Assertion and denial: A contribution from logical notations

Ahti Veikko Pietarinen; Francesco Bellucci

doi:10.1016/j.jal.2017.01.001

Assertion and denial: A contribution from logical notations

Ahti Veikko Pietarinen^*, Francesco Bellucci

^*Corresponding author for this work

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

19 Citations (Scopus)

Abstract

This paper presents two major aspects of Frege's and Peirce's views on assertion and denial: first, their arguments for the notational choices concerning the representation of assertion and denial in Begriffsschrift (BS) and Existential Graphs (EGs), respectively; and second, those properties of BS and EGs which reflect their inventors' views on assertion and denial. We show that while Frege's notation has an ad hoc sign of assertion and an ad hoc sign of negation, Peirce has a sign of assertion which is also a sign of logical conjunction, and a sign of scope which is also a sign of negation.

Original language	English
Pages (from-to)	1-22
Number of pages	22
Journal	Journal of Applied Logic
Volume	25
DOIs	https://doi.org/10.1016/j.jal.2017.01.001
Publication status	Published - Dec 2017

Scopus Subject Areas

Logic
Applied Mathematics

User-Defined Keywords

Assertion
Begriffsschrift
Denial
Existential graphs
Frege
Peirce

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10.1016/j.jal.2017.01.001

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title = "Assertion and denial: A contribution from logical notations",

abstract = "This paper presents two major aspects of Frege's and Peirce's views on assertion and denial: first, their arguments for the notational choices concerning the representation of assertion and denial in Begriffsschrift (BS) and Existential Graphs (EGs), respectively; and second, those properties of BS and EGs which reflect their inventors' views on assertion and denial. We show that while Frege's notation has an ad hoc sign of assertion and an ad hoc sign of negation, Peirce has a sign of assertion which is also a sign of logical conjunction, and a sign of scope which is also a sign of negation.",

keywords = "Assertion, Begriffsschrift, Denial, Existential graphs, Frege, Peirce",

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

note = "Funding Information: Research supported by the Estonian Research Council, PUT1305 (“Abduction in the Age of Fundamental Uncertainty”, 2016–2018, PI Ahti-Veikko Pietarinen), and PUTJD72 (“The Philosophy of Notation”, 2015–2017, PI Francesco Bellucci). Our thanks go to the two anonymous reviewers of this journal for eminently helpful comments and suggestions. Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

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AU - Pietarinen, Ahti Veikko

AU - Bellucci, Francesco

N1 - Funding Information: Research supported by the Estonian Research Council, PUT1305 (“Abduction in the Age of Fundamental Uncertainty”, 2016–2018, PI Ahti-Veikko Pietarinen), and PUTJD72 (“The Philosophy of Notation”, 2015–2017, PI Francesco Bellucci). Our thanks go to the two anonymous reviewers of this journal for eminently helpful comments and suggestions. Publisher Copyright: © 2017 Elsevier B.V.

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N2 - This paper presents two major aspects of Frege's and Peirce's views on assertion and denial: first, their arguments for the notational choices concerning the representation of assertion and denial in Begriffsschrift (BS) and Existential Graphs (EGs), respectively; and second, those properties of BS and EGs which reflect their inventors' views on assertion and denial. We show that while Frege's notation has an ad hoc sign of assertion and an ad hoc sign of negation, Peirce has a sign of assertion which is also a sign of logical conjunction, and a sign of scope which is also a sign of negation.

AB - This paper presents two major aspects of Frege's and Peirce's views on assertion and denial: first, their arguments for the notational choices concerning the representation of assertion and denial in Begriffsschrift (BS) and Existential Graphs (EGs), respectively; and second, those properties of BS and EGs which reflect their inventors' views on assertion and denial. We show that while Frege's notation has an ad hoc sign of assertion and an ad hoc sign of negation, Peirce has a sign of assertion which is also a sign of logical conjunction, and a sign of scope which is also a sign of negation.

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KW - Begriffsschrift

KW - Denial

KW - Existential graphs

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KW - Peirce

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ER -

Assertion and denial: A contribution from logical notations

Abstract

Scopus Subject Areas

User-Defined Keywords

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