25 ideas
18915 | If facts are the truthmakers, they are not in the world [Engelbretsen] |
18919 | There are no 'falsifying' facts, only an absence of truthmakers [Engelbretsen] |
18913 | Traditional term logic struggled to express relations [Engelbretsen] |
18907 | Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen] |
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] |
18912 | Was logic a branch of mathematics, or mathematics a branch of logic? [Engelbretsen] |
18922 | Logical syntax is actually close to surface linguistic form [Engelbretsen] |
18905 | Propositions can be analysed as pairs of terms glued together by predication [Engelbretsen] |
18908 | Standard logic only negates sentences, even via negated general terms or predicates [Engelbretsen] |
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] |
18917 | Existence and nonexistence are characteristics of the world, not of objects [Engelbretsen] |
18916 | Facts are not in the world - they are properties of the world [Engelbretsen] |
18921 | Individuals are arranged in inclusion categories that match our semantics [Engelbretsen] |
19402 | The actual universe is the richest composite of what is possible [Leibniz] |
18918 | Terms denote objects with properties, and statements denote the world with that property [Engelbretsen] |
18920 | 'Socrates is wise' denotes a sentence; 'that Socrates is wise' denotes a proposition [Engelbretsen] |
18906 | Negating a predicate term and denying its unnegated version are quite different [Engelbretsen] |