60 ideas
| 10468 | A metaphysics has an ontology (objects) and an ideology (expressed ideas about them) [Oliver] |
| 10471 | Ockham's Razor has more content if it says believe only in what is causal [Oliver] |
| 10749 | Necessary truths seem to all have the same truth-maker [Oliver] |
| 10750 | Slingshot Argument: seems to prove that all sentences have the same truth-maker [Oliver] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 10747 | Accepting properties by ontological commitment tells you very little about them [Oliver] |
| 10748 | Reference is not the only way for a predicate to have ontological commitment [Oliver] |
| 10719 | There are four conditions defining the relations between particulars and properties [Oliver] |
| 10721 | If properties are sui generis, are they abstract or concrete? [Oliver] |
| 10716 | There are just as many properties as the laws require [Oliver] |
| 10720 | We have four options, depending whether particulars and properties are sui generis or constructions [Oliver] |
| 10714 | The expressions with properties as their meanings are predicates and abstract singular terms [Oliver] |
| 10715 | There are five main semantic theories for properties [Oliver] |
| 10738 | Tropes are not properties, since they can't be instantiated twice [Oliver] |
| 10739 | The property of redness is the maximal set of the tropes of exactly similar redness [Oliver] |
| 10740 | The orthodox view does not allow for uninstantiated tropes [Oliver] |
| 10741 | Maybe concrete particulars are mereological wholes of abstract particulars [Oliver] |
| 10742 | Tropes can overlap, and shouldn't be splittable into parts [Oliver] |
| 10472 | 'Structural universals' methane and butane are made of the same universals, carbon and hydrogen [Oliver] |
| 10724 | Located universals are wholly present in many places, and two can be in the same place [Oliver] |
| 7963 | Aristotle's instantiated universals cannot account for properties of abstract objects [Oliver] |
| 10730 | If universals ground similarities, what about uniquely instantiated universals? [Oliver] |
| 10727 | Uninstantiated universals seem to exist if they themselves have properties [Oliver] |
| 7962 | Uninstantiated properties are useful in philosophy [Oliver] |
| 10722 | Instantiation is set-membership [Oliver] |
| 10744 | Nominalism can reject abstractions, or universals, or sets [Oliver] |
| 10726 | Things can't be fusions of universals, because two things could then be one thing [Oliver] |
| 10725 | Abstract sets of universals can't be bundled to make concrete things [Oliver] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 10745 | Science is modally committed, to disposition, causation and law [Oliver] |
| 10746 | Conceptual priority is barely intelligible [Oliver] |
| 23897 | Once money is the main aim, society needs everyone to think wealth is possible [Weil] |