A. Peruzzi: Delle Categorie (Ed. Via Laura, Firenze 2018).
Complementary readings suggested during the course.
Understanding of the main differences characterising the approaches by Aristotle, Kant and Mac Lane to the concept of category.
Knowledge of the elementary phenomenology of mathematical categories. Ability in using the formal concept in modelling basic metaphoric patterns.
General Knowledge provided by a first degree in philosophy.
The course favours the open-mindedness needed to connect subjects of different domains, by focusing epistemological, logico-foundational, and semantic topics.
Type of Assessment
Oral examinations on lessons' contents by questions and answers: each examination last for about 25 m.
Among the main concerns of 20th century philosophy was the logical analysis of concepts through language and the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the philosophical notion of category, and the semantic architecture of metaphorical language. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its ‘‘received view'', so that the issues faced by Aristotle and Kant disappeared through logical analysis. There are specific issues, in philosophy of language, epistemology and philosophy of mind, where this oblivion turns out to be misleading, e.g, in dealing with metaphors. The classical issues with "categories" suggest the gain in understanding coming from category theory. The very notion of "foundations of mathematics, however, is a metaphor to be analysed. Thus we need to classify the main patterns of metaphor as a process of partial structure-transfer, as introduced by the cognitive view of metaphors.
After presenting the views by Aristotle and Kant and the reasons of their oblivion, the formal notion of category is presented and applied to the investigation of metaphorical patterns. The relevance of a category-theoretic perspective leads to wide-ranging consequences for the semantics of natural language as it makes large use of metaphors. The course provides examples of functorial constraints activated in metaphors and shows how such constraints are mainly spatial, rather than logical. Basic geometrical intuitions thus come to the fore and supply the very access to the general architecture of categories.