30 ideas
192 | Only one thing can be contrary to something [Plato] |
14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
14240 | The empty set is something, not nothing! [Oliver/Smiley] |
14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
9169 | A statement can be metaphysically necessary and epistemologically contingent [Putnam] |
5819 | Conceivability is no proof of possibility [Putnam] |
20184 | The only real evil is loss of knowledge [Plato] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
191 | Everything resembles everything else up to a point [Plato] |
9168 | I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam] |
5820 | 'Water' has an unnoticed indexical component, referring to stuff around here [Putnam] |
9170 | We need to recognise the contribution of society and of the world in determining reference [Putnam] |
5817 | Language is more like a cooperative steamship than an individual hammer [Putnam] |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
202 | No one willingly and knowingly embraces evil [Plato] |
193 | Some things are good even though they are not beneficial to men [Plato] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
188 | Socrates did not believe that virtue could be taught [Plato] |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
5818 | If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam] |