Paradox si individuatie
Studiul meu, „The solo numero paradox”, tocmai a fost acceptat spre publicare de catre American Philosophical Quarterly. Propun un nou principiu al identitatii indiscernibililor menit sa rezolve o trilema (una dintre optiunile trilemei fiind un paradox pe care l-am descoperit). Rezumatul:
„I put forward a new interpretation of the principle of the identity of indiscernibles (PII), based on the idea that when asserting the principle one should quantify over properties in a fixed derivational context, so that derivational context is explicitly mentioned in the principle. The properties that will therefore figure in evaluating the truth-value of the principle will be what I call `instantial properties`, that is, the properties that the variables have in a derivational structure by being subject to the natural deduction rules of Existential Instantiation (EI) and Universal Generalization (UI). What is peculiar with these rules is that they require the reasoner to postulate so-called instantial terms (free variables, dummy-names, temporary constants, mathematical variables) assumed to designate an arbitrary member of the relevant domain depending on what has been (in the case of EI, by which they get introduced) or will be (in the case of UI, by which they get eliminated) asserted in the process of derivation. Drawing on work by Kit Fine and Jeffrey King on instantial terms, I show that the new PII can (a) accommodate the counter-examples to the old principle based on the possibility of symmetric universes, (b) can also accommodate in a paradox-free way the intuition behind those counter-examples to the effect that there can be objects different solo numero, and (c) its postulation of instantial properties does not make PII trivial, as these are pure properties, that is, not ones essentially involving particular objects. The novelty consists in introducing properties that objects have qua objects of reasoning, which derivational discourse will bring out, and which will discern the objects even when they are otherwise indiscernible.”
Lucrarea va fi continuata de o alta, in care aplic teoria, pe care o numesc „structuralism derivational”, asupra a trei probleme: cea a individuatiei particulelor cuantice, cea a acomodarii teoriei „bundle” cu aparentele contraexemple la principiul lui Leibniz bazate pe conceptibilitatea universurilor simetrice, si cea a individuarii numerelor imaginare i si –i. Aceasta din urma s-ar putea sa apara intr-o carte dedicata diverselor teorii structuraliste ale individuarii.