Abstract This paper defends a conceptualistic version of structuralism as the most convincing way elaborating philosophical understanding in line with classical tradition. The argument begins revision tradition “conceptual mathematics”, incarnated key figures period 1850 to 1940 like Riemann, Dedekind, Hilbert or Noether, showing how it led structuralist methodology. Then tension between ‘presu...

ii This thesis aims to explain the nature and justification of mathematical knowledge using an epistemic version of mathematical structuralism, that is a hybrid of Aristotelian structuralism and Hellman’s modal structuralism. Structuralism, the theory that mathematical entities are recurring structures or patterns, has become an increasingly prominent theory of mathematical ontology in the late...

I use an old challenge to motivate a new view. The old challenge is due to variation in our perceptions of secondary qualities. The challenge is to say whose perceptions are accurate. The new view is about how we manage to perceive secondary qualities, and thus manage to perceive them accurately or inaccurately. I call it perceptual structuralism. I first introduce the challenge and point out d...

Structuralism is a view about the subject matter of mathematics according to which what matters are structural relationships in abstraction from the intrinsic nature of the related objects. Mathematics is seen as the free exploration of structural possibilities, primarily through creative concept formation, postulation, and deduction. The items making up any particular system exemplifying the s...

Algebra, Mathematical Structuralism and

Under what conditions does a physical system implement or realize a computation? Structuralism about computational implementation, espoused by Chalmers and others, holds that a physical system realizes a computation just in the case the system instantiates a pattern of causal organization isomorphic to the computation‟s formal structure. I argue against structuralism through counter-examples dr...