Ideas of Peter Geach, by Theme

[British, 1916 - 2013, Married to Elizabeth Anscombe. University of Leeds.]

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
Abstraction from objects won't reveal an operation's being performed 'so many times'
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Attributes are functions, not objects; this distinguishes 'square of 2' from 'double of 2'
9. Objects / A. Existence of Objects / 6. Nihilism about Objects
We should abandon absolute identity, confining it to within some category
9. Objects / F. Identity among Objects / 3. Relative Identity
Denial of absolute identity has drastic implications for logic, semantics and set theory
Identity is relative. One must not say things are 'the same', but 'the same A as'
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Leibniz's Law is incomplete, since it includes a non-relativized identity predicate
9. Objects / F. Identity among Objects / 9. Sameness
Being 'the same' is meaningless, unless we specify 'the same X'
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
A big flea is a small animal, so 'big' and 'small' cannot be acquired by abstraction
We cannot learn relations by abstraction, because their converse must be learned too
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
If concepts are just recognitional, then general judgements would be impossible
17. Mind and Body / B. Behaviourism / 2. Behavioural Dispositions
You can't define real mental states in terms of behaviour that never happens
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
Beliefs aren't tied to particular behaviours
18. Thought / D. Concepts / 2. Ontology of Concepts / b. Concepts as abilities
For abstractionists, concepts are capacities to recognise recurrent features of the world
18. Thought / D. Concepts / 4. Concepts and Language / c. Concepts without language
If someone has aphasia but can still play chess, they clearly have concepts
18. Thought / D. Concepts / 5. Origin of Concepts / a. Origin of concepts
The mind does not lift concepts from experience; it creates them, and then applies them
18. Thought / D. Concepts / 6. Abstract Concepts / c. Abstracta by ignoring
'Abstractionism' is acquiring a concept by picking out one experience amongst a group
18. Thought / D. Concepts / 6. Abstract Concepts / h. Abstractionism critique
We can form two different abstract concepts that apply to a single unified experience
The abstractionist cannot explain 'some' and 'not'
Only a judgement can distinguish 'striking' from 'being struck'
'Or' and 'not' are not to be found in the sensible world, or even in the world of inner experience
We can't acquire number-concepts by extracting the number from the things being counted
Abstractionists can't explain counting, because it must precede experience of objects
The numbers don't exist in nature, so they cannot have been abstracted from there into our languages
Blind people can use colour words like 'red' perfectly intelligently
If 'black' and 'cat' can be used in the absence of such objects, how can such usage be abstracted?