SOPhiA 2018

Salzburgiense Concilium Omnibus Philosophis Analyticis

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Programme - Talk

Aristotle's Posterior Analytics: Euclidean Axiomatic Sciences or Husserlian Regional Ontologies?
(History of Philosophy, English)

Since the commentary of Philoponus, Aristotle's Posterior Analytics (APo) has been interpreted as an account and defence of axiomatic sciences, most notably Euclid's axiomatization of geometry. This is still a popular interpretation (cf. Scholz 1930; Betti & Jong 2010). I argue that Aristotle's APo is not best interpreted as defending Euclidean axiomatic sciences. Rather, it is closer to Husserlian regional/material ontologies.
While the two interpretations are similar, they also differ on some important issues. Both aim at a systematization of the special sciences (e.g., geometry, algebra, biology). For both, this systematization involves a hierarchical structure. Both are (mainly) concerned with generalizations and laws, rather than particular individuals. Last, both involve deductive reasoning not only in the construction but also in the application of the system.
First of the differences is that in an axiomatic science the nodes (i.e., any axiom, postulate, thesis, definition, etc.) are propositions (or facts, or states of affairs), such as ''a point is that which has no part'' and ''if in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another''. In contrast, in a Husserlian regional ontology the nodes are universals, such as Triangle, Angle, and Point.
Second, in an axiomatic science the relation connecting the nodes is that of deducibility, along the lines of proof-theory. In contrast, a Husserlian regional ontology includes several distinct relations which can connect a node to several other nodes. E.g., Isosceles is a species of Triangle (taxonomic relation), Isosceles has part two equal angles (parthood relation), and Isosceles encloses an area (spatial relation).
An upshot of this is that while the axiomatic view of sciences (e.g., Hilbert's view) is generally held to have been a failure, in contrast the Husserlian program (cf. Arp, Smith, & Spear 2015) is a recent and very promising scientific program.

Chair: Rareș Fogaș
Time: 14:00-14:30, 12 September 2018 (Wednesday)
Location: HS E.002

Petter Sandstad 
(Rostock, Germany)

Petter Sandstad is a doctoral student at the University of Rostock. He is a research assistant in the DFG-project, Formal Causation in Aristotle and in Analytic Metaphysics and Philosophy of Science (2018-2020). He has published both on ancient philosophy and on contemporary metaphysics. And most importantly, he has presented papers at two previous SOPhiA-conferences.

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