21 ideas
20109 | Hegel inserted society and history between the God-world, man-nature, man-being binary pairs [Hegel, by Safranski] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
23274 | World history has no room for happiness [Hegel] |
23275 | The state of nature is one of untamed brutality [Hegel] |
23276 | The soul of the people is an organisation of its members which produces an essential unity [Hegel] |
23272 | The human race matters, and individuals have little importance [Hegel] |
23273 | In a good state the goal of the citizens and of the whole state are united [Hegel] |
23271 | The goal of the world is Spirit's consciousness and enactment of freedom [Hegel] |
23270 | We should all agree that there is reason in history [Hegel] |
1497 | For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius] |