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Single Idea 9833

[filed under theme 18. Thought / E. Abstraction / 8. Abstractionism Critique ]

Full Idea

To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either.

Gist of Idea

To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too

Source

Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8)

Book Ref

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.86

A Reaction

[compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'.

The 28 ideas with the same theme [reasons to reject the abstractionist explanation]:

9075 If health happened to be white, the science of health would not study whiteness [Aristotle]
15385 Abelard's problem is the purely singular aspects of things won't account for abstraction [Panaccio on Abelard]
9096 The mind must produce by its own power an image of the individual species [Aquinas]
8638 Thomae's idea of abstract from peculiarities gives a general concept, and leaves the peculiarities [Frege on Thomae]
9979 Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait]
11846 If we abstract the difference between two houses, they don't become the same house [Frege]
9588 Number-abstraction somehow makes things identical without changing them! [Frege]
5816 Frege said concepts were abstract entities, not mental entities [Frege, by Putnam]
9819 Psychologism blunders in focusing on concept-formation instead of delineating the concepts [Dummett on Husserl]
9851 Husserl wanted to keep a shadowy remnant of abstracted objects, to correlate them [Dummett on Husserl]
10733 The abstractionist cannot explain 'some' and 'not' [Geach]
10734 Only a judgement can distinguish 'striking' from 'being struck' [Geach]
8771 'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience [Geach]
8772 We can't acquire number-concepts by extracting the number from the things being counted [Geach]
8773 Abstractionists can't explain counting, because it must precede experience of objects [Geach]
8774 The numbers don't exist in nature, so they cannot have been abstracted from there into our languages [Geach]
8778 Blind people can use colour words like 'red' perfectly intelligently [Geach]
8777 If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted? [Geach]
8779 We can form two different abstract concepts that apply to a single unified experience [Geach]
9833 To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
8165 To 'abstract from' is a logical process, as opposed to the old mental view [Dummett]
16289 We can't account for an abstraction as 'from' something if the something doesn't exist [Lewis]
9074 Abstraction cannot produce the concept of a 'game', as there is no one common feature [Barnes,J]
9073 Abstraction from an ambiguous concept like 'mole' will define them as the same [Barnes,J]
9072 Defining concepts by abstractions will collect together far too many attributes from entities [Barnes,J]
9146 After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]
9972 Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait]
9980 If abstraction produces power sets, their identity should imply identity of the originals [Tait]