Peano, Logicism, and Formalism

Segre, Michael

doi:10.1007/978-94-011-0471-5_8

Cited by 3 publications

(3 citation statements)

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“…Although there has been a debate in the literature, some consensus has arisen over the thesis that Peano did not endorse Frege's logicist project. Most historical studies plainly deny that Peano was a logicist (see [Kennedy 1963, 264], [Segre 1995], [Lolli 2011]), while others also emphasise his rejection of philosophical discussions see [Geymonat 1955]. See also [Grattan-Guinness 2000, 247-249].…”

Section: Peano's Ideographymentioning

confidence: 99%

Frege, Peano and the Interplay between Logic and Mathematics

Millán¹

2021

philosophiascientiae

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Dans les études historiques contemporaines, les contributions de Peano sont généralement envisagées dans le cadre de la tradition logiciste initiée par Frege. Dans cet article, je vais d'abord démontrer que Frege et Peano ont développé de manière indépendante des approches semblables visant à s'appuyer sur la logique pour exprimer rigoureusement des lois mathématiques et les prouver. Ensuite, je soutiendrai cependant que Peano a également utilisé sa logique mathématique d'une manière qui anticipait la formalisation des théories mathématiques, laquelle est incompatible avec la conception de la logique défendue par Frege.

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Section: Peano's Ideographymentioning

confidence: 99%

Frege, Peano and the Interplay between Logic and Mathematics

Millán¹

2021

philosophiascientiae

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“…Although there has been a debate in the literature, some consensus has arisen over the thesis that Peano did not endorse Frege's logicist project. Most historical studies plainly deny that Peano was a logicist (see [Kennedy 1963, 264], [Segre 1995], , while others also emphasise his rejection of philosophical discussions see [Geymonat 1955]. See also [Grattan-Guinness 2000, 247-249].…”

Section: Peano's Ideographymentioning

confidence: 99%

Untitled

2021

philosophiascientiae

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“…(Peano wished to increase rigor, so that his interest was more traditional than that of Frege and Russell. [Segre 1995]) Logicism, the theory that mathematics is a part of logic, was not new; the novelty was in the effort to prove it. This demanded the construction of a system of logic as a language that encompasses mathematical assertions.…”

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The Advantage of Theft over Honest Toil

Agassi

2009

Philosophy of the Social Sciences

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Gregory Landini offers a new and an illuminating reading of Ludwig Wittgenstein’s idea about his own innovation: it is the invention of a notation that removes the mystery from all theorems of logic and of mathematics as it renders their proofs part of their wordings. This makes all theorems in principle as boring as “all four-legged animals are animals.” This idea is Wittgenstein’s doctrine of showing. It is worthless; yet, as Landini shows, every time Wittgenstein offered an elaboration on it, Russell checked it carefully and found it of no value. This, let me add, shows that Russell was in error in suggesting that intellectually there is no “advantage of theft over honest toil”: at times one may pay back and with high interest. Other cases may be due to misjudgment rather than to sloth.

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Peano, Logicism, and Formalism

Cited by 3 publications

References 4 publications

Frege, Peano and the Interplay between Logic and Mathematics

Frege, Peano and the Interplay between Logic and Mathematics

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The Advantage of Theft over Honest Toil

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