16 ideas
| 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] |
| 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] |
| 5062 | First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz] |
| 19377 | A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz] |
| 19353 | 'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz] |
| 5061 | Animals are semi-rational because they connect facts, but they don't see causes [Leibniz] |
| 5063 | Music charms, although its beauty is the harmony of numbers [Leibniz] |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |