Abstract
Logicians have often suggested that the use of Euler-type diagrams has influenced the idea of the quantification of the predicate. This is mainly due to the fact that Euler-type diagrams display more information than is required in traditional syllogistics. The paper supports this argument and extends it by a further step: Euler-type diagrams not only illustrate the quantification of the predicate, but also solve problems of traditional proof theory, which prevented an overall quantification of the predicate. Thus, Euler-type diagrams can be called the natural basis of syllogistic reasoning and can even go beyond. In the paper, these arguments are presented in connection with the book Nucleus Logicae Weisaniae by Johann Christian Lange from 1712.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gardner, M. (1958). Logic machines and diagrams. New York: McGraw-Hill.
Englebretson, G. (1996). Something to reckon with: The logic of terms. Ottawa Ont.: University of Ottawa Press.
Peckhaus, V. (1997). Logik, Mathesis universalis und allgemeine Wissenschaft: Leibniz und die Wiederentdeckung der formalen Logik im 19 Jahrhundert. Berlin: Akademie.
Mignucci, M. (1983). La teoria della quantificazione del predicato nell’antichità classica. Anuario Filosofico, 16, 11–42.
Copi, I.M., Cohen, C., McMahon, K. (2014). Introduction to logic, 14th edn. New York: Pearson.
Bonevac, D. (2012). A history of quantification. In Gabbay, D., & Woods, J. (Eds.) Handbook of the history of logic, (Vol. 11 pp. 63–126). Amsterdam: Elsevier.
Weidemann, H. (1985). Textkritische Bemerkungen zum siebten Kapitel der aristotelischen Hermeneutik: Int. 7, 17 b 12–16/16–20. In Wiesner, J. (Ed.) Aristoteles – Werk und Wirkung, Bd I, Aristoteles und seine Schule (pp. 45–56). Berlin: De Gruyter.
Heinemann, A.-S. (2015). Quantifikation des Pradikats und numerisch definiter Syllogismus: Die Kontroverse zwischen August De Morgan und William Hamilton: Formale Logik zwischen Algebra und Syllogistik̈. Münster: mentis.
Smiley, T. (1962). Syllogism and quantification. The Journal of Symbolic Logic, 27(1), 58–72.
Fogelin, R. J. (1976). Hamilton’s quantification of the predicate. The Philosophical Quarterly, 26(104), 217–228.
Hartmann, I. -A. (2011). The hamiltonian syllogistic. Journal of logic Language and Information, 20(4), 445–474.
Lenzen, W. (2015). Caramuel and the quantification of the predicate. In Koslow, A., & Buchsbaum, A. (Eds.) The road to universal logic: Festschrift for 50th birthday of Jean-Yves Béziau, (Vol. I pp. 361–385). Cham: Birkhäuser.
Moktefi, A., & Shin, S.-J. (2012). A history of logic diagrams. In Gabbay, D.M., Pelletier, F. J., Woods, J. (Eds.) Logic: A history of its central concepts 11 (pp. 611–83). Burlington: Elsevier Science.
Weise, C. (1696). Curieuse Fragen uber die Logicä [...] Leipzig: Joh. Grossens sel. Erben.
Lange, J. C. (1714). Inventvm novvm qvadrati logici vniversalis [...] Müller: Gissa Hassorum.
Lange, J. C. (1712). Nvclevs Logicae Weisianae. [...] Editus antehac Avctore Christiano Weisio. Müller: Gissae-Hassorum.
Bernhard, P. (2001). Euler-Diagramme: Zur Morphologie einer Reprasentationsform in der Logik̈. Paderborn: mentis.
Shimojima A. (2001). The graphic-linguistic distinction. In Blackwell, A.F. (Ed.) Thinking with diagrams (pp. 5–27). Dordrecht: Springer.
Bellucci, F., Moktefi, A., Pietarinen, A.-V. (2013). Diagrammatic autarchy: Linear diagrams in the 17th and 18th century. CEUR Workshop Proceedings, 1132, 31–35.
Lemanski, J. (2017). Periods in the use of Euler-Type diagrams. Acta Baltica Historiae et Philosophiae Scientiarum, 5(1), 50–69.
De Morgan, A. (1864). Logical bibliography. Notes and Queries, 3(6), 101–104.
Lange, J. C. (1720). Ausfuhrliche Vorstellung von einer neuen & gemeinersprießlichen̈ [...] Anstalt [...] unter dem Namen & Titul [...] einer societatis universalis recognoscentium. Itzstein: Lyce.
Hamilton, W. (1860). Lectures in metaphysics and logic. In Mansei, H.L., & Veitch, J. (Eds.), Vol. IV. Edinburgh: W. Blackwood and Sons.
Veitch, J. (1885). Institutes of logic. Edinburgh: W. Blackwood and sons.
Ueberweg, F. (1871). System of logic and history of logical doctrines. In Lindsay, T.M. (Ed.) Transl. Longmans, Grenn, and Co: London.
Barwise, J., & Etchemendy, J. (1990). Visual information and valid reasoning. In Zimmerman, W. (Ed.) Visualization in mathematics (pp. 9–24). Washington: Mathematical Association of America.
Macbeth, D. (2009). Meaning, use, and diagrams. Ethics & Politics XI, 1, 369–384.
Acknowledgments
I would like to thank the two anonymous reviewers who commented with care and attention to detail on the original draft of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Lemanski, J. Euler-type Diagrams and the Quantification of the Predicate. J Philos Logic 49, 401–416 (2020). https://doi.org/10.1007/s10992-019-09522-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-019-09522-y