The Blot

Ahti Veikko Pietarinen; Francesco Bellucci; Angelina Bobrova; Nathan Haydon; Mohammad Shafiei

doi:10.1007/978-3-030-54249-8_18

The Blot

Ahti Veikko Pietarinen^*, Francesco Bellucci, Angelina Bobrova, Nathan Haydon, Mohammad Shafiei

^*Corresponding author for this work

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

4 Citations (Scopus)

Abstract

The blot is a sign in Peirce’s diagrammatic syntax of existential graphs that has hitherto been neglected in the literature on logical graphs. It is needed in order to trigger the cut-as-negation to come out from the scroll, namely from the implicational sign of a positive implicational (paradisiacal) logic. Since the cut-as-negation presupposes the blot and the scroll, what does the blot represent? On the one hand, it stands for constant absurdity, but on the other hand, Peirce takes it to be an affirmative sign. This paper explores the blot and its logical and conceptual properties from the multiple perspectives of notation, rules of transformation, icons, and scriptibility of graphs. It explains the apparent conflict in the blot’s meaning in its capacity of giving rise to the pseudo-graph that exploits positive character of absurdity. In effect, the blot is the mirror image of the sheet of assertion, not its complementation. On the sheet, it acts as a non-juxtaposable singularity.

Original language	English
Title of host publication	Diagrammatic Representation and Inference
Subtitle of host publication	11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings
Editors	Ahti-Veikko Pietarinen, Peter Chapman, Leonie Bosveld-de Smet, Valeria Giardino, James Corter, Sven Linker
Publisher	Springer Cham
Pages	225-238
Number of pages	14
Edition	1st
ISBN (Electronic)	9783030542498
ISBN (Print)	9783030542481
DOIs	https://doi.org/10.1007/978-3-030-54249-8_18
Publication status	Published - 29 Jul 2020
Event	11th International Conference on the Theory and Application of Diagrams, Diagrams 2020 - Tallinn, Estonia Duration: 24 Aug 2020 → 28 Aug 2020 https://link.springer.com/book/10.1007/978-3-030-54249-8

Publication series

Name	Lecture Notes in Computer Science
Volume	12169
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	Lecture Notes in Artificial Intelligence

Name	Diagrams: International Conference on Theory and Application of Diagrams

Conference

Conference	11th International Conference on the Theory and Application of Diagrams, Diagrams 2020
Country/Territory	Estonia
City	Tallinn
Period	24/08/20 → 28/08/20
Internet address	https://link.springer.com/book/10.1007/978-3-030-54249-8

Scopus Subject Areas

Theoretical Computer Science
Computer Science(all)

User-Defined Keywords

Absurdity
Blot
Existential graphs
Pseudo-graph
Scriptibility
Scroll

Access to Document

10.1007/978-3-030-54249-8_18

Cite this

Pietarinen, A. V., Bellucci, F., Bobrova, A., Haydon, N., & Shafiei, M. (2020). The Blot. In A.-V. Pietarinen, P. Chapman, L. Bosveld-de Smet, V. Giardino, J. Corter, & S. Linker (Eds.), Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings (1st ed., pp. 225-238). (Lecture Notes in Computer Science; Vol. 12169), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams). Springer Cham. https://doi.org/10.1007/978-3-030-54249-8_18

Pietarinen, Ahti Veikko ; Bellucci, Francesco ; Bobrova, Angelina et al. / The Blot. Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. editor / Ahti-Veikko Pietarinen ; Peter Chapman ; Leonie Bosveld-de Smet ; Valeria Giardino ; James Corter ; Sven Linker. 1st. ed. Springer Cham, 2020. pp. 225-238 (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams).

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abstract = "The blot is a sign in Peirce{\textquoteright}s diagrammatic syntax of existential graphs that has hitherto been neglected in the literature on logical graphs. It is needed in order to trigger the cut-as-negation to come out from the scroll, namely from the implicational sign of a positive implicational (paradisiacal) logic. Since the cut-as-negation presupposes the blot and the scroll, what does the blot represent? On the one hand, it stands for constant absurdity, but on the other hand, Peirce takes it to be an affirmative sign. This paper explores the blot and its logical and conceptual properties from the multiple perspectives of notation, rules of transformation, icons, and scriptibility of graphs. It explains the apparent conflict in the blot{\textquoteright}s meaning in its capacity of giving rise to the pseudo-graph that exploits positive character of absurdity. In effect, the blot is the mirror image of the sheet of assertion, not its complementation. On the sheet, it acts as a non-juxtaposable singularity.",

keywords = "Absurdity, Blot, Existential graphs, Pseudo-graph, Scriptibility, Scroll",

author = "Pietarinen, {Ahti Veikko} and Francesco Bellucci and Angelina Bobrova and Nathan Haydon and Mohammad Shafiei",

note = "Funding Information: A.-V. Pietarinen—The paper was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project {\textquoteleft}5-100{\textquoteright}. N. Haydon—Research supported by the ESF funded Estonian IT Academy research measure (project 2014-2020.4.05.19-0001). Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020 ; Conference date: 24-08-2020 Through 28-08-2020",

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Pietarinen, AV, Bellucci, F, Bobrova, A, Haydon, N & Shafiei, M 2020, The Blot. in A-V Pietarinen, P Chapman, L Bosveld-de Smet, V Giardino, J Corter & S Linker (eds), Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. 1st edn, Lecture Notes in Computer Science, vol. 12169, Lecture Notes in Artificial Intelligence, Diagrams: International Conference on Theory and Application of Diagrams, Springer Cham, pp. 225-238, 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, Tallinn, Estonia, 24/08/20. https://doi.org/10.1007/978-3-030-54249-8_18

The Blot. / Pietarinen, Ahti Veikko; Bellucci, Francesco; Bobrova, Angelina et al.
Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. ed. / Ahti-Veikko Pietarinen; Peter Chapman; Leonie Bosveld-de Smet; Valeria Giardino; James Corter; Sven Linker. 1st. ed. Springer Cham, 2020. p. 225-238 (Lecture Notes in Computer Science; Vol. 12169), (Lecture Notes in Artificial Intelligence), (Diagrams: International Conference on Theory and Application of Diagrams).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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AU - Pietarinen, Ahti Veikko

AU - Bellucci, Francesco

AU - Bobrova, Angelina

AU - Haydon, Nathan

AU - Shafiei, Mohammad

N1 - Funding Information: A.-V. Pietarinen—The paper was prepared within the framework of the HSE University Basic Research Program and funded by the Russian Academic Excellence Project ‘5-100’. N. Haydon—Research supported by the ESF funded Estonian IT Academy research measure (project 2014-2020.4.05.19-0001). Publisher Copyright: © 2020, Springer Nature Switzerland AG.

PY - 2020/7/29

Y1 - 2020/7/29

N2 - The blot is a sign in Peirce’s diagrammatic syntax of existential graphs that has hitherto been neglected in the literature on logical graphs. It is needed in order to trigger the cut-as-negation to come out from the scroll, namely from the implicational sign of a positive implicational (paradisiacal) logic. Since the cut-as-negation presupposes the blot and the scroll, what does the blot represent? On the one hand, it stands for constant absurdity, but on the other hand, Peirce takes it to be an affirmative sign. This paper explores the blot and its logical and conceptual properties from the multiple perspectives of notation, rules of transformation, icons, and scriptibility of graphs. It explains the apparent conflict in the blot’s meaning in its capacity of giving rise to the pseudo-graph that exploits positive character of absurdity. In effect, the blot is the mirror image of the sheet of assertion, not its complementation. On the sheet, it acts as a non-juxtaposable singularity.

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Pietarinen AV, Bellucci F, Bobrova A, Haydon N, Shafiei M. The Blot. In Pietarinen AV, Chapman P, Bosveld-de Smet L, Giardino V, Corter J, Linker S, editors, Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings. 1st ed. Springer Cham. 2020. p. 225-238. (Lecture Notes in Computer Science). (Lecture Notes in Artificial Intelligence). (Diagrams: International Conference on Theory and Application of Diagrams). doi: 10.1007/978-3-030-54249-8_18

The Blot

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