46 ideas
| 7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
| 19466 | The word 'true' seems to be unique and indefinable [Frege] |
| 19465 | There cannot be complete correspondence, because ideas and reality are quite different [Frege] |
| 19468 | The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 19470 | Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege] |
| 19471 | A fact is a thought that is true [Frege] |
| 9877 | Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19469 | We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege] |
| 8162 | Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett] |
| 9818 | A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett] |
| 16379 | Thoughts about myself are understood one way to me, and another when communicated [Frege] |
| 19467 | A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege] |
| 19472 | A sentence is only a thought if it is complete, and has a time-specification [Frege] |
| 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] |
| 23932 | Art is the expression of an emotion for ultimate reality [Bell,C] |
| 23927 | Aestheticism invites artist to create beauty, but with no indication of how to do it [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] |
| 23930 | Religion sees infinite value in some things, and irrelevance in the rest [Bell,C] |