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Single Idea 18067

[filed under theme 9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta ]

Full Idea

The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure.

Gist of Idea

Abstract objects were a bad way of explaining the structure in mathematics

Source

Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)

Book Ref

Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.107

A Reaction

I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing.

The 5 ideas with the same theme [why we might postulate non-physical objects]:

13387 Our conceptual scheme becomes more powerful when we posit abstract objects [Quine]
16980 We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P]
18950 Physics is full of non-physical entities, such as space-vectors [Putnam]
10555 If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett]
18067 Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]