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Single Idea 8700

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism ]

Full Idea

In the 'in re' version of mathematical structuralism, pattern-spotting is the process of abstraction.

Clarification

For 'in re' structuralism, see Idea 8699

Gist of Idea

'In re' structuralism says that the process of abstraction is pattern-spotting

Source

Michèle Friend (Introducing the Philosophy of Mathematics [2007], 4.4)

Book Ref

Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.91

A Reaction

This might work for non-mathematical abstraction as well, if we are allowed to spot patterns within sensual experience, and patterns within abstractions. Properties are causal patterns in the world? No - properties cause patterns.

The 12 ideas with the same theme [structuralism with real objects or real structures]:

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]