64 ideas
| 501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
| 5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
| 13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
| 457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
| 462 | One vision is produced by both eyes [Empedocles] |
| 22765 | Wisdom and thought are shared by all things [Empedocles] |
| 1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
| 514 | Beauty is merely animal without intelligence [Democritus (attr)] |
| 525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
| 502 | Good breeding in men means having a good character [Democritus (attr)] |
| 507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
| 552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
| 521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
| 505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
| 508 | Only accept beneficial pleasures [Democritus (attr)] |
| 520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
| 522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
| 506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
| 523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
| 503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
| 518 | A bad life is just a drawn-out death [Democritus (attr)] |
| 497 | Be virtuous from duty, not from fear [Democritus (attr)] |
| 499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
| 524 | Virtue comes more from practice than from nature [Democritus (attr)] |
| 519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
| 500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
| 1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
| 526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
| 511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
| 498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
| 1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |
| 589 | 'Nature' is just a word invented by people [Empedocles] |
| 21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
| 2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
| 6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
| 13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
| 459 | All change is unity through love or division through hate [Empedocles] |
| 13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
| 13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
| 460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
| 5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
| 466 | God is pure mind permeating the universe [Empedocles] |
| 461 | God is a pure, solitary, and eternal sphere [Empedocles] |
| 1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
| 1522 | It is wretched not to want to think clearly about the gods [Empedocles] |