Matteo Bianchetti (Notre Dame)

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May 15 MON — 10.30-12.30

Sala "Enzo Paci" — Direzione del Dipartimento (Via Festa del Perdono 7, Milano)

Veronese's Constructional Geometry

Reacting to the late XIX century skepticism about the geometric value or meaning of higher-dimensional ``geometry'', Veronese extended the synthetic method to the investigation of higher-dimensional spaces. To justify his approach he reflected on what it takes for a method to be \e{appropriate} to geometry and on the epistemic value of constructional and intuitive reasoning in geometry. I show that his justification is grounded on a preference for what can be called the etiological model of knowledge and the presentist model of knowledge. I also show that, unlike many supporters of the presentist ideal of knowledge, Veronese attributed great importance to abstractionist ideals of rigor. In particular, he endorsed Pasch's abstractionist ideal of rigor and proposed a way to integrate it to his constructional and intuitive approach to geometry.