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All the ideas for 'The philosophical basis of intuitionist logic', 'Are there propositions?' and 'Philosophy of Mathematics'

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26 ideas

3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
A true proposition seems true of one fact, but a false proposition seems true of nothing at all. [Ryle]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Two maps might correspond to one another, but they are only 'true' of the country they show [Ryle]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
5. Theory of Logic / G. Quantification / 1. Quantification
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
Many sentences do not state facts, but there are no facts which could not be stated [Ryle]
12. Knowledge Sources / B. Perception / 3. Representation
Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
If you like judgments and reject propositions, what are the relata of incoherence in a judgment? [Ryle]
19. Language / A. Nature of Meaning / 1. Meaning
Husserl and Meinong wanted objective Meanings and Propositions, as subject-matter for Logic [Ryle]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
When I utter a sentence, listeners grasp both my meaning and my state of mind [Ryle]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
19. Language / D. Propositions / 1. Propositions
'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle]
19. Language / D. Propositions / 4. Mental Propositions
Several people can believe one thing, or make the same mistake, or share one delusion [Ryle]
We may think in French, but we don't know or believe in French [Ryle]
19. Language / D. Propositions / 6. Propositions Critique
There are no propositions; they are just sentences, used for thinking, which link to facts in a certain way [Ryle]
If we accept true propositions, it is hard to reject false ones, and even nonsensical ones [Ryle]