19 ideas
| 18274 | Analysis complicates a statement, but only as far as the complexity of its meaning [Wittgenstein] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 16908 | We can dispense with self-evidence, if language itself prevents logical mistakes [Jeshion on Wittgenstein] |
| 18276 | A statement's logical form derives entirely from its constituents [Wittgenstein] |
| 6563 | 'And' and 'not' are non-referring terms, which do not represent anything [Wittgenstein, by Fogelin] |
| 23472 | The sense of propositions relies on the world's basic logical structure [Wittgenstein] |
| 23500 | My main problem is the order of the world, and whether it is knowable a priori [Wittgenstein] |
| 22363 | You have only begun to do real science when you can express it in numbers [Kelvin] |
| 22323 | The philosophical I is the metaphysical subject, the limit - not a part of the world [Wittgenstein] |
| 23481 | Propositions assemble a world experimentally, like the model of a road accident [Wittgenstein] |
| 4678 | Absolute prohibitions are the essence of ethics, and suicide is the most obvious example [Wittgenstein] |
| 20644 | Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin] |