A Higher-order Dialogical Logic to demonstrate Leibniz’s Law of Identity of Indiscernibles

Authors

  • Mohammad Shafiei University of Paris 1

DOI:

https://doi.org/10.22370/rhv2017iss9pp73-88

Keywords:

Identity of Indiscernibles, Dialogical Logic, Identity, Equality

Abstract

In this note I discuss some issues around the law of Identity of Indiscernibles and, above all, its difference with the so-called law of indiscernibilty of identicals. In this way I distinguish between the notions identity, sameness and equality, through a phenomenological discussion and using the key idea of intentionality. In order to formulate the Leibnizian law of Identity of Indiscernibles, and examine its validity, we need higher order logic. I will give semantic rules for a second-order logic with identity in the framework of the dialogical logic, introduced by P. Lorenzen. Then I will demonstrate the validity of the law of Identity of Indiscernibles by means of the introduced logic.

References

Clerbout, N. (2014). Finiteness of plays and the dialogical problem of decidability. IfCoLog Journal of Logics and their Applications, 1, 115-130.

Husserl, E. (1973). Experience and judgment, trl. J. Churchill, and K. Ameriks. London : Routledge.

Husserl, E. (1982). Cartesian meditations, trl. Dorian Cairns.

Husserl, E. (2002). Logische untersuchungen. Ergänzungsband. Erster teil, ed. U. Melle (Vol. XX/1).

Leibniz, G. (1989). Philosophical papers and letters, Ed. L. E. Loemker. Kluwer Academic Publishers.

Leibniz, G. (2008). New essays on human understanding, book ii: Ideas, trl. J. Bennett.

Mugnai, M. (1997). An unpublished latin text on terms and relations. The Leibniz Review, 7, 125–127.

Rahman, S., & Keiff, L. (2005). On how to be a dialogician. In D. Vanderveken (Ed.), Logic, thought and action (Vol. 2, p. 359-408). Springer Netherlands.

Rebuschi, M. (2009). Implicit versus explicit knowledge in dialogical logic. In O. Majer, A.-V. Pietarinen, & T. Tulenheimo (Eds.), Games: Unifying logic, language, and philosophy (pp. 229–246). Springer Verlag.

Rückert, H. (2001). Why dialogical logic? In H. Wansing (Ed.), Essays on non- classical logic (pp. 165–185). River Edge: World Scientific.

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Published

2017-07-15

How to Cite

Shafiei, M. (2017). A Higher-order Dialogical Logic to demonstrate Leibniz’s Law of Identity of Indiscernibles. Revista De Humanidades De Valparaíso, (9), 73–88. https://doi.org/10.22370/rhv2017iss9pp73-88

Issue

No. 9 (2017): No 9 (2017)

Section

Articles

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