35 ideas
| 6675 | The heart has its reasons of which reason knows nothing [Pascal] |
| 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] |
| 10121 | Contradiction is not a sign of falsity, nor lack of contradiction a sign of truth [Pascal] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 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] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 22011 | The first principles of truth are not rational, but are known by the heart [Pascal] |
| 20921 | How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus] |
| 6681 | We only want to know things so that we can talk about them [Pascal] |
| 6676 | Painting makes us admire things of which we do not admire the originals [Pascal] |
| 6680 | It is a funny sort of justice whose limits are marked by a river [Pascal] |
| 6677 | Imagination creates beauty, justice and happiness, which is the supreme good [Pascal] |
| 6678 | We live for the past or future, and so are never happy in the present [Pascal] |
| 20732 | If man considers himself as lost and imprisoned in the universe, he will be terrified [Pascal] |
| 6682 | Majority opinion is visible and authoritative, although not very clever [Pascal] |
| 6679 | It is not good to be too free [Pascal] |
| 5990 | Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk] |
| 7455 | Pascal knows you can't force belief, but you can make it much more probable [Pascal, by Hacking] |
| 7457 | Pascal is right, but relies on the unsupported claim of a half as the chance of God's existence [Hacking on Pascal] |
| 7456 | The libertine would lose a life of enjoyable sin if he chose the cloisters [Hacking on Pascal] |
| 6684 | If you win the wager on God's existence you win everything, if you lose you lose nothing [Pascal] |