29 ideas
19342 | Reason avoids multiplying hypotheses or principles [Leibniz] |
5831 | The new view is that "water" is a name, and has no definition [Schwartz,SP] |
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] |
5829 | We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP] |
5830 | The traditional theory of names says some of the descriptions must be correct [Schwartz,SP] |
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] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
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] |
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] |
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] |
5826 | The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP] |
5026 | Animals lack morality because they lack self-reflection [Leibniz] |