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


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DOI: http://dx.doi.org/10.22370/rhv.2017.9.849


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