Rules and Refereeing in Football

Recent developments in international football governance seem to be progressively leading toward an increasing use of technological devices for refereeing purposes. Opponents to change are often portrayed as old-fashioned and conservative. Philosophy might be of some help to overcome the dispute. In this paper, we first explore several concepts that are central to the current debate on football refereeing. Then, we determine the business of referees in relation to rules. We assess different arguments displayed regarding the role of chance and skills in competitions. Finally, we argue for the idea of referees as full players in football games.

Depicting Negation in Diagrammatic Logic: Legacy and Prospects

Here are considered the conditions under which the method of diagrams is liable to include non-classical logics, among which the spatial representation of non-bivalent negation. This will be done with two intended purposes, namely: to review the basic concepts involved in the definition of logical negation; to account for a variety of epistemological obstacles against the introduction of non-classical negations within diagrammatic logic. It will be mainly argued that non-classical logics dont challenge dichotomy as such but merely show that a logical operator may be a negation without operating as a dichotomy.