65 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] |
| 19086 | Does the pragmatic theory of meaning support objective truth, or make it impossible? [Macbeth] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 12920 | There is no multiplicity without true units [Leibniz] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 19093 | Greek mathematics is wholly sensory, where ours is wholly inferential [Macbeth] |
| 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] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 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] |
| 19091 | Seeing reality mathematically makes it an object of thought, not of experience [Macbeth] |
| 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] |
| 19088 | For pragmatists a concept means its consequences [Macbeth] |
| 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] |