Combining Texts

All the ideas for 'teaching', 'A Completeness Theorem in Modal Logic' and 'The Folly of Trying to Define Truth'

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20 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]
3. Truth / A. Truth Problems / 2. Defining Truth
23295 Truth cannot be reduced to anything simpler [Davidson]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
23298 Neither Aristotle nor Tarski introduce the facts needed for a correspondence theory [Davidson]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
23297 The language to define truth needs a finite vocabulary, to make the definition finite [Davidson]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
23296 We can elucidate indefinable truth, but showing its relation to other concepts [Davidson]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
10163 Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic
10760 With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
16189 The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
15132 The Barcan formulas fail in models with varying domains [Kripke, by Williamson]
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]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
23294 It is common to doubt truth when discussing it, but totally accept it when discussing knowledge [Davidson]
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]
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]