52 ideas
| 19342 | Reason avoids multiplying hypotheses or principles [Leibniz] |
| 18696 | The vagueness of truthmaker claims makes it easier to run anti-realist arguments [Button] |
| 18701 | The coherence theory says truth is coherence of thoughts, and not about objects [Button] |
| 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] |
| 18694 | Permutation Theorem: any theory with a decent model has lots of models [Button] |
| 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] |
| 18692 | Realists believe in independent objects, correspondence, and fallibility of all theories [Button] |
| 18693 | Indeterminacy arguments say if a theory can be made true, it has multiple versions [Button] |
| 18695 | An ideal theory can't be wholly false, because its consistency implies a true model [Button] |
| 12711 | The immediate cause of movements is more real [than geometry] [Leibniz] |
| 19349 | The complete notion of a substance implies all of its predicates or attributes [Leibniz] |
| 7558 | Substances mirror God or the universe, each from its own viewpoint [Leibniz] |
| 16761 | Forms are of no value in physics, but are indispensable in metaphysics [Leibniz] |
| 13088 | Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 13085 | Leibniz is some form of haecceitist [Leibniz, by Cover/O'Leary-Hawthorne] |
| 5024 | Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz] |
| 18700 | Cartesian scepticism doubts what is true; Kantian scepticism doubts that it is sayable [Button] |
| 18698 | Predictions give the 'content' of theories, which can then be 'equivalent' or 'adequate' [Button] |
| 5027 | If a person's memories became totally those of the King of China, he would be the King of China [Leibniz] |
| 5023 | Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz] |
| 2119 | People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason [Leibniz] |
| 5025 | Mind and body can't influence one another, but God wouldn't intervene in the daily routine [Leibniz] |
| 18697 | A sentence's truth conditions are all the situations where it would be true [Button] |
| 5026 | Animals lack morality because they lack self-reflection [Leibniz] |