39 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] |
8143 | Self is the rider, intellect the charioteer, mind the reins, and body the chariot [Anon (Upan)] |
8147 | We have an apparent and a true self; only the second one exists, and we must seek to know it [Anon (Upan)] |
8155 | Without speech we cannot know right/wrong, true/false, good/bad, or pleasant/unpleasant [Anon (Upan)] |
8142 | The wise prefer good to pleasure; the foolish are drawn to pleasure by desire [Anon (Upan)] |
23262 | Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling] |
23263 | Politics is driven by power cliques [Grayling] |
23255 | It is essential for democracy that voting is free and well informed [Grayling] |
23254 | Democracies should require a supermajority for major questions [Grayling] |
23260 | A cap on time of service would restrict party control and career ambitions [Grayling] |
23253 | Majority decisions are only acceptable if the minority interests are not vital [Grayling] |
23256 | Liberty and equality cannot be reconciled [Grayling] |
23258 | The very concept of democracy entails a need for justice [Grayling] |
23259 | There should be separate legislative, executive and judicial institutions [Grayling] |
8151 | Let your teacher be a god to you [Anon (Upan)] |
8153 | By knowing one piece of clay or gold, you know all of clay or gold [Anon (Upan)] |
8154 | Originally there must have been just Existence, which could not come from non-existence [Anon (Upan)] |
8148 | Brahma, supreme god and protector of the universe, arose from the ocean of existence [Anon (Upan)] |
8144 | Brahman is the Uncaused Cause [Anon (Upan)] |
8152 | Earth, food, fire, sun are all forms of Brahman [Anon (Upan)] |
8156 | The gods are not worshipped for their own sake, but for the sake of the Self [Anon (Upan)] |
8157 | A man with desires is continually reborn, until his desires are stilled [Anon (Upan)] |
8159 | Damayata - be self-controlled! Datta - be charitable! Dayadhwam - be compassionate! [Anon (Upan)] |
8145 | Those ignorant of Atman return as animals or plants, according to their merits [Anon (Upan)] |
8149 | Charity and ritual observance distract from the highest good of religion [Anon (Upan)] |
8158 | Do not seek to know Brahman by arguments, for arguments are idle and vain [Anon (Upan)] |
8146 | The immortal in us is the part that never sleeps, and shapes our dreams [Anon (Upan)] |
8150 | The immortal Self and the sad individual self are like two golden birds perched on one tree [Anon (Upan)] |