13 ideas
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 16641 | Whiteness does not exist, but by it something can exist-as-white [Aquinas] |
| 22170 | Senses grasp external properties, but the understanding grasps the essential natures of things [Aquinas] |
| 22169 | Initial universal truths are present within us as potential, to be drawn out by reason [Aquinas] |
| 22168 | Minds take in a likeness of things, which activates an awaiting potential [Aquinas] |
| 5655 | Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton] |