On Linear Existential Graphs

Francesco Bellucci; Xinwen Liu; Ahti Veikko Pietarinen

doi:10.2143/LEA.251.0.3288641

On Linear Existential Graphs

Francesco Bellucci, Xinwen Liu, Ahti Veikko Pietarinen

Research output: Contribution to journal › Review article › peer-review

6 Citations (Scopus)

Abstract

Peirce's linear versions of the language of his Existential Graphs (EGs), presented in 1902, are examined. Differences between linear and non-linear languages are explained by permutational invariance and type- vs. occurrence-referentiality: Standard EGs are permutationally invariant with respect to linear EGs, while the Beta part of the system, which corresponds to first-order quantificational theory with identity, is occurrence-referential. However, occurrence-referentiality of Beta graphs constitutes a defect of expressivity: Since the meaning of a quantifier is inextricably connected to the meaning of the sign of identity, certain complex assertions cannot be expressed in the language of Beta graphs without a new extension of its standard notation.

Original language	English
Pages (from-to)	261-296
Number of pages	36
Journal	Logique et Analyse
Volume	251
DOIs	https://doi.org/10.2143/LEA.251.0.3288641
Publication status	Published - May 2020

Scopus Subject Areas

Philosophy

User-Defined Keywords

Existential Graphs
Linear Notations
Quantification and Identity
Type vs. Occurrence-Referentiality

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10.2143/LEA.251.0.3288641

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title = "On Linear Existential Graphs",

abstract = "Peirce's linear versions of the language of his Existential Graphs (EGs), presented in 1902, are examined. Differences between linear and non-linear languages are explained by permutational invariance and type- vs. occurrence-referentiality: Standard EGs are permutationally invariant with respect to linear EGs, while the Beta part of the system, which corresponds to first-order quantificational theory with identity, is occurrence-referential. However, occurrence-referentiality of Beta graphs constitutes a defect of expressivity: Since the meaning of a quantifier is inextricably connected to the meaning of the sign of identity, certain complex assertions cannot be expressed in the language of Beta graphs without a new extension of its standard notation.",

keywords = "Existential Graphs, Linear Notations, Quantification and Identity, Type vs. Occurrence-Referentiality",

author = "Francesco Bellucci and Xinwen Liu and Pietarinen, {Ahti Veikko}",

note = "Funding Information: Supported by the Academy of Finland; the Estonian Research Council (PUT 1305, Abduction in the Age of Fundamental Uncertainty, 2016–2018), Nazarbayev University Social Policy Grant 2018, and within the framework of the HSE University Basic Research Program funded by the Russian Academic Excellence Project “5–100”, 2018–2020, Principle Investigator A.-V. Pietarinen. Our thanks go to the reviewers and editors of this special issue for comments and suggestions. Publisher Copyright: {\textcopyright} 2020 by Peeters Publishers.",

year = "2020",

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doi = "10.2143/LEA.251.0.3288641",

language = "English",

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AU - Bellucci, Francesco

AU - Liu, Xinwen

AU - Pietarinen, Ahti Veikko

N1 - Funding Information: Supported by the Academy of Finland; the Estonian Research Council (PUT 1305, Abduction in the Age of Fundamental Uncertainty, 2016–2018), Nazarbayev University Social Policy Grant 2018, and within the framework of the HSE University Basic Research Program funded by the Russian Academic Excellence Project “5–100”, 2018–2020, Principle Investigator A.-V. Pietarinen. Our thanks go to the reviewers and editors of this special issue for comments and suggestions. Publisher Copyright: © 2020 by Peeters Publishers.

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N2 - Peirce's linear versions of the language of his Existential Graphs (EGs), presented in 1902, are examined. Differences between linear and non-linear languages are explained by permutational invariance and type- vs. occurrence-referentiality: Standard EGs are permutationally invariant with respect to linear EGs, while the Beta part of the system, which corresponds to first-order quantificational theory with identity, is occurrence-referential. However, occurrence-referentiality of Beta graphs constitutes a defect of expressivity: Since the meaning of a quantifier is inextricably connected to the meaning of the sign of identity, certain complex assertions cannot be expressed in the language of Beta graphs without a new extension of its standard notation.

AB - Peirce's linear versions of the language of his Existential Graphs (EGs), presented in 1902, are examined. Differences between linear and non-linear languages are explained by permutational invariance and type- vs. occurrence-referentiality: Standard EGs are permutationally invariant with respect to linear EGs, while the Beta part of the system, which corresponds to first-order quantificational theory with identity, is occurrence-referential. However, occurrence-referentiality of Beta graphs constitutes a defect of expressivity: Since the meaning of a quantifier is inextricably connected to the meaning of the sign of identity, certain complex assertions cannot be expressed in the language of Beta graphs without a new extension of its standard notation.

KW - Existential Graphs

KW - Linear Notations

KW - Quantification and Identity

KW - Type vs. Occurrence-Referentiality

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DO - 10.2143/LEA.251.0.3288641

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JO - Logique et Analyse

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On Linear Existential Graphs

Abstract

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