26 ideas
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] |
5953 | For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch] |
19542 | It is nonsense that understanding does not involve knowledge; to understand, you must know [Dougherty/Rysiew] |
19543 | To grasp understanding, we should be more explicit about what needs to be known [Dougherty/Rysiew] |
19541 | Rather than knowledge, our epistemic aim may be mere true belief, or else understanding and wisdom [Dougherty/Rysiew] |
19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
3023 | Even the foolish may have some virtues [Aristippus young, by Diog. Laertius] |
3026 | Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius] |
3024 | Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius] |
3025 | For a Cyrenaic no one is of equal importance to himself [Aristippus young, by Diog. Laertius] |
3019 | No one pleasure is different from or more pleasant than another [Aristippus young, by Diog. Laertius] |
3021 | The Cyrenaics asserted that corporeal pleasures were superior to mental ones [Aristippus young, by Diog. Laertius] |
3027 | Cyrenaics say wise men are self-sufficient, needing no friends [Aristippus young, by Diog. Laertius] |