Abstract
Charles Sanders Peirce (1839–1914) is one of the “grounding fathers” of mathematical logic, having developed all of the key formal results of modern logic. He did it firstly (from 1860 on) in the algebraic tradition of mathematical logic stemming from Boole, combining it with the logic of relations, explicitly developed by Augustus De Morgan. From this, Peirce obtained a system that included quantifiers—a term he seems to have invented—and relative predicates. Developing his own system of relative terms, Peirce started from Boole’s system, trying to apply it to De Morgan’s logic of relations. Indeed, Peirce’s aim is to include the logic of relations into the calculus of algebra using his own system of algebraic signs. On the one hand, Peirce’s algebraic notation will be presented, specially: (a) relative terms as iconic representations of logical relations; (b) Peirce’s quantifiers and the passage from a linear notation to a diagrammatic one. On the other hand, Peirce’s graphical notation will be presented, specially: (a) his Alpha and Beta systems, which are fully compatible with what is nowadays called first-order logic, (b) and his unfinished Gamma system, designed for second-order logic and modal logic.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Peirce, C.S.: Description of a notation for the logic of relatives, resulting from an amplification of the conceptions of Boole’s Calculus of logic (1867). In: Moore, E., et al. (eds.) Writings of Charles Sanders Peirce: A Chronological Edition, vol. 2: 1867–1971, pp. 359–429. Indiana University Press, Bloomington (1984)
Peirce, C.S.: Of reasoning in general (1895). In: The Peirce Edition Project (ed.) The Essential Peirce: Selected Philosophical Writings, vol. 2: 1893–1913, pp. 11–26. Indiana University Press, Bloomington (1998)
Legris, J.: Peirce’s diagrammatic logic and the opposition between logic as calculus vs. logic as Universal language. Rev. Port. De Filos. 73(3/4), 1095–1114 (2017). https://doi.org/10.17990/RPF/2017_73_3_1095
Harel, D.: On visual formalisms. In: Glasgow, J., Narayanan, N.H., Chandrasekaran, B. (eds.) Diagrammatic Reasoning: Cognitive and Computational Perspective, pp. 235–271. The AAAI Press/The MIT Press, Menlo Park, Cambridge (1995)
Rodrigues, C.T.: The method of scientific discovery in Peirce’s philosophy: deduction, induction, and abduction. Log. Univ. 5(1), 127–164 (2011)
Peirce, C.S.: Carnegie application (L 75, 1902). In: Eisele, C. (ed.) The New Elements of Mathematics, vol. 4, pp. 36–73. Mouton Publishers/Humanities Press, The Hague, Atlantic Highlands (1976)
Peirce, C.S.: On the algebra of logic: contribution to a philosophy of notation (1885). In: Fisch, M.H., Kloesel, C.J.W., et al. (eds.) Writings of Charles Sanders Peirce: A Chronological Edition, vol. 5: 1884–1886, pp. 161–190. Indiana University Press, Bloomington (1993)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Legris, J., Rodrigues, C.T. (2018). Peirce on Diagrammatic Reasoning and Semeiotic. In: Chapman, P., Stapleton, G., Moktefi, A., Perez-Kriz, S., Bellucci, F. (eds) Diagrammatic Representation and Inference. Diagrams 2018. Lecture Notes in Computer Science(), vol 10871. Springer, Cham. https://doi.org/10.1007/978-3-319-91376-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-91376-6_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91375-9
Online ISBN: 978-3-319-91376-6
eBook Packages: Computer ScienceComputer Science (R0)