15 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] |
| 5040 | Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz] |
| 13159 | Only God sees contingent truths a priori [Leibniz] |
| 5039 | If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz] |
| 7845 | When we need to do something, we depute an inner servant to remind us of it [Proust] |
| 5041 | God does everything in a perfect way, and never acts contrary to reason [Leibniz] |