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

Mohammad Shafiei


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.


Identity of Indiscernibles; Dialogical Logic; Identity; Equality


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 An unpublished latin text on terms and relations.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.

DOI: https://doi.org/10.22370/rhv.2017.9.849

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