58 ideas
1502 | Parmenides was much more cautious about accepting ideas than his predecessors [Simplicius on Parmenides] |
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] |
448 | No necessity could produce Being either later or earlier, so it must exist absolutely or not at all [Parmenides] |
447 | Being must be eternal and uncreated, and hence it is timeless [Parmenides] |
449 | Being is not divisible, since it is all alike [Parmenides] |
1503 | There is no such thing as nothing [Parmenides] |
445 | The realm of necessary non-existence cannot be explored, because it is unknowable [Parmenides] |
21820 | Parmenides at least saw Being as the same as Nous, and separate from the sensed realm [Parmenides, by Plotinus] |
452 | All our concepts of change and permanence are just names, not the truth [Parmenides] |
1504 | Something must be unchanging to make recognition and knowledge possible [Aristotle on Parmenides] |
444 | The first way of enquiry involves necessary existence [Parmenides] |
450 | Necessity sets limits on being, in order to give it identity [Parmenides] |
451 | Thinking implies existence, because thinking depends on it [Parmenides] |
1506 | Parmenides treats perception and intellectual activity as the same [Theophrastus on Parmenides] |
3058 | Only reason can prove the truth of facts [Parmenides] |
23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
23128 | The opposite of liberalism is dogmatism [Gopnik] |
23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
23136 | Liberal free speech is actually paid speech [Gopnik] |
23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |
5081 | There could be movement within one thing, as there is within water [Aristotle on Parmenides] |
1509 | The one can't be divisible, because if it was it could be infinitely divided down to nothing [Parmenides, by Simplicius] |
20900 | Defenders of the One say motion needs the void - but that is not part of Being [Parmenides, by Aristotle] |
226 | The one is without any kind of motion [Parmenides] |
1505 | Reason sees reality as one, the senses see it as many [Aristotle on Parmenides] |
453 | Reality is symmetrical and balanced, like a sphere, with no reason to be greater one way rather than another [Parmenides] |
555 | People who say that the cosmos is one forget that they must explain movement [Aristotle on Parmenides] |
1792 | He taught that there are two elements, fire the maker, and earth the matter [Parmenides, by Diog. Laertius] |
5115 | It is feeble-minded to look for explanations of everything being at rest [Aristotle on Parmenides] |
13217 | The void can't exist, and without the void there can't be movement or separation [Parmenides, by Aristotle] |
22918 | What could have triggered the beginning [of time and being]? [Parmenides] |
1791 | He was the first person to say the earth is spherical [Parmenides, by Diog. Laertius] |
1794 | He was the first to discover the identity of the Morning and Evening Stars [Parmenides, by Diog. Laertius] |