45 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] |
21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |
21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
10284 | There are three different standard presentations of semantics [Hodges,W] |
10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
21691 | Antinomies contradict accepted ways of reasoning, and demand revisions [Quine] |
21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
21689 | A barber shaves only those who do not shave themselves. So does he shave himself? [Quine] |
21694 | Membership conditions which involve membership and non-membership are paradoxical [Quine] |
21692 | If we write it as '"this sentence is false" is false', there is no paradox [Quine] |
10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
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] |
20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
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] |
17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
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] |
1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |