31 ideas
| 4642 | No fact can be real and no proposition true unless there is a Sufficient Reason (even if we can't know it) [Leibniz] |
| 2115 | Everything in the universe is interconnected, so potentially a mind could know everything [Leibniz] |
| 10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
| 10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
| 10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
| 10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
| 10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
| 2111 | Falsehood involves a contradiction, and truth is contradictory of falsehood [Leibniz] |
| 10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
| 10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
| 10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
| 10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| 7644 | The monad idea incomprehensibly spiritualises matter, instead of materialising soul [La Mettrie on Leibniz] |
| 11857 | He replaced Aristotelian continuants with monads [Leibniz, by Wiggins] |
| 7843 | Is a drop of urine really an infinity of thinking monads? [Voltaire on Leibniz] |
| 12751 | It is unclear in 'Monadology' how extended bodies relate to mind-like monads. [Garber on Leibniz] |
| 19363 | Changes in a monad come from an internal principle, and the diversity within its substance [Leibniz] |
| 19352 | A 'monad' has basic perception and appetite; a 'soul' has distinct perception and memory [Leibniz] |
| 7931 | If a substance is just a thing that has properties, it seems to be a characterless non-entity [Leibniz, by Macdonald,C] |
| 17554 | There must be some internal difference between any two beings in nature [Leibniz] |
| 2112 | Truths of reason are known by analysis, and are necessary; facts are contingent, and their opposites possible [Leibniz] |
| 9344 | Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated [Leibniz] |
| 2110 | We all expect the sun to rise tomorrow by experience, but astronomers expect it by reason [Leibniz] |
| 19679 | 'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig] |
| 19678 | Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig] |
| 2109 | Increase a conscious machine to the size of a mill - you still won't see perceptions in it [Leibniz] |
| 19362 | We know the 'I' and its contents by abstraction from awareness of necessary truths [Leibniz] |
| 12707 | The true elements are atomic monads [Leibniz] |
| 2114 | This is the most perfect possible universe, in its combination of variety with order [Leibniz] |
| 2113 | God alone (the Necessary Being) has the privilege that He must exist if He is possible [Leibniz] |