<i>Simplex sigillum veri:</i> Peano, Frege, and Peirce on the Primitives of Logic

Bellucci, Francesco; Moktefi, Amirouche; Pietarinen, Ahti‐Veikko

doi:10.1080/01445340.2017.1358414

Cited by 16 publications

(11 citation statements)

References 19 publications

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“…18. This is in contrast to Frege, who invoked a notion of simplicity of content to choose the conditional as a primitive connective in his system; see [Bellucci, Moktefi et al 2018 , 6-7] and [Schlimm 2018, 71-73].…”

Section: Practical Considerations Against Minimalitymentioning

confidence: 94%

Peano on Symbolization, Design Principles for Notations, and the Dot Notation

Schlimm¹

2021

philosophiascientiae

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Peano a été l'une des forces motrices dans le développement du formalisme mathématique actuel. Dans cet article, nous étudions son approche particulière de la conception notationnelle et présentons quelques caractéristiques originales de ses notations. Pour motiver l'approche de Peano, nous présentons d'abord sa vision de la logique comme méthode d'analyse et son désir d'un symbolisme rigoureux et concis pour représenter les idées mathématiques. Sur la base à la fois de sa pratique et de ses réflexions explicites sur les notations, nous discutons des principes qui ont guidé Peano dans l'introduction de nouveaux symboles, le choix des caractères et la mise en forme des formules. Enfin, nous examinons de plus près, d'un point de vue systématique et historique, l'une des innovations les plus marquantes de Peano, à savoir l'usage de points pour regrouper des sous-formules.

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Section: Practical Considerations Against Minimalitymentioning

confidence: 94%

Peano on Symbolization, Design Principles for Notations, and the Dot Notation

Schlimm¹

2021

philosophiascientiae

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“…Univers. 11 . Hence, Carroll eventually obtained only two views that may be logically held: the second and the fifth.…”

Section: The Theory Of Existential Importmentioning

confidence: 99%

“…First, let us assume that Propositions I do assert the existence of their Subject while Propositions E do not. Then, let us consider what impact the existential import of Propositions A has on their symbolic 11 Carroll apparently tested this view in 1894, as shown by his journal entry of 19 June that year: "I have been testing the theory that the Copula in Logic does not assert the existence of the subject, but that "all x are y" only means "if any x exist, all of them are y." It works out right with "Barbara" etc., but fails in "Darapti," which, with this interpretation, gives no conclusion" [81, p. 151].…”

Section: The Theory Of Existential Importmentioning

confidence: 99%

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Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic

Moktefi

2021

Log. Univers.

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Lewis Carroll (1832-1898) published a system of logic in the symbolic tradition that developed in his time. Carroll's readers may be puzzled by his system. On the one hand, it introduced innovations, such as his logic notation, his diagrams and his method of trees, that secure Carroll's place on the path that shaped modern logic. On the other hand, Carroll maintained the existential import of universal affirmative Propositions, a feature that is rather characteristic of traditional logic. The object of this paper is to untangle this dilemma by exploring Carroll's guidelines in the design of his logic, and in particular his theory of existential import. It will be argued that Carroll's view reflected his belief in the social utility of symbolic logic.

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“…For more on the goal-oriented nature of simplicity in logic, in particular in logical notation see[Bellucci et al, 2018] and[Woleński, 1989, Ch. V].15 For example, the history of logic and philosophy of mathematics in the twentieth century would have been different if Frege's theory in the Grundgesetze would have immediately been reduced to its minimum, i.e.…”

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confidence: 99%

Incorporating the Relation into the Language?

Estrada-González

Giordani

Jarmużek³

et al. 2021

LLP

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In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.

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Simplex sigillum veri: Peano, Frege, and Peirce on the Primitives of Logic

Cited by 16 publications

References 19 publications

Peano on Symbolization, Design Principles for Notations, and the Dot Notation

Peano on Symbolization, Design Principles for Notations, and the Dot Notation

Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic

Incorporating the Relation into the Language?

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