Pranciškus Gricius (St Hilda’s College): 'Rigid Classicism'
Abstract: Classicism is a theory of grain according to which being provably equivalent in the classical higher-order logic is sufficient for higher-order identity. It is arguably one of the most natural and principled theories of grain that elegantly steers its way between the too-coarse-grained view called Extensionalism and the too-fine-grained view called Structuralism. Classicism has also been employed in the program of modal logicism, that is, in the program of reductively defining central notions of modal metaphysics in higher-order logic. Classicism, however, allows us to reduce some but only some central notions of modal metaphysics. Also, the modal logic of metaphysical necessity in Classicism is quite unnatural. In light of this, we shall propose Rigid Classicism, a strengthening of Classicism which integrates Extensional Comprehension into Classicism. If one uses Rigid Classicism, one can execute the program of modal logicism in a more principled manner. Rigid Classicism additionally allows us to reduce actuality operation and talk of possible worlds. It also codifies a more principled, strong, and simple modal logic for metaphysical necessity. Time permitting, we shall compare Rigid Classicism with a system recently defended by Peter Fritz.
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