28 ideas
22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
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] |
22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
19400 | Possibles demand existence, so as many of them as possible must actually exist [Leibniz] |
19401 | God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz] |
22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
19402 | The actual universe is the richest composite of what is possible [Leibniz] |
22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |