34 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] |
1553 | No perceptible object is truly straight or curved [Protagoras] |
1549 | Everything that exists consists in being perceived [Protagoras] |
1545 | Protagoras was the first to claim that there are two contradictory arguments about everything [Protagoras, by Diog. Laertius] |
1547 | Man is the measure of all things - of things that are, and of things that are not [Protagoras] |
3305 | There is no more purely metaphysical doctrine than Protagorean relativism [Benardete,JA on Protagoras] |
3317 | You can only state the problem of the relative warmth of an object by agreeing on the underlying object [Benardete,JA on Protagoras] |
3313 | If my hot wind is your cold wind, then wind is neither hot nor cold, and so not as cold as itself [Benardete,JA on Protagoras] |
247 | God is "the measure of all things", more than any man [Plato on Protagoras] |
606 | Protagoras absurdly thought that the knowing or perceiving man is 'the measure of all things' [Aristotle on Protagoras] |
612 | Relativists think if you poke your eye and see double, there must be two things [Aristotle on Protagoras] |
8122 | True works of art transmit completely new feelings [Tolstoy] |
8121 | Art is when one man uses external signs to hand on his feelings to another man [Tolstoy] |
8124 | The highest feelings of mankind can only be transmitted by art [Tolstoy] |
8123 | The purpose of art is to help mankind to evolve better, more socially beneficial feelings [Tolstoy] |
22710 | People estimate art according to their moral values [Tolstoy] |
8125 | The upper classes put beauty first, and thus freed themselves from morality [Tolstoy] |
8064 | We separate the concept of beauty from goodness, unlike the ancients [Tolstoy] |
6016 | Early sophists thought convention improved nature; later they said nature was diminished by it [Protagoras, by Miller,FD] |
1580 | For Protagoras the only bad behaviour is that which interferes with social harmony [Protagoras, by Roochnik] |
205 | Protagoras contradicts himself by saying virtue is teachable, but then that it is not knowledge [Plato on Protagoras] |
1659 | Protagoras seems to have made the huge move of separating punishment from revenge [Protagoras, by Vlastos] |
532 | Successful education must go deep into the soul [Protagoras] |
1552 | He spent public money on education, as it benefits the individual and the state [Protagoras, by Diodorus of Sicily] |
1551 | He said he didn't know whether there are gods - but this is the same as atheism [Diogenes of Oen. on Protagoras] |