Andreas Frenzel
LMU Munich (MCMP)
Timothy Williamson is a prominent defender of classical logic, which he regards as sufficient for the analysis of all philosophical concepts, including vague predicates. His epistemic theory of vagueness holds that such predicates have sharp but unknowable boundaries. The Sorites paradox, on this view, arises not because of any logical or semantic indeterminacy, but from our epistemic limitations in identifying where these sharp boundaries lie. Williamson’s commitment to classical logic leads him to accept counterintuitive consequences, such as the claim that there is a precise number of grains of sand that marks the boundary between a heap and a non-heap, even if we can never know what it is.
In this paper, I challenge the monistic assumptions that underlie Williamson’s position. Rather than arguing that his view is false, or that an alternative such as fuzzy logic or supervaluationism is true, I examine the role of goals in selecting a formalization for vague predicates. By “”goals”” I mean the subjective normative considerations – such as explanatory purpose, intuitive fit, or formal elegance – that
shape which features a formalization should have.
Admissibility criteria, as I use the term, are constraints informed by these goals. They determine which kinds of formalizations are even considered suitable for a given task. Williamson’s analysis is coherent within a framework where preserving classical logic is desired, and where sharp boundaries are not disqualifying. But if we shift our admissibility criteria – for instance, by placing greater value on tolerance – Williamson’s solution to the Sorites paradox ceases to appear uniquely correct.
Depending on the goals at play, different formalizations may be preferable: fuzzy logic may better capture gradual category change, while supervaluationism may better preserve classical tautologies. In this sense, the choice of formalization is not strictly objective, but partly subjective.
Chair: Tobias Lipinski
Time: 04 September, 10:00 – 10:30
Location: SR 1.006
SOPhiA 2026 