44 ideas
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 15845 | It seems absurd that seeing a person's limbs, the one is many, and yet the many are one [Plato] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 9867 | It is absurd to define a circle, but not be able to recognise a real one [Plato] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 9865 | Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 14503 | If a mixture does not contain measure and proportion, it is corrupted and destroyed [Plato] |
| 15857 | Any mixture which lacks measure and proportion doesn't even count as a mixture at all [Plato] |
| 4447 | If the good is one, is it unchanged when it is in particulars, and is it then separated from itself? [Plato] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 15856 | A thing can become one or many, depending on how we talk about it [Plato] |
| 374 | If one object is divided into its parts, someone can then say that one are many and many is one [Plato] |
| 389 | How can you be certain about aspects of the world if they aren't constant? [Plato] |
| 390 | If goodness involves moderation and proportion, then it seems to be found in beauty [Plato] |
| 392 | Neither intellect nor pleasure are the good, because they are not perfect and self-sufficient [Plato] |
| 391 | The good involves beauty, proportion and truth [Plato] |
| 393 | Good first, then beauty, then reason, then knowledge, then pleasure [Plato, by PG] |
| 385 | Some of the pleasures and pains we feel are false [Plato] |
| 387 | A small pure pleasure is much finer than a large one contaminated with pain [Plato] |
| 373 | Pleasure is certainly very pleasant, but it doesn't follow that all pleasures are good [Plato] |
| 379 | The good must be sufficient and perfect, and neither intellect nor pleasure are that [Plato] |
| 371 | Reason, memory, truth and wisdom are far better than pleasure, for those who can attain them [Plato] |
| 376 | Would you prefer a life of pleasure without reason, or one of reason without pleasure? [Plato] |
| 382 | It is unlikely that the gods feel either pleasure or pain [Plato] |
| 381 | We feel pleasure when we approach our natural state of harmony [Plato] |
| 386 | Intense pleasure and pain are not felt in a good body, but in a worthless one [Plato] |
| 388 | Hedonists must say that someone in pain is bad, even if they are virtuous [Plato] |
| 377 | If you lived a life of maximum pleasure, would you still be lacking anything? [Plato] |
| 378 | A life of pure pleasure with no intellect is the life of a jellyfish [Plato] |
| 467 | A virtue is a combination of intelligence, strength and luck [Ion] |