19 ideas
21405 | Cicero sees wisdom in terms of knowledge, but earlier Stoics saw it as moral [Cicero, by Long] |
20871 | Unfortunately we choose a way of life before we are old enough to think clearly [Cicero] |
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] |
6031 | The essence of propriety is consistency [Cicero] |
22265 | I can't defend the view that the majority values of a community are thereby right [Sandel] |
22268 | If persons define themselves by a group membership, insults to that group are a real harm [Sandel] |
22267 | In the liberal view an insult to my group doesn't hurt me, since I'm defined by choices not groups [Sandel] |
22266 | The case for religious liberty depends on the religion contributing to a morally good life [Sandel] |