more from John P. Burgess

### Single Idea 10189

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

One might meet the 'Van Inwagen Problem' by saying that the intrinsic properties of the object playing the role of 2 will differ from one model to another, so that no statement about the intrinsic properties of 'the' real numbers will make sense.

Clarification

See Idea 10188 for the Van Ingwagen Problem

Gist of Idea

There is no one relation for the real number 2, as relations differ in different models

Source

John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5)

A Reaction

There seems to be a potential confusion among opponents of structuralism between relations at the level of actual mathematical operations, and generalisations about relations, which are captured in the word 'patterns'. Call them 'meta-relations'?

Related Idea

Idea 10188
How can mathematical relations be either internal, or external, or intrinsic? **[Burgess]**