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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]
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |