Abstract
The following two review papers have a common origin. Pietarinen’s book Signs of Logic (2006) and Stjernfelt’s book Diagrammatology (2007) were both published in the same Synthese Library Series being published by Springer. The two books also share the common topic of diagrammatic reasoning in Charles Peirce’s work. Beginning in a conference Applying Peirce held in Helsinki in conjunction with the World Congress of Semiotics in June 2007, two authors have commented upon these books under the headline of Synthese Library Book Session on several occasions, including the Aarhus meeting on Signs and Meaning held in February 2008, the Diagrammatology and Diagram Praxis workshop in Lisboa in March 2009, and the Peirce and Early Analytic Philosophy symposium in Helsinki in June 2009. Therefore, these two review papers form a continuing discussion on the contributions Peirce’s diagrammatic epistemology and logic will have to a broad range of issues at the intersections of philosophy, logic, cognitive sciences and beyond.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The received linear system of logic formalization is often referred to as the Frege–Russell–Peano system, but it actually originates in Peirce’s “Algebra of Logic” from the 1880s. The Existential Graphs from the years around 1900 thus forms an explicit alternative to Peirce’s own earlier system.
Roberts (1973) is the only published source on Peirce’s logic of potentials.
I am grateful to Risto Hilpinen’s suggestion that the logic of potentials may differ from other parts of EGs in that the higher-order diagrams are no longer languages.
The overall diagrammatism of EGs, in their ‘endoporeutic’ meaning and in the way ligatures (networks of quantificational lines) function, raises further doubts about the viability of compositional semantics in general (Pietarinen 2005).
This is not far removed from the ways in which analytic philosophers have analysed action: by assuming that actions are preceded by intentions to act. Fulfilling these intentions by volitional action materialises the action created in the mind. Yet both phenomenological and analytic approaches put the cart before the horse and are different from Peirce’s which seeks no ‘proper place’ for intentions at the forefront of action. Action precedes forms of knowing and our actions are guided by general habits of acting in certain ways in certain kinds of situations.
Peirce writes, “I have found few books on logic so instructive. I do not mean that the reader will find Lange’s views exactly reproduced in this work, by any means, upon a single topic. But it has influenced me considerably, and I can recommend it as one of the very few works on logic that I have found too short” (CP 2.76). “Upon the nature of proof see Lange, Logische Studien, who maintains that deductive proof must be mathematical; that is, must depend upon observation of diagrammatic images or schemata” (CP 2.782; Dictionary of Philosophy and Psychology 2, p. 359).
Peirce was the likely author of Bain’s Logic review published in the Nation 11, 4 August 1870, 77–78. The reviewer attacks Bain for “ignoring all logical writings not English”, which is “the more reprehensible, as logic has by no means received its greatest development in England”.
Husserl to Bain’s “Part first, Appendix B”, Hua XII: 372, and Peirce to “Logic, Pt. I, Bk. I, chap. iii, sec. 27”. See CP 2.551, where Peirce quotes from Bain 1870, pp. 109–110 (the word “called” should be “named”).
The paragraph published in the Collected Papers reads as follows: “How many writers of our generation (if I must call names, in order to direct the reader to further acquaintance with a generally described character—let it be in this case the distinguished Husserl), after underscored protestations that their discourse shall be of logic exclusively and not by any means of psychology (almost all logicians protest that on file), forthwith become intent upon those elements of the process of thinking which seem to be special to a mind like that of the human race, as we find it, to too great neglect of those elements which must belong, as much to any one as to any other mode of embodying the same thought” (CP 4.7, 1906).
“[W]hen I say that Existential Graphs put before us moving pictures of thought, I mean of thought in its essence free from physiological and other accidents” (CP 4.8). See also Pietarinen (2011b).
References
Bain, A. (1870). Logic. London/New York: Longmans/D. Appleton & Co.
Gilman, B. I. (1892). On the properties of a one-dimensional manifold. Mind, 1, 518–526.
Gray, J. (2009). Plato’s ghost: The modernist transformation of mathematics. Princeton: Princeton University Press.
Hartimo, M. (2007). Towards completeness: Husserl on theories of manifolds 1890–1901. Synthese, 156, 281–310.
Lange, F. A. (1877). Logische Studien: Ein Beitrag Zur Neubegrundung Der Formalen Logik Und Der Erkenntnisstheorie. Iserlohn: J. Baedeker.
Mancosu, P., Zach, R., & Badesa, C. (2009). The development of mathematical logic from Russell to Tarski, 1900–1935. In L. Haaparanta (Ed.), The development of modern logic (pp. 318–470). Oxford: Oxford University Press.
Peirce, C. S. (1931–1958). In C. Hartshorne, P. Weiss & A. W. Burks (Eds.), Collected papers of Charles Sanders Peirce, vol 8. Cambridge, MA: Harvard University Press. Cited as CP x.yyy.
Peirce, C. S. (1967). Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin, “Annotated Catalogue of the Papers of Charles S. Peirce”, Amherst: University of Massachusetts Press, 1967, and in “The Peirce Papers: A supplementary catalogue”, Transactions of the C. S. Peirce Society 7 (1971): 37–57. Cited as MS followed by manuscript number.
Pietarinen, A.-V. (2005). Compositionality, relevance and Peirce’s logic of Existential Graphs. Axiomathes, 15, 513–540.
Pietarinen, A.-V. (2006). Signs of logic: Peircan themes on the philosophy of language, games, and communication. Synthese Library 329 Dordrecht: Springer.
Pietarinen, A.-V., & Snellman, L. (2006). On Peirce’s late proof of pragmaticism. In T. Aho & A.-V. Pietarinen (Eds.), Truth and games (Vol. 78, pp. 275–288). Helsinki: Acta Philosophica Fennica.
Pietarinen, A.-V. (2010a). Which philosophy of mathematics is pragmaticism? In M. Moore (Ed.), New essays on Peirce’s mathematical philosophy (pp. 59–79). Chicago: Open Court.
Pietarinen, A.-V. (2010b). Pragmaticism as an anti-foundationalist philosophy of mathematics. In B. Van Kerkhove, R. Desmet, & J. P. Van Bendegem (Eds.), Philosophical perspectives on mathematical practice (pp. 156–183). London: College Publications.
Pietarinen, A.-V. (2011a). Moving pictures of thought: Graphs, games, and pragmaticism’s proof. Semiotica, 186, 315–331.
Pietarinen, Ahti-Veikko. (2011b). Existential graphs: What the diagrammatic logic of cognition might look like. History and Philosophy of Logic, 32(3), 265–281.
Roberts, D. D. (1973). The existential graphs of Charles S. Peirce. The Hague: Mouton.
Sandu, G., & Hintikka, J. (1999). Tarski’s guilty secret: Compositionality. In J. Wolenski & E. Kölher (Eds.), Alfred Tarski and the Vienna circle (pp. 217–230). Dordrecht: Kluwer Academic Publishers.
Smith, B. (2005). Against fantology. In M. Reicher & J. Marek (Eds.), Experience and analysis (pp. 153–170). Vienna: ÖBV & HPT.
Spiegelberg, H. (1956). Husserl’s and Peirce’s phenomenologies: Coincidence or interaction? Philosophy and Phenomenological Research, 17, 164–185.
Stjernfelt, F. (2006). Two iconicity notions in Peirce’s diagrammatology. In Conceptual structures: Inspiration and application. Lecture Notes in Artificial Intelligence 4068 (pp. 70–86). Berlin: Springer.
Stjernfelt, F. (2007). Diagrammatology. An investigation on the borderlines of phenomenology, ontology, and semiotics. Synthese Library 336. Dordrecht: Springer.
Stjernfelt, F. (2014). Natural propositions. The actuality of Peirce’s doctrine of dicisigns. Boston: Docent Press.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pietarinen, AV., Stjernfelt, F. Peirce and diagrams: two contributors to an actual discussion review each other. Synthese 192, 1073–1088 (2015). https://doi.org/10.1007/s11229-015-0658-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-015-0658-8