39 ideas
162 | Can we understand an individual soul without knowing the soul in general? [Plato] |
160 | The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato] |
166 | A speaker should be able to divide a subject, right down to the limits of divisibility [Plato] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
7953 | Reasoning needs to cut nature accurately at the joints [Plato] |
16121 | I revere anyone who can discern a single thing that encompasses many things [Plato] |
153 | It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato] |
154 | We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato] |
151 | True knowledge is of the reality behind sense experience [Plato] |
335 | Do the gods also hold different opinions about what is right and honourable? [Plato] |
165 | If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato] |
9296 | The soul is self-motion [Plato] |
23997 | Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie] |
159 | Only a good philosopher can be a good speaker [Plato] |
5946 | 'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato] |
158 | An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato] |
155 | Beauty is the clearest and most lovely of the Forms [Plato] |
143 | The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato] |
157 | Most pleasure is release from pain, and is therefore not worthwhile [Plato] |
144 | Reason impels us towards excellence, which teaches us self-control [Plato] |
156 | Bad people are never really friends with one another [Plato] |
148 | If the prime origin is destroyed, it will not come into being again out of anything [Plato] |
152 | The mind of God is fully satisfied and happy with a vision of reality and truth [Plato] |
337 | It seems that the gods love things because they are pious, rather than making them pious by loving them [Plato] |
336 | Is what is pious loved by the gods because it is pious, or is it pious because they love it? (the 'Euthyphro Question') [Plato] |
150 | We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato] |
149 | There isn't a single reason for positing the existence of immortal beings [Plato] |
146 | Soul is always in motion, so it must be self-moving and immortal [Plato] |