Combining Texts

All the ideas for 'teaching', 'Russell's Metaphysical Logic' and 'Presidential Address of Am. Math. Soc'

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23 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 / D. Definition / 8. Impredicative Definition
21704 'Impredictative' definitions fix a class in terms of the greater class to which it belongs [Linsky,B]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21705 Reducibility says any impredicative function has an appropriate predicative replacement [Linsky,B]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
10247 We have no adequate logic at the moment, so mathematicians must create one [Veblen]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
21727 Definite descriptions theory eliminates the King of France, but not the Queen of England [Linsky,B]
5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism
21719 Extensionalism means what is true of a function is true of coextensive functions [Linsky,B]
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 / a. Early logicism
21723 The task of logicism was to define by logic the concepts 'number', 'successor' and '0' [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
21721 Higher types are needed to distinguished intensional phenomena which are coextensive [Linsky,B]
21703 Types are 'ramified' when there are further differences between the type of quantifier and its range [Linsky,B]
21714 The ramified theory subdivides each type, according to the range of the variables [Linsky,B]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
21713 Did logicism fail, when Russell added three nonlogical axioms, to save mathematics? [Linsky,B]
21715 For those who abandon logicism, standard set theory is a rival option [Linsky,B]
8. Modes of Existence / B. Properties / 11. Properties as Sets
21729 Construct properties as sets of objects, or say an object must be in the set to have the property [Linsky,B]
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
644 For Pythagoreans the entire universe is made of numbers [Pythagoras, by Aristotle]
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]
375 When musical harmony and rhythm were discovered, similar features were seen in bodily movement [Pythagoras, by Plato]
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]