24 ideas
14519 | It is a great good to show reverence for a wise man [Epicurus] |
14518 | In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus] |
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] |
10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [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] |
14524 | Bodies are combinations of shape, size, resistance and weight [Epicurus] |
14521 | If everything is by necessity, then even denials of necessity are by necessity [Epicurus] |
14522 | What happens to me if I obtain all my desires, and what if I fail? [Epicurus] |
3563 | Pleasure and virtue entail one another [Epicurus] |
3560 | Justice is merely a contract about not harming or being harmed [Epicurus] |
467 | A virtue is a combination of intelligence, strength and luck [Ion] |
14517 | We value our own character, whatever it is, and we should respect the characters of others [Epicurus] |
14513 | Justice is a pledge of mutual protection [Epicurus] |
14515 | A law is not just if it is not useful in mutual associations [Epicurus] |
14520 | It is small-minded to find many good reasons for suicide [Epicurus] |