74 ideas
12926 | Wisdom is the science of happiness [Leibniz] |
12903 | Wise people have fewer acts of will, because such acts are linked together [Leibniz] |
12914 | Metaphysics is geometrical, resting on non-contradiction and sufficient reason [Leibniz] |
12915 | Definitions can only be real if the item is possible [Leibniz] |
19333 | A truth is just a proposition in which the predicate is contained within the subject [Leibniz] |
12910 | The predicate is in the subject of a true proposition [Leibniz] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9707 | 'F(x)' is the unique value which F assumes for a value of x [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] |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [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] |
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] |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [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] |
9706 | A 'function' is a relation in which each object is related to just one other object [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] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [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] |
12920 | There is no multiplicity without true units [Leibniz] |
12319 | What is not truly one being is not truly a being either [Leibniz] |
12922 | A thing 'expresses' another if they have a constant and fixed relationship [Leibniz] |
13079 | A substance contains the laws of its operations, and its actions come from its own depth [Leibniz] |
12745 | Philosophy needs the precision of the unity given by substances [Leibniz] |
12921 | Accidental unity has degrees, from a mob to a society to a machine or organism [Leibniz] |
12746 | We find unity in reason, and unity in perception, but these are not true unity [Leibniz] |
12916 | A body is a unified aggregate, unless it has an indivisible substance [Leibniz] |
12919 | Unity needs an indestructible substance, to contain everything which will happen to it [Leibniz] |
12923 | Every bodily substance must have a soul, or something analogous to a soul [Leibniz] |
12704 | Aggregates don’t reduce to points, or atoms, or illusion, so must reduce to substance [Leibniz] |
13077 | Basic predicates give the complete concept, which then predicts all of the actions [Leibniz] |
12908 | Essences exist in the divine understanding [Leibniz] |
12706 | Bodies need a soul (or something like it) to avoid being mere phenomena [Leibniz] |
12906 | Truths about species are eternal or necessary, but individual truths concern what exists [Leibniz] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
12904 | If varieties of myself can be conceived of as distinct from me, then they are not me [Leibniz] |
11981 | If someone's life went differently, then that would be another individual [Leibniz] |
12905 | I cannot think my non-existence, nor exist without being myself [Leibniz] |
19334 | I can't just know myself to be a substance; I must distinguish myself from others, which is hard [Leibniz] |
5033 | Nothing should be taken as certain without foundations [Leibniz] |
12913 | Nature is explained by mathematics and mechanism, but the laws rest on metaphysics [Leibniz] |
13089 | To fully conceive the subject is to explain the resulting predicates and events [Leibniz] |
5034 | Mind is a thinking substance which can know God and eternal truths [Leibniz] |
5032 | It seems probable that animals have souls, but not consciousness [Leibniz] |
5031 | Everything which happens is not necessary, but is certain after God chooses this universe [Leibniz] |
12911 | Concepts are what unite a proposition [Leibniz] |
20062 | If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm] |
20054 | There has to be a brain event which is not caused by another event, but by the agent [Chisholm] |
12925 | Beauty increases with familiarity [Leibniz] |
12927 | Happiness is advancement towards perfection [Leibniz] |
15955 | I think the corpuscular theory, rather than forms or qualities, best explains particular phenomena [Leibniz] |
12907 | Each possible world contains its own laws, reflected in the possible individuals of that world [Leibniz] |
12924 | Motion alone is relative, but force is real, and establishes its subject [Leibniz] |
12909 | Everything, even miracles, belongs to order [Leibniz] |
5030 | Miracles are extraordinary operations by God, but are nevertheless part of his design [Leibniz] |
12912 | Immortality without memory is useless [Leibniz] |
12917 | The soul is indestructible and always self-aware [Leibniz] |
12918 | Animals have souls, but lack consciousness [Leibniz] |