22 ideas
1765 | Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius] |
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] |
1762 | When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius] |
7813 | Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling] |
1763 | Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius] |
5071 | The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.] |
7812 | For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
1764 | Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius] |
5968 | Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch] |
1766 | Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius] |