31 ideas
14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
13838 | A decent modern definition should always imply a semantics [Hacking] |
13833 | 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking] |
13834 | Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking] |
13835 | Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking] |
13845 | The various logics are abstractions made from terms like 'if...then' in English [Hacking] |
13840 | First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking] |
13844 | A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking] |
13842 | Second-order completeness seems to need intensional entities and possible worlds [Hacking] |
13837 | With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking] |
13839 | Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking] |
13843 | If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking] |
10245 | One geometry cannot be more true than another [Poincaré] |
1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
180 | We call a person the same throughout life, but all their attributes change [Plato] |
4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
172 | Love of ugliness is impossible [Plato] |
173 | Beauty and goodness are the same [Plato] |
183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
14177 | Love assists men in achieving merit and happiness [Plato] |
179 | Love is desire for perpetual possession of the good [Plato] |
177 | If a person is good they will automatically become happy [Plato] |
14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
175 | Gods are not lovers of wisdom, because they are already wise [Plato] |