64 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] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 21812 | Being is the product of pure intellect [Plotinus] |
| 21817 | The One does not exist, but is the source of all existence [Plotinus] |
| 21824 | The One is a principle which transcends Being [Plotinus] |
| 21813 | Number determines individual being [Plotinus] |
| 14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
| 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] |
| 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] |
| 565 | The Forms cannot be changeless if they are in changing things [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] |
| 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] |
| 5506 | If soul was like body, its parts would be separate, without communication [Plotinus] |
| 21827 | The movement of Soul is continuous, but we are only aware of the parts of it that are sensed [Plotinus] |
| 21828 | A person is the whole of their soul [Plotinus] |
| 21809 | Our soul has the same ideal nature as the oldest god, and is honourable above the body [Plotinus] |
| 21825 | The soul is outside of all of space, and has no connection to the bodily order [Plotinus] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 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] |
| 21826 | The Soul reasons about the Right, so there must be some permanent Right about which it reasons [Plotinus] |
| 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] |
| 6922 | Ecstasy is for the neo-Platonist the highest psychological state of man [Plotinus, by Feuerbach] |
| 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] |
| 21814 | How can multiple existence arise from the unified One? [Plotinus] |
| 21816 | Soul is the logos of Nous, just as Nous is the logos of the One [Plotinus] |
| 21815 | Because the One is immobile, it must create by radiation, light the sun producing light [Plotinus] |
| 1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
| 21808 | Soul is author of all of life, and of the stars, and it gives them law and movement [Plotinus] |
| 21811 | Even the soul is secondary to the Intellectual-Principle [Nous], of which soul is an utterance [Plotinus] |