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

Ahti-Veikko Pietarinen, Francesco Bellucci, Amirouche Moktefi

Research output: Contribution to journalArticle

Abstract

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.
Original languageEnglish
JournalHistory and Philosophy of Logic
Publication statusAccepted/In press - 2017

Fingerprint

Gottlob Frege
Logic
Notation
Constellation
Logical Analysis

Cite this

Simplex sigillum veri: Peano, Frege, and Peirce on the Primitives of Logic. / Pietarinen, Ahti-Veikko; Bellucci, Francesco; Moktefi, Amirouche.

In: History and Philosophy of Logic, 2017.

Research output: Contribution to journalArticle

@article{139e53a258a6453eb83877ab74583e6c,
title = "Simplex sigillum veri: Peano, Frege, and Peirce on the Primitives of Logic",
abstract = "We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.",
author = "Ahti-Veikko Pietarinen and Francesco Bellucci and Amirouche Moktefi",
year = "2017",
language = "English",
journal = "History and Philosophy of Logic",
issn = "0144-5340",
publisher = "Taylor and Francis",

}

TY - JOUR

T1 - Simplex sigillum veri: Peano, Frege, and Peirce on the Primitives of Logic

AU - Pietarinen, Ahti-Veikko

AU - Bellucci, Francesco

AU - Moktefi, Amirouche

PY - 2017

Y1 - 2017

N2 - We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.

AB - We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis.

M3 - Article

JO - History and Philosophy of Logic

JF - History and Philosophy of Logic

SN - 0144-5340

ER -