75 ideas
| 23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
| 3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
| 23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 6504 | For physicalists, the only relations are spatial, temporal and causal [Robinson,H] |
| 14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
| 6520 | If reality just has relational properties, what are its substantial ontological features? [Robinson,H] |
| 20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
| 3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
| 17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
| 556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
| 563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
| 557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
| 565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
| 9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
| 13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
| 13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
| 13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
| 593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
| 13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
| 11237 | Only universals have essence [Plato, by Politis] |
| 11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
| 6485 | When a red object is viewed, the air in between does not become red [Robinson,H] |
| 6521 | Representative realists believe that laws of phenomena will apply to the physical world [Robinson,H] |
| 6509 | Representative realists believe some properties of sense-data are shared by the objects themselves [Robinson,H] |
| 6522 | Phenomenalism can be theistic (Berkeley), or sceptical (Hume), or analytic (20th century) [Robinson,H] |
| 6502 | Can we reduce perception to acquisition of information, which is reduced to causation or disposition? [Robinson,H] |
| 6513 | Would someone who recovered their sight recognise felt shapes just by looking? [Robinson,H] |
| 6512 | Secondary qualities have one sensory mode, but primary qualities can have more [Robinson,H] |
| 6497 | We say objects possess no intrinsic secondary qualities because physicists don't need them [Robinson,H] |
| 6494 | If objects are not coloured, and neither are sense-contents, we are left saying that nothing is coloured [Robinson,H] |
| 6499 | Shape can be experienced in different ways, but colour and sound only one way [Robinson,H] |
| 6500 | If secondary qualities match senses, would new senses create new qualities? [Robinson,H] |
| 6484 | Most moderate empiricists adopt Locke's representative theory of perception [Robinson,H] |
| 6508 | Sense-data leads to either representative realism or phenomenalism or idealism [Robinson,H] |
| 6480 | Sense-data do not have any intrinsic intentionality [Robinson,H] |
| 6482 | For idealists and phenomenalists sense-data are in objects; representative realists say they resemble objects [Robinson,H] |
| 6505 | Sense-data are rejected because they are a veil between us and reality, leading to scepticism [Robinson,H] |
| 6506 | 'Sense redly' sounds peculiar, but 'senses redly-squarely tablely' sounds far worse [Robinson,H] |
| 6507 | Adverbialism sees the contents of sense-experience as modes, not objects [Robinson,H] |
| 6511 | If there are only 'modes' of sensing, then an object can no more be red or square than it can be proud or lazy. [Robinson,H] |
| 6515 | An explanation presupposes something that is improbable unless it is explained [Robinson,H] |
| 6517 | If all possibilities are equal, order seems (a priori) to need an explanation - or does it? [Robinson,H] |
| 17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
| 6481 | If intentional states are intrinsically about other things, what are their own properties? [Robinson,H] |
| 6503 | Physicalism cannot allow internal intentional objects, as brain states can't be 'about' anything [Robinson,H] |
| 1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
| 3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
| 7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
| 2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
| 9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
| 94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
| 17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
| 6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
| 2912 | Plato is boring [Nietzsche on Plato] |
| 6519 | Locke's solidity is not matter, because that is impenetrability and hardness combined [Robinson,H] |
| 1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |