18 ideas
6021 | It is only when we say a proposition that we speak truly or falsely [Sext.Empiricus] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [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] |
6020 | 'Man is a rational mortal animal' is equivalent to 'if something is a man, that thing is a rational mortal animal' [Sext.Empiricus] |
14212 | A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis] |
14213 | Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis] |
14210 | A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis] |
6026 | How can you investigate without some preconception of your object? [Sext.Empiricus] |
14215 | Causal theories of reference make errors in reference easy [Lewis] |
14209 | Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis] |
6032 | Right actions, once done, are those with a reasonable justification [Sext.Empiricus] |
1517 | The tektraktys (1+2+3+4=10) is the 'fount of ever-flowing nature' [Sext.Empiricus] |