88 ideas
| 1642 | We must fight fiercely for knowledge, understanding and intelligence [Plato] |
| 1645 | The desire to split everything into its parts is unpleasant and unphilosophical [Plato] |
| 20910 | Everything happens necessarily, and for a reason [Democritus] |
| 1644 | Dialectic should only be taught to those who already philosophise well [Plato] |
| 287 | Good analysis involves dividing things into appropriate forms without confusion [Plato] |
| 20478 | In discussion a person's opinions are shown to be in conflict, leading to calm self-criticism [Plato] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 16146 | Two can't be a self-contained unit, because it would need to be one to do that [Democritus, by Aristotle] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 20901 | True Being only occurs when it is completely full, with atoms and no void [Democritus, by Aristotle] |
| 20902 | Being does not exist more than non-being [Democritus, by Aristotle] |
| 20904 | The non-existent exists as much as the existent, because it has causal powers [Democritus] |
| 11278 | What does 'that which is not' refer to? [Plato] |
| 1643 | If statements about non-existence are logically puzzling, so are statements about existence [Plato] |
| 20903 | The only distinctions are Configuration (shape), Disposition (order) and Turning (position) [Democritus, by Aristotle] |
| 7022 | To be is to have a capacity, to act on other things, or to receive actions [Plato] |
| 20893 | Nothing comes from non-existence, or passes into it [Democritus, by Diog. Laertius] |
| 1641 | Some alarming thinkers think that only things which you can touch exist [Plato] |
| 10784 | Whenever there's speech it has to be about something [Plato] |
| 20896 | It is not possible to know what sort each thing is [Democritus] |
| 16122 | Good thinkers spot forms spread through things, or included within some larger form [Plato] |
| 10422 | The not-beautiful is part of the beautiful, though opposed to it, and is just as real [Plato] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 15855 | If we see everything as separate, we can then give no account of it [Plato] |
| 3357 | Democritus denies reality to large objects, because atomic entities can't combine to produce new ones [Benardete,JA on Democritus] |
| 598 | Democritus said that substances could never be mixed, so atoms are the substances [Democritus, by Aristotle] |
| 1532 | Sensible qualities can't be real if they appear different to different creatures [Democritus, by Theophrastus] |
| 20894 | Man is separated from reality [Democritus] |
| 517 | All evidence comes from senses, so they are indispensable to the mind [Democritus] |
| 20897 | Obscure knowledge belongs to the five senses, and genuine knowledge is the other type [Democritus] |
| 1637 | A soul without understanding is ugly [Plato] |
| 577 | Democritus says there is either no truth, or it is concealed from us [Democritus, by Aristotle] |
| 20895 | We actually know nothing, and opinions are mere flux [Democritus] |
| 1528 | We in fact know nothing, but we each restructure our reality with beliefs [Democritus] |
| 492 | It is obviously impossible to understand the reality of each thing [Democritus] |
| 515 | We know nothing in reality; for truth lies in an abyss [Democritus] |
| 20892 | Democritus was devoted to discovering causal explanations [Democritus, by Eusebius] |
| 5882 | Democritus says soul consists of smooth round bodies brought together in accidental collision [Democritus, by Cicero] |
| 6034 | Atomists say soul has a rational part in the chest, and a diffused non-rational part [Democritus, by Aetius] |
| 20912 | The soul is the same as the mind [Democritus, by Aristotle] |
| 20916 | Animals have a share of reason [Democritus, by Porphyry] |
| 20914 | The directive centre is located in the whole head [Democritus, by Ps-Plutarch] |
| 6033 | Democritus said everything happens of necessity, by natural motion of atoms [Democritus, by Cicero] |
| 5088 | Some say there is a determinate cause for every apparently spontaneous event [Democritus, by Aristotle] |
| 21670 | Democritus said atoms only move by their natural motions, which are therefore necessary [Democritus, by Cicero] |
| 24041 | Democritus says spherical atoms are fire, and constitute the soul [psuche] [Democritus, by Aristotle] |
| 20913 | Democritus says the soul is the body, and thinking is thus the mixture of the body [Democritus, by Theophrastus] |
| 1540 | Pleasure and pain guide our choices of good and bad [Democritus] |
| 495 | Wisdom creates a healthy passion-free soul [Democritus] |
| 1537 | Happiness is identifying and separating the pleasures [Democritus, by Stobaeus] |
| 1636 | Wickedness is an illness of the soul [Plato] |
| 20917 | Contentment comes from moderation and proportion in life [Democritus, by Stobaeus] |
| 13551 | Democritus says wealth is a burden to the virtuous mind [Democritus, by Seneca] |
| 1638 | Didactic education is hard work and achieves little [Plato] |
| 20899 | Atoms cling together, until a stronger necessity disperses them [Democritus, by Aristotle] |
| 20898 | Atoms are irregular, hooked, concave, convex, and many other shapes [Democritus, by Aristotle] |
| 17542 | 'Full' and 'Void' secularised Parmenides's Being and Not-being [Democritus, by Heisenberg] |
| 1525 | Atomists say there are only three differences - in shape, arrangement and position [Democritus, by Aristotle] |
| 493 | Experiences are merely convention; only atoms and the void are real [Democritus] |
| 5947 | If only atoms are real and the rest is convention, we wouldn't bother to avoid pain [Democritus, by Diogenes of Oen.] |
| 13219 | When atoms touch, why don't they coalesce, like water drops? [Aristotle on Democritus] |
| 1533 | Because appearance is infinitely varied, atomists assume infinitely many shapes of atom [Democritus, by Aristotle] |
| 20908 | There could be an atom the size of the world [Democritus, by Ps-Plutarch] |
| 1527 | There must be atoms, to avoid the absurdity of infinite division down to nothing [Democritus, by Aristotle] |
| 20909 | The basic atoms are without qualities - which only arise from encounters between atoms [Democritus, by Galen] |
| 1536 | If a cone is horizontally sliced the surfaces can't be equal, so it goes up in steps [Democritus] |
| 23314 | Greeks explained regularity by intellectual design, not by laws [Democritus, by Frede,M] |
| 20905 | Growth and movement would not exist if there were no void to receive them [Democritus] |
| 24059 | Democritus is wrong: in a void we wouldn't see a distant ant in exact detail [Aristotle on Democritus] |
| 5101 | Movement is impossible in a void, because nothing can decide the direction of movement [Aristotle on Democritus] |
| 20911 | There are unlimited worlds of varying sizes, some without life or water [Democritus, by Hippolytus] |
| 1535 | Democritus said people imagined gods as the source of what awed or frightened them [Democritus, by Sext.Empiricus] |
| 20915 | The soul is destroyed with the body [Democritus, by Ps-Plutarch] |