57 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] |
| 12910 | The predicate is in the subject of a true proposition [Leibniz] |
| 19333 | A truth is just a proposition in which the predicate is contained within the subject [Leibniz] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 12920 | There is no multiplicity without true units [Leibniz] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 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] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 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] |
| 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] |
| 7518 | If folk psychology gives a network of causal laws, that fits neatly with functionalism [Churchland,PM] |
| 7519 | Many mental phenomena are totally unexplained by folk psychology [Churchland,PM] |
| 7520 | Folk psychology never makes any progress, and is marginalised by modern science [Churchland,PM] |
| 12911 | Concepts are what unite a proposition [Leibniz] |
| 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] |