Leibniz's laws of consistency and the philosophical foundations of connexive logic
DOI:
https://doi.org/10.12775/LLP.2019.004Keywords
connexive logic, Leibniz’s logic, term logic vs. propositional logicAbstract
As an extension of the traditional theory of the syllogism, Leibniz’s algebra of concepts is built up from the term-logical operators of conjunction, negation, and the relation of containment.
Leibniz’s laws of consistency state that no concept contains its own negation, and that if concept A contains concept B, then A cannot also contain Not-B. Leibniz believed that these principles would be universally valid, but he eventually discovered that they have to be restricted to self-consistent concepts.
This result is of utmost importance for the philosophical foundations of connexive logic, i.e. for the question how far either “Aristotle’s Thesis”, ¬(α → ¬α), or “Boethius’s Thesis”, (α → β) → ¬(α → ¬β), should be accepted as reasonable principles of a logic of conditionals.
References
Arnauld, Antoine, and Pierre Nicole, La Logique ou L’Art de Penser, 5th edition 1683. Reprint Paris 1965.
Bocheński, Jóżef M., Formale Logik, Verlag Karl Alber GmbH, Freiburg, München, 1956.
Couturat, Louis, Opuscules et fragments inédits de Leibniz, Paris, 1903. Reprint Hildesheim 1961.
Leibniz, Gottfried Wilhelm, “Generales inquisitiones de analysi notionum et veritatum”, pages 739–788 in Academy Edition (i.e. Gottfried Wilhelm Leibniz, Sämtliche Schriften und Briefe, hrg. von der Berlin-Brandenburgischen Akademie der Wissenschaften und der Akademie der Wissenschaften in Göttingen), Series VI, vol. 4, Berlin, 1999.
Leibniz, Gottfried Wilhelm, “Notationes generales”, pages 550–557 in Academy Edition, Series VI, vol. 4, 1999.
Leibniz, Gottfried Wilhelm, Nouveaux essais sur l’entendement, in G.W. Leibniz, Die philosophischen Schriften, edited by C.J. Gerhard, vol. 5, Berlin, 1882. Reprint Georg Olms Verlag, Hildesheim/New York, 1978.
Lenzen, Wolfgang, “Leibniz’s calculus of strict implication”, pages 1–35 in J. Srzednicki (ed.), Initiatives in Logic, Martinus Nijhoff Publishers, Dordrecht, 1987. DOI: http://dx.doi.org/10.1007/978-94-009-3673-7
Lenzen, Wolfgang, “Leibniz’s logic”, pages 1–83 in D. Gabbay and J. Woods (eds.), Handbook of the History of Logic, Vol. 3, The Rise of Modern Logic: From Leibniz to Frege, Elsevier North Holland, Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo, 2004. DOI: http://dx.doi.org/10.1016/S1874-5857(04)80014-1
Lenzen, Wolfgang, “Leibniz: Logic”, in J. Fieser and B. Dowden (eds.), Internet Encyclopedia of Philosophy. http://www.iep.utm.edu/leib-log
Martin, Christopher J., “Logic”, pages 158–199 in J.E. Brower and K. Guilfoy (eds.), The Cambridge Companion to Abelard, Chapter 5, Cambridge University Press, Cambridge UK, New York, 2006. DOI: http://dx.doi.org/10.1017/CCOL0521772478
McCall, Storrs, “Connexive implication”, pages 434–452 in A.R. Anderson and N.D. Belnap (eds.), Entailment: The Logic of Relevance and Necessity, Vol. 1, Princeton University Press, Princeton, 1975.
McCall, Storrs, “A history of connexivity”, pages 415–449 in D. Gabbay et al. (eds.), Handbook of the History of Logic, vol. 11, Elsevier, 2012. DOI: http://dx.doi.org/10.1016/B978-0-444-52937-4.50008-3
Pizzi, C., and T. Williamson, “Strong Boethius’ thesis and consequential implication”, Journal of Philosophical Logic 26, 5 (1997): 569–588. DOI: http://dx.doi.org/10.1023/A:1004230028063
Wansing, Heinrich, “Connexive logic”, in E.N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2014 edition, 2014. http://plato.stanford.edu/archives/fall2014/entries/logic-connexive/
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 808
Number of citations: 11
