profile picture

Owain Griffin

Ohio State University
 More details
  •  11
    Foundations of Mathematics
    Internet Encyclopedia of Philosophy. 2026.
    The Foundations of Mathematics This article examines what is meant by ‘foundation’ in different contexts, and it focuses on four prominent mathematical theories, each of which have been claimed to play some kind of foundational role. As we will see, different features which might be desired from a foundation has led to a variety of … Continue reading Foundations of Mathematics →
  •  34
    Platonism vs. Pluralism in advance
    Thought: A Journal of Philosophy. forthcoming.
    Platonism about mathematical objects and pluralism about logic are two widely discussed views in contemporary philosophy. In this paper I show that despite their popularity a tension arises when the two are combined: one and the same collection of objects are ascribed mutually inconsistent properties. In light of this, I consider the ways in which those tempted by the platonist-pluralist combination might respond to the problem without abandoning the view entirely.
  •  37
    Skepticism and Mathematics
    Erkenntnis 1-16. forthcoming.
    Model-theoretic skepticism is a challenge to purported a priori mathematical knowledge. According to this challenge, elementary results from mathematical logic undermine our grasp of basic mathematical concepts such as finitude and countability. Despite generating rich discussion over the years, most philosophers don’t feel worried by model-theoretic skepticism, in part due to a number of notable anti-skeptical arguments. In this paper, I evaluate these arguments, and explore the question of whe…Read more
  •  105
    The Problem of Isomorphic Structures
    Thought: A Journal of Philosophy 11 (4): 206-214. 2022.
    Structuralism is one of the most popular contemporary accounts of mathematics. Despite its popularity, it has been challenged on the grounds of consistency. In this paper, I show that existing arguments purporting to establish an inconsistency miss the mark. I then proceed to develop a new argument against realist structuralism, to show that the commitment to mathematical pluralism and the structural identity criterion embraced by the realist structuralist jointly entail a contradiction.
  •  49
    To Infinity... and Beyond?
    Philosophy Now 137 28-30. 2020.