Universals and Measurement


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Universals and Measurement

I argue in U&M that Rand's measurement-omission analysis of concepts implies a distinctive magnitude structure for metaphysics. This is structure beyond logical structure, constraint on possibility beyond logical constraint. Yet, it is structure ranging as widely as logical structure through all the sciences and common experience. I uncover this distinctive magnitude structure, characterizing it by its automorphisms, by its location among mathematical categories, and by the types of measurements it affords. I uncover a structure to universals implicit in Rand's theory that is additional to recurrence structure. ~Note on mathematics and philosophy~

Several years after writing U&M, I developed my own metaphysics, akin to Rand's, but significantly different from hers. For the future, on the ontology side, I expect my own philosophy of mathematics to have taken for definition at the outset: mathematics is the discipline studying the formalities of situation, where situation is one of my categories as presented in my fundamental paper Existence, We, and the formal is divided between the foundational formalities which in that paper I introduced as belonging-formalities (in the world regardless of our discernment) and tooling-formalities (our set-theoretic [or better, perhaps, categoric-theoretic {in the sense of categories in mathematics; sets being one such category}] characterization of belonging-formalities.) Formalities of situation would cover both of those formalities. Formalities of my other two categories that are not entity—character and passage—would belong to logic, rather than mathematics. If this allotment to these disciplines can indeed be shown appropriate, it would show a big advantage of my category-division of existence over Rand's category-division: entity, action, attribute, relationship. Although, whatever I am able to come up with for using my categories in ontology of mathematics, I could also probably mimic using Rand's categories, though that would be less tidy. It is important that I amend Rand's measurement-omission analysis of concepts, expanding it to give theory of mathematical concepts, beyond kind-concepts, in order to bring forth for her a serious epistemology of mathematics—one competitive, notably, with Kant's epistemology of mathematics.

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