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Full Idea
Epistemology is a big worry for structuralists. ..To conjecture that something has a particular structure, we must already have conceived of the idea of the structure itself; we cannot be discovering structures by conjecturing them.
Gist of Idea
To see a structure in something, we must already have the idea of the structure
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.59
A Reaction
This has to be a crucial area of discussion. Do we have our heads full of abstract structures before we look out of the window? Externalism about the mind is important here; mind and world are not utterly distinct things.
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] |
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] |
10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
8700 | 'In re' structuralism says that the process of abstraction is pattern-spotting [Friend] |