31 ideas
10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [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] |
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] |
23928 | Good art produces exaltation and detachment [Bell,C] |
23922 | The word 'beauty' leads to confusion, because it denotes distinct emotions [Bell,C] |
23921 | Our feeling for natural beauty is different from the aesthetic emotion of art [Bell,C] |
23929 | We only see landscapes as artistic if we ignore their instrumental value [Bell,C] |
23923 | Visual form can create a sublime mental state [Bell,C] |
23927 | Aestheticism invites artist to create beauty, but with no indication of how to do it [Bell,C] |
23932 | Art is the expression of an emotion for ultimate reality [Bell,C] |
8115 | Only artists can discern significant form; other people must look to art to find it [Bell,C, by Gardner] |
23924 | Maybe significant form gives us a feeling for ultimate reality [Bell,C] |
23931 | Significant form is the essence of art, which I believe expresses an emotion about reality [Bell,C] |
20434 | 'Form' is visual relations, and it is 'significant' if it moves us aesthetically; art needs both [Bell,C, by Feagin] |
23934 | The only expression art could have is the emotion resulting from pure form [Bell,C] |
23925 | Mere copies of pictures are not significant - unless the copies are very exact [Bell,C] |
23926 | Art is distinguished by its aesthetic emotion, which produces appropriate form [Bell,C] |
23933 | Aesthetic contemplation is the best and most intense mental state [Bell,C] |
23935 | Aesthetic experience is an exaltation which increases the possibilities of life [Bell,C] |
22691 | Only artistic qualities matter in art, because they also have the highest moral value [Bell,C] |
7825 | The politics of Leibniz was the reunification of Christianity [Stewart,M] |
23930 | Religion sees infinite value in some things, and irrelevance in the rest [Bell,C] |