A Formal Reconstruction of Buridan's Modal Syllogism

Johnston, Spencer

doi:10.1080/01445340.2014.934090

Cited by 14 publications

(5 citation statements)

References 4 publications

(2 reference statements)

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“…Some formulas are explicitly provided in the paper by Hodges and Johnston (2017), where they use the proposition function Ox to represent the dedicated predicate of existence at a world. They only provide the example of the formula for La, but following the semantic reconstruction provided by Johnston (2015) the complete list of formulas for the modal propositions can be reconstructed as follows:…”

Section: Qlamentioning

confidence: 99%

Inferences Between Buridan’s Modal Propositions

Dagys

Giedra

Pabijutaitė

2022

PRB

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In recent years modal syllogistic provided by 14th century logician John Buridan has attracted increasing attention of historians of medieval logic. The widespread use of quantified modal logic with the apparatus of possible worlds semantics in current analytic philosophy has encouraged the investigation of the relation of Buridan’s theory of modality with the modern developments of symbolic modal logic. We focus on the semantics of and the inferential relations among the propositions that underlie Buridan’s theory of modal syllogism. First, we review all inferences between propositions of necessity, possibility, contingency, and non-contingency, with or without quod est locution, that are valid in Buridan’s semantics, and offer a comprehensive diagrammatic representation that includes them all. We then ask the question if there is a way to model those results in first order modal logic. Three ways of formalizing Buridan’s propositions in quantified modal logic are considered. Comparison of inferences between the quantified formulas and Buridan’s propositions reveals that, when supplied with a suitable formalization, Buridan’s semantics of categorical statements and immediate inferences among them can be fully captured by the quantified modal system T.

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Section: Qlamentioning

confidence: 99%

Inferences Between Buridan’s Modal Propositions

Dagys

Giedra

Pabijutaitė

2022

PRB

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“…One of those propositions is interesting for this paper. That proposition is derived from the framework presented by Hodges and Johnston (2017) and Johnston (2015). However, the derivation also considers Buridan's works such as Treatise on Consequences and Quaestiones in Analytica Priora.…”

Section: Introductionmentioning

confidence: 98%

“…Based on works such as those of Hodges and Johnston (2017), Johnston (2015), and Read (2015), Dagys, Giedra and Pabijutaitė (2022) offer a number of propositions related to the theory of modal syllogism Buridan proposes. One of those propositions is interesting for this paper.…”

Section: Introductionmentioning

confidence: 99%

Buridan’s logic: testability and models

López-Astorga

2024

ARF

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A teoria da modalidade que Buridan desenvolve está vinculada com diferentes proposições. Este trabalho aborda uma dessas proposições. O objetivo é mostrar que, se o operador de necessidade incluído nela é ignorado, a proposição permite derivar, dentro da lógica de predicados de primeira ordem, uma sentença de redução com as características requeridas no framework de Carnap. Ademais, o artigo tenta argumentar que o mencionado operador de necessidade pode ser compreendido não apenas em um sentido técnico (como a lógica modal faz), mas também do modo como um indivíduo inocente (sem treinamento em lógica modal) poderia interpretá-lo. Estes últimos argumentos são dados a partir da teoria dos modelos mentais.

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“…Similarly, a strong Jacoby-Sesmat-Blanché hexagon can be encoded with bitstrings of length three, whereas its weak counterpart requires length four [1][2][3][4][5][6]. On the level of octagons, the Aristotelian family of Buridan octagons has Boolean subtypes of bitstring lengths four, five and six [7][8][9][10][11], whereas the Aristotelian family of Keynes-Johnson octagons has Boolean subtypes of bitstring lengths six and seven [12][13][14]. Finally, logic sensitivity and existential import also distinguish the two octagons studied in the present Special Issue Volume for the interaction between the quantifiers all and most: the logical system without existential import requires bitstrings of length six, whereas the one with existential import requires bitstings of length five.…”

Section: Introductionmentioning

confidence: 99%

Aristotelian Fragments and Subdiagrams for the Boolean Algebra B5

Roelandt

Smessaert

2023

Axioms

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On a descriptive level, this paper presents a number of logical fragments which require the Boolean algebra B5, i.e., bitstrings of length five, for their semantic analysis. Two categories from the realm of natural language quantification are considered, namely, proportional quantification with fractions and percentages—as in two thirds/66 percent of the children are asleep—and normative quantification—as in not enough/too many children are asleep. On a more theoretical level, we study two distinct Aristotelian subdiagrams in B5, which are the result of moving from B5 to B4 either by collapsing bit positions or by deleting bit positions. These two operations are also argued to shed a new light on earlier results from Logical Geometry, in which the collapsing or deletion of bit positions triggers a shift from B4 to B3.

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A Formal Reconstruction of Buridan's Modal Syllogism

Cited by 14 publications

References 4 publications

Inferences Between Buridan’s Modal Propositions

Inferences Between Buridan’s Modal Propositions

Buridan’s logic: testability and models

Aristotelian Fragments and Subdiagrams for the Boolean Algebra B5

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