Combining Texts

All the ideas for 'The philosophical basis of intuitionist logic', 'Abstraction Reconsidered' and 'The Limits of Abstraction'

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21 ideas

2. Reason / D. Definition / 3. Types of Definition
10143 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K]
9143 Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18073 Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
5. Theory of Logic / G. Quantification / 1. Quantification
19057 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
10735 Abstraction from objects won't reveal an operation's being performed 'so many times' [Geach]
7. Existence / A. Nature of Existence / 4. Abstract Existence
10145 Abstracts cannot be identified with sets [Fine,K]
10136 Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K]
10144 Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
10732 If concepts are just recognitional, then general judgements would be impossible [Geach]
18. Thought / D. Concepts / 3. Ontology of Concepts / b. Concepts as abilities
10731 For abstractionists, concepts are capacities to recognise recurrent features of the world [Geach]
18. Thought / E. Abstraction / 1. Abstract Thought
9144 Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10141 Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10135 We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
9142 Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
10137 Abstractionism can be regarded as an alternative to set theory [Fine,K]
10138 An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
18. Thought / E. Abstraction / 8. Abstractionism Critique
10733 The abstractionist cannot explain 'some' and 'not' [Geach]
10734 Only a judgement can distinguish 'striking' from 'being struck' [Geach]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
19055 Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
19056 If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
19. Language / A. Nature of Meaning / 6. Meaning as Use
19054 Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]