23 ideas
1922 | Spiritual qualities only become advantageous with the growth of wisdom [Plato] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [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] |
11259 | How can you seek knowledge of something if you don't know it? [Plato] |
20219 | True opinions only become really valuable when they are tied down by reasons [Plato] |
5985 | Seeking and learning are just recollection [Plato] |
5986 | The slave boy learns geometry from questioning, not teaching, so it is recollection [Plato] |
1923 | As a guide to action, true opinion is as good as knowledge [Plato] |
1919 | You don't need to learn what you know, and how do you seek for what you don't know? [Plato] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
1913 | Is virtue taught, or achieved by practice, or a natural aptitude, or what? [Plato] |
1921 | If virtue is a type of knowledge then it ought to be taught [Plato] |
1927 | It seems that virtue is neither natural nor taught, but is a divine gift [Plato] |
1918 | How can you know part of virtue without knowing the whole? [Plato] |
1916 | Even if virtues are many and various, they must have something in common to make them virtues [Plato] |