more on this theme | more from this thinker
Full Idea
In present-day mathematics, it is set theory that serves as the background theory in which other branches of mathematics are developed.
Gist of Idea
Set theory is the standard background for modern mathematics
Source
John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1)
A Reaction
[He cites Bourbaki as an authority for this] See Benacerraf for a famous difficulty here, when you actually try to derive an ontology from the mathematicians' working practices.
| 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] |