# Benjamin Wilck M.A.

## Ancient Philosophy (APhil)

Philosophie

Research Training Group

Philosophy Science and the Sciences

Hannoversche Straße 6

10115 Berlin

### Education

**2014 – 2022**

Doctoral Candidate in Philosophy, Humboldt University Berlin, Germany

Doctoral supervisors: Jonathan Beere (Humboldt University Berlin) & Benjamin Morison (Princeton University)

**2014**

Magister Artium degree (equals a combined B.A. + M.A.) in Philosophy and Cultural Studies, Humboldt University Berlin.

### Awards and Fellowships

**2019**

Trends in Classics Poster Prize by De Gruyter

**2018**

Doctoral scholarship by the German Research Foundation (DFG)

**2017**

Visiting fellowship at Princeton University funded by the German Research Foundation (DFG)

**2014 – 17**

Doctoral scholarship by the German Research Foundation (DFG)

**2014**

M.A. thesis award by the Carl & Max Schneider Foundation

**2009**

Erasmus Exchange Student Scholarship at Sorbonne University Paris-1 by the European Union

For more information, please visit https://benjamin-wilck.org

**Testing Definitions. Aristotelian Dialectic and Euclidean Mathematics**

In my dissertation *Euclid’s Philosophy*, I argue that Euclid’s philosophical views pertaining to the ontology and epistemology of mathematical objects can be reconstructed from his mathematical practice in the *Elements*, and, in particular, from the ways in which he formulates his mathematical definitions. While Euclid does not expressly formulate a philosophical theory, he implicitly––yet systematically––introduces ontological distinctions and conceptual hierarchies.

In Chapter 1 “The Types of Definitions”, I reconstruct Euclid’s ontology of mathematical objects. While the general ontological theory adopted in the *Elements* resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at all. Instead, as I show, Euclid systematically uses different types of definition to distinguish between metaphysically different kinds of mathematical object.

In Chapter 2 “The Order of Definitions”, I reconstruct Euclid’s aspects of epistemology of mathematical objects. In particular, I show that Euclid systematically uses ordered sequences of definitions to introduce conceptual hierarchies among the different kinds of mathematical object he distinguishes. In addition, I argue that the fact the Euclid regularly defines a term before using it in the definition of another term discloses a crucial requirement for scientific definitions: one term can enter the definition of another only if the former is conceptually more fundamental than the latter.

**2020**

Euclid’s Kinds and (Their) Attributes. History of Philosophy & Logical Analysis 23(2):362–397.

Can the Pyrrhonian Sceptic Suspend Belief Regarding a Scientific Definition?. History of Philosophy & Logical Analysis 23(1):253–288.