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Full Idea
Mathematical realism is the doctrine that mathematical objects exist, that much contemporary mathematics is true, and that the existence and truth in question is independent of our constructions, beliefs and proofs.
Gist of Idea
Mathematical realism says that maths exists, is largely true, and is independent of proofs
Source
Michael D. Resnik (Maths as a Science of Patterns [1997], Three.12.9)
Book Ref
Resnik,Michael D.: 'Mathematics as a Science of Patterns' [OUP 1999], p.271
A Reaction
As thus defined, I would call myself a mathematical realist, but everyone must hesitate a little at the word 'exist' and ask, how does it exist? What is it 'made of'? To say that it exists in the way that patterns exist strikes me as very helpful.
| 6295 | There are too many mathematical objects for them all to be mental or physical [Resnik] |
| 6296 | Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik] |
| 6299 | Axioms are often affirmed simply because they produce results which have been accepted [Resnik] |
| 6300 | Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik] |
| 6301 | Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik] |
| 6302 | Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik] |
| 6303 | Sets are positions in patterns [Resnik] |
| 6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |