Combining Texts

All the ideas for 'On Interpretation', 'works' and 'Philosophy of Mathematics'

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29 ideas

2. Reason / B. Laws of Thought / 4. Contraries
1708 In "Callias is just/not just/unjust", which of these are contraries? [Aristotle]
3. Truth / B. Truthmakers / 10. Making Future Truths
1703 It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
1704 Statements are true according to how things actually are [Aristotle]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
22272 Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle]
9405 Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9728 Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn]
9729 Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9730 Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9731 Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9732 Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9733 Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
23445 Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
21593 In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
1701 A prayer is a sentence which is neither true nor false [Aristotle]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
23447 In classical semantics singular terms refer, and quantifiers range over domains [Linnebo]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
23443 The axioms of group theory are not assertions, but a definition of a structure [Linnebo]
23444 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
23446 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
23448 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
23441 Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
23442 Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
1706 Non-existent things aren't made to exist by thought, because their non-existence is part of the thought [Aristotle]
7. Existence / A. Nature of Existence / 5. Reason for Existence
1707 Maybe necessity and non-necessity are the first principles of ontology [Aristotle]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
2337 For Aristotle meaning and reference are linked to concepts [Aristotle, by Putnam]
19. Language / D. Propositions / 4. Mental Propositions
13763 Spoken sounds vary between people, but are signs of affections of soul, which are the same for all [Aristotle]
19. Language / F. Communication / 3. Denial
1705 It doesn't have to be the case that in opposed views one is true and the other false [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
1702 Things may be necessary once they occur, but not be unconditionally necessary [Aristotle]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]