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Single Idea 8774

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

Full Idea

The pattern of the numeral series that is grasped by a child exists nowhere in nature outside human languages, so the human race cannot possibly have discerned this pattern by abstracting it from some natural context.

Gist of Idea

The numbers don't exist in nature, so they cannot have been abstracted from there into our languages

Source

Peter Geach (Mental Acts: their content and their objects [1957], §8)

Book Ref

Geach,Peter: 'Mental Acts: Their content and their objects' [RKP 1971], p.31

A Reaction

This is a spectacular non sequitur, which begs the question. Abstractionists precisely claim that the process of abstraction brings numerals into human language from the natural context. Structuralism is an attempt to explain the process.

The 16 ideas from 'Mental Acts: their content and their objects'

2567 You can't define real mental states in terms of behaviour that never happens [Geach]
2568 Beliefs aren't tied to particular behaviours [Geach]
8769 If someone has aphasia but can still play chess, they clearly have concepts [Geach]
8770 'Abstractionism' is acquiring a concept by picking out one experience amongst a group [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]
8775 A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction [Geach]
8776 We cannot learn relations by abstraction, because their converse must be learned too [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]
8780 Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2' [Geach]
8781 The mind does not lift concepts from experience; it creates them, and then applies them [Geach]
11910 Being 'the same' is meaningless, unless we specify 'the same X' [Geach]