Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions

Moktefi, Amirouche; Schang, Fabien

doi:10.1080/01445340.2022.2143711

Cited by 6 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, bitstring semantics is a combinatorial technique that allows us to systematically compute compact representations of the formulas that appear in a given diagram, thus providing a concrete grip on its logical behavior. The wideranging significance of the present paper should be clear, since logic-sensitivity and bitstring semantics are not only among the most important research topics in logical geometry today [8,13,15,38], but are also regularly discussed across the broad field of philosophical logic [2,16,23,27,28,31,32]. These two topics are well-understood by themselves, but the precise details of their interaction turn out to be far more complicated.…”

Section: Introductionmentioning

confidence: 84%

“…The technique of bitstring semantics was initially developed within the specific context of logical geometry [38], but in recent years it has started to find applications across the disciplines of logic [9,15,16,27], philosophy [10,11,23] and linguistics [34,39]. In general, bitstring semantics allows us to systematically compute combinatorial representations of a given number of propositions, thus providing a concrete grip on their logical behavior.…”

Section: Bitstring Semanticsmentioning

confidence: 99%

See 1 more Smart Citation

Logic-Sensitivity and Bitstring Semantics in the Square of Opposition

Demey,

Frijters

2023

J Philos Logic

View full text Add to dashboard Cite

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term 'bitstring semantics'!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective.

show abstract

Section: Introductionmentioning

confidence: 84%

Section: Bitstring Semanticsmentioning

confidence: 99%

Logic-Sensitivity and Bitstring Semantics in the Square of Opposition

Demey,

Frijters

2023

J Philos Logic

View full text Add to dashboard Cite

show abstract

“…These rules could be called "a posteriori rules" because they are deduced from Ockham's account. 10 We shall take only the case of necessity and possibility 11 into account. Indeed, Ockham's squares that will be considered here involved just necessity and possibility.…”

Section: ♦(S Is P)mentioning

confidence: 99%

A Relational Semantics for Ockham’s Modalities

Falessi¹,

Schang²

2023

Preprint

View full text Add to dashboard Cite

This article aimed at providing some extension of the modal square of opposition in the 1 light of Ockham’s account of the modal operators. Moreover, we shall set forth some significant 2 remarks on the de re-de dicto distinction and on the modal operator of contingency by means of a 3 Boolean algebra called Bitstring Semantics. This generalisation starting from Ockham’s account of 4 modalities will allow us to take into consideration whether Ockham’s thought on this matter holds 5 water or not, and in which case it should be changed in order to make it coherent.

show abstract

“…Figure 1. Several of these diagrams have a long history, which can be traced back anywhere from a few decades [8][9][10][11][12][13][14][15] to several centuries [16][17][18][19][20][21][22][23]. Today, Aristotelian diagrams are studied in a variety of areas, including philosophy [24][25][26], linguistics [27][28][29], legal theory [30][31][32], and computer science [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Boolean Subtypes of the U4 Hexagon of Opposition

Demey,

Erbas

2024

Axioms

View full text Add to dashboard Cite

This paper investigates the so-called ‘unconnectedness-4 (U4) hexagons of opposition’, which have various applications across the broad field of philosophical logic. We first study the oldest known U4 hexagon, the conversion closure of the square of opposition for categorical statements. In particular, we show that this U4 hexagon has a Boolean complexity of 5, and discuss its connection with the so-called ‘Gergonne relations’. Next, we study a simple U4 hexagon of Boolean complexity 4, in the context of propositional logic. We then return to the categorical square and show that another (quite subtle) closure operation yields another U4 hexagon of Boolean complexity 4. Finally, we prove that the Aristotelian family of U4 hexagons has no other Boolean subtypes, i.e., every U4 hexagon has a Boolean complexity of either 4 or 5. These results contribute to the overarching goal of developing a comprehensive typology of Aristotelian diagrams, which will allow us to systematically classify these diagrams into various Aristotelian families and Boolean subfamilies.

show abstract

Another Side of Categorical Propositions: The Keynes–Johnson Octagon of Oppositions

Cited by 6 publications

References 15 publications

Logic-Sensitivity and Bitstring Semantics in the Square of Opposition

Logic-Sensitivity and Bitstring Semantics in the Square of Opposition

A Relational Semantics for Ockham’s Modalities

Boolean Subtypes of the U4 Hexagon of Opposition

Contact Info

Product

Resources

About