Combining Texts

All the ideas for 'teaching', 'Mathematical logic and theory of types' and 'On Interpretation'

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39 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
5896 Speak the truth, for this alone deifies man [Pythagoras, by Porphyry]
1. Philosophy / B. History of Ideas / 2. Ancient Thought
3051 Pythagoras discovered the numerical relation of sounds on a string [Pythagoras, by Diog. Laertius]
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 / 8. Critique of Set Theory
11064 Classes can be reduced to propositional functions [Russell, by Hanna]
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 / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
6407 The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
7485 For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10418 Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
10047 Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
23478 Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
18126 A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
18128 Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
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]
22. Metaethics / B. Value / 2. Values / d. Health
3053 Pythagoras taught that virtue is harmony, and health, and universal good, and God [Pythagoras, by Diog. Laertius]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
5244 For Pythagoreans, justice is simply treating all people the same [Pythagoras, by Aristotle]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
375 When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato]
638 Pythagoreans define timeliness, justice and marriage in terms of numbers [Pythagoras, by Aristotle]
553 Pythagoreans think mathematical principles are the principles of all of nature [Pythagoras, by Aristotle]
554 Pythagoreans say things imitate numbers, but Plato says things participate in numbers [Pythagoras, by Aristotle]
644 For Pythagoreans the entire universe is made of numbers [Pythagoras, by 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 / D. Religious Issues / 2. Immortality / a. Immortality
7467 The modern idea of an immortal soul was largely created by Pythagoras [Pythagoras, by Watson]