What is it about?
Sextus Empiricus’ method of Pyrrhonian Scepticism (named after the ancient Greek philosopher Pyrrho of Elis) is designed to enable us to live life without holding any beliefs: by finding for any argument in favour of a given claim an equally convincing counter-argument in favour of a conflicting claim, the Sceptic is supposed to suspend belief about everything. While commentators have debated whether there is some kind of belief that the Sceptic is able to hold, my paper shifts the focus to whether there is any kind of belief about which the Sceptic cannot suspend belief. Specifically, I identify one kind of belief that seems to defy the sceptical method, namely scientific principles such as axioms and definitions in geometry.
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Why is it important?
The results of my article are important for both exegetical and philosophical reasons. Firstly, the difficulty discovered in my article might explain a fact that has puzzled many commentators, namely why arguments in support of particular definitions are absent in Adversus Mathematicos III, Against the Geometers, where Sextus launches a sceptical attack on particular geometrical definitions such as Euclid’s definition of a straight line. Secondly, my article shows that not every scientific statement can equally be a target of philosophical scepticism.
Perspectives
I hope that my article provides a fresh look at Sextus’ method of Pyrrhonian Scepticism and, in particular, at the question of the applicability of that philosophical method to the specialized sciences, such as mathematics. One way to systematically develop the ideas expressed here further is to explore the extent to which Pyrrhonian Scepticism matches up to the so-called undecidable statements in mathematics (such as the Continuum Hypothesis or the Axiom of Choice).
Benjamin Wilck
Humboldt-Universitat zu Berlin
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This page is a summary of: Can the Pyrrhonian Sceptic Suspend Belief Regarding Scientific Definitions?, History of Philosophy & Logical Analysis, September 2020, Brill Deutschland GmbH,
DOI: 10.30965/26664275-02301014.
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