Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T07:29:55.129Z Has data issue: false hasContentIssue false
  • English
  • Français

EXISTENTIAL GRAPHS AS AN INSTRUMENT OF LOGICAL ANALYSIS: PART I. ALPHA

Published online by Cambridge University Press:  26 February 2016

FRANCESCO BELLUCCI  and
AHTI-VEIKKO PIETARINEN
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 2 , June 2016 , pp. 209 - 237
Copyright
Copyright © Association for Symbolic Logic 2016 

References

BIBLIOGRAPHY

Bellucci, F. (2015). Charles S. Peirce and the Medieval Doctrine of consequentiae, History and Philosophy of Logic, DOI:10.1080/01445340.2015.1118338.CrossRefGoogle Scholar
Cajori, F. (1929). A History of Mathematical Notations, Vol. 1. Chicago: Open Court.Google Scholar
Cheung, L. K. C. (1999). The Proofs of the Grundgedanke in Wittgenstein’s Tractatus. Synthese, 120, 395–410.CrossRefGoogle Scholar
Church, A. (1956). Introduction to Mathematical Logic. Princeton: Princeton University Press.Google Scholar
De Cruz, H. & De Smedt, J. (2013). Mathematical Symbols as Epistemic Actions. Synthese, 190 (1), 3–19.CrossRefGoogle Scholar
Dipert, R. (1981). Peirce’s Propositional Logic. Review of Metaphysics, 34 (3), 569–595.Google Scholar
Dipert, R. (2006). Peirce’s Deductive Logic: Its Development, Influence, and Philosophical Significance. In: Misak, C., editor. The Cambridge Companion to Peirce. Cambridge: Cambridge University Press, pp. 287–324.Google Scholar
Dutilh Novaes, C. (2012). Formal Languages in Logic. A Philosophical and Cognitive Analysis. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Macbeth, D. (2006). Frege’s Logic. Cambridge, MA: Harvard University Press.Google Scholar
Marquand, A. (1879). Logic Notes, 1878–1879, Marquand Papers, Princeton University Library.Google Scholar
Milne, P. (2013). Tractatus 5.4611: ‘Signs for logical operations are punctuation marks’. In: Sullivan, P. and Potter, M., editors. Wittgenstein’s Tractatus. History and Interpretation. Oxford: Oxford University Press, pp. 97–124.CrossRefGoogle Scholar
Peano, G. (1958). Opere scelte. Volume II. Logica matematica. Interlingua ed algebra della grammatica. Roma: Edizioni Cremonese.Google Scholar
Peirce, C. S. (1870). Description of a Notation for the Logic of Relatives. Memoirs of the American Academy of Arts and Sciences, 9 (2), 317–378.CrossRefGoogle Scholar
Peirce, C. S. (1880). On the Algebra of Logic. American Journal of Mathematics, 3 (1), 15–57.CrossRefGoogle Scholar
Peirce, C. S. (1885). On the Algebra of Logic. A Contribution to the Philosophy of Notation. American Journal of Mathematics, 7 (3), 197–202.CrossRefGoogle Scholar
Peirce, C. S. (1897). The Logic of Relatives. The Monist, 7 (2), 161–217.CrossRefGoogle Scholar
Peirce, C. S. (1906). Prolegomena to an Apology for Pragmaticism. The Monist, 16, 492–546.CrossRefGoogle Scholar
Peirce, C. S. (1931–1966). The Collected Papers of Charles S. Peirce, 8 vols., ed. by Hartshorne, C., Weiss, P., and Burks, A. W., Cambridge: Harvard University Press. Cited as CP followed by volume and paragraph number.Google Scholar
Peirce, C. S. (1967). Manuscripts in the Houghton Library of Harvard University, as identified by Robin, Richard, 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 and, when available, page number.Google Scholar
Peirce, C. S. (1976). The New Elements of Mathematics by Charles S. Peirce, 4 vols.,Eisele, C.,editor. The Hague: Mouton. Cited as NEM followed by volume and page number.Google Scholar
Peirce, C. S. (1982-). Writings of Charles S. Peirce: A Chronological Edition, 7 vols., Moore, et al., editors, Bloomington: Indiana University Press. Cited as W followed by volume and page number.Google Scholar
Pietarinen, A.-V. (2005). Compositionality, Relevance and Peirce’s Logic of Existential Graphs. Axiomathes, 15, 513–540.CrossRefGoogle Scholar
Pietarinen, A.-V. (2011). Existential Graphs: What a Diagrammatic Logic of Cognition Might Look Like. History and Philosophy of Logic, 32 (3), 265–281.CrossRefGoogle Scholar
Pietarinen, A.-V. (2015a). Exploring the Beta Quadrant. Synthese, 192 (4), 941–970.CrossRefGoogle Scholar
Pietarinen, A.-V. (2015b). Is There a General Diagram Concept? In: Krämer, S. & Ljundberg, C., editors, Thinking in Diagrams, De Gruyter, in press.Google Scholar
Pietarinen, A.-V. (ed.). (2015c). Logic of the Future: Peirce’s Writings on Existential Graphs. Bloomington: Indiana University Press, to appear.Google Scholar
Pietarinen, A.-V. & Bellucci, F. (2015a). What is So Special about Logical Diagrams? ManuscriptGoogle Scholar
Pietarinen, A.-V. & Bellucci, F. (2015b). Two Dogmas of Diagrammatic Reasoning: A View from Existential Graphs. In: Hull, K. & Atkins, R., editors, Perception, Icons, and Graphical Systems, to appear.Google Scholar
Prior, A. N. (1958). Peirce’s Axioms for Propositional Calculus. The Journal of Symbolic Logic, 23(2), 135–136.CrossRefGoogle Scholar
Roberts, D. D. (1973). The Existential Graphs of Charles S. Peirce. The Hague: Mouton.CrossRefGoogle Scholar
Russell, B. (1903). The Principles of Mathematics, Cambridge: Cambridge University Press; 2nd edn., London: Allen & Unwin, 1937.Google Scholar
Shields, P. (2012). Charles S. Peirce on the Logic of Number. Boston: Docent Press (Doctoral Dissertation, Fordham, 1981).Google Scholar
Shin, S. -J. (2002). The Iconic Logic of Peirce’s Graphs. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Shin, S. -J. (2011). Peirce’s Alpha Graphs and Propositional Languages. Semiotica, 186, 333–346.Google Scholar
Shimojima, A. (1996a). On the Efficacy of Representation. Doctoral Dissertation, Indiana University.Google Scholar
Shimojima, A. (1996b). Operational Constraints in Diagrammatic Reasoning. In: Allwein, G. and Barwise, J., editors. Logical Reasoning with Diagrams. Oxford: Oxford University Press, pp. 27–48.Google Scholar
Wittgenstein, L. (1922). Tractatus Logico-Philosophicus, London: Kegan Paul.Google Scholar
Wittgenstein, L. (2012). Wittgenstein in Cambridge. Letters and documents 1911–1951, McGuinness, B., editor, Oxford: Blackwell.Google Scholar
Zeman, Jay J. (1968). Peirce’s Graphs - the Continuity Interpretation. Transactions of the Charles S. Peirce Society, 4 (3), 144–154.Google Scholar