40 ideas
20801 | A wise man's chief strength is not being tricked; nothing is worse than error, frivolity or rashness [Zeno of Citium, by Cicero] |
1771 | When shown seven versions of the mowing argument, he paid twice the asking price for them [Zeno of Citium, by Diog. Laertius] |
20770 | Philosophy has three parts, studying nature, character, and rational discourse [Zeno of Citium, by Diog. Laertius] |
6022 | Someone who says 'it is day' proposes it is day, and it is true if it is day [Zeno of Citium, by Diog. Laertius] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
7555 | Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium] |
20860 | Whatever participates in substance exists [Zeno of Citium, by Stobaeus] |
21397 | Perception an open hand, a fist is 'grasping', and holding that fist is knowledge [Zeno of Citium, by Long] |
20799 | A grasp by the senses is true, because it leaves nothing out, and so nature endorses it [Zeno of Citium, by Cicero] |
20797 | If a grasped perception cannot be shaken by argument, it is 'knowledge' [Zeno of Citium, by Cicero] |
21398 | A presentation is true if we judge that no false presentation could appear like it [Zeno of Citium, by Cicero] |
1770 | When a slave said 'It was fated that I should steal', Zeno replied 'Yes, and that you should be beaten' [Zeno of Citium, by Diog. Laertius] |
3799 | A dog tied to a cart either chooses to follow and is pulled, or it is just pulled [Zeno of Citium, by Hippolytus] |
21402 | Incorporeal substances can't do anything, and can't be acted upon either [Zeno of Citium, by Cicero] |
20816 | A body is required for anything to have causal relations [Zeno of Citium, by Cicero] |
1773 | A sentence always has signification, but a word by itself never does [Zeno of Citium, by Diog. Laertius] |
20841 | Zeno said live in agreement with nature, which accords with virtue [Zeno of Citium, by Diog. Laertius] |
1774 | Since we are essentially rational animals, living according to reason is living according to nature [Zeno of Citium, by Diog. Laertius] |
20863 | The goal is to 'live in agreement', according to one rational consistent principle [Zeno of Citium, by Stobaeus] |
2662 | Zeno saw virtue as a splendid state, not just a source of splendid action [Zeno of Citium, by Cicero] |
21395 | One of Zeno's books was 'That Which is Appropriate' [Zeno of Citium, by Long] |
5964 | Zeno says there are four main virtues, which are inseparable but distinct [Zeno of Citium, by Plutarch] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
20822 | There is no void in the cosmos, but indefinite void outside it [Zeno of Citium, by Ps-Plutarch] |
2648 | Things are more perfect if they have reason; nothing is more perfect than the universe, so it must have reason [Zeno of Citium] |
20811 | Since the cosmos produces what is alive and rational, it too must be alive and rational [Zeno of Citium] |
20810 | Rational is better than non-rational; the cosmos is supreme, so it is rational [Zeno of Citium] |
2649 | If tuneful flutes grew on olive trees, you would assume the olive had some knowledge of the flute [Zeno of Citium] |
20807 | The cosmos and heavens are the substance of god [Zeno of Citium, by Diog. Laertius] |