Combining Texts

All the ideas for 'Are there propositions?', 'The Foundations of Mathematics' and 'Goodbye Descartes'

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34 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
Logic was merely a branch of rhetoric until the scientific 17th century [Devlin]
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 / A. Syllogistic Logic / 2. Syllogistic Logic
'No councillors are bankers' and 'All bankers are athletes' implies 'Some athletes are not councillors' [Devlin]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Modern propositional inference replaces Aristotle's 19 syllogisms with modus ponens [Devlin]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Predicate logic retains the axioms of propositional logic [Devlin]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
Situation theory is logic that takes account of context [Devlin]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Golden ages: 1900-1960 for pure logic, and 1950-1985 for applied logic [Devlin]
Montague's intensional logic incorporated the notion of meaning [Devlin]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Where a conditional is purely formal, an implication implies a link between premise and conclusion [Devlin]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
Sentences of apparent identical form can have different contextual meanings [Devlin]
5. Theory of Logic / L. Paradox / 1. Paradox
Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
Space and time are atomic in the arrow, and divisible in the tortoise [Devlin]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
I just confront the evidence, and let it act on me [Ramsey]
12. Knowledge Sources / B. Perception / 3. Representation
Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
People still say the Hopi have no time concepts, despite Whorf's later denial [Devlin]
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 / C. Assigning Meanings / 1. Syntax
How do we parse 'time flies like an arrow' and 'fruit flies like an apple'? [Devlin]
19. Language / D. Propositions / 1. Propositions
'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
The distinction between sentences and abstract propositions is crucial in logic [Devlin]
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]