Philosophical Monologues: Formalizing Aristotle's Topics

Sunday, October 15, 2023

Formalizing Aristotle's Topics

After this preliminary study on the practice of definition in antiquity and in modern mathematics

Modern Definition and Ancient Definition

we present a proposal for an axiomatic system to capture the topoi in Aristotle's Topics:

Towards a Formalization of Aristotle's Topics

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Logic, therefore, is not a tool; it is an open-ended, evolving science having an ontology of its own. Mathematics is but one of its parts, and its full scope is yet to be discovered. Given the definition of validity, every necessary thought whose analysis contains only purely logical objects is valid. So every time we discover a purely logical analysis of a concept previously thought to belong to a discipline outside logic, the acknowledged scope of logic must be expanded accordingly. The purely logical analysis of number is just one case in point, and I submit that there are many more (...) If there is anything in the analyses I will offer, then the conception of logic that emerges is very far indeed from that of Aristotle, for whom logic is primarily a tool; instead, it is more like that of Plato, for whom logic is akin to reason itself. George Bealer

Sunday, October 15, 2023

Formalizing Aristotle's Topics

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Prolegomena to a future logico-mathematical metaphysics