33 ideas
| 1848 | We are coerced into assent to a truth by reason's violence [Aquinas] |
| 1858 | The mind is compelled by necessary truths, but not by contingent truths [Aquinas] |
| 15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
| 1852 | For the mind Good is one truth among many, and Truth is one good among many [Aquinas] |
| 17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
| 17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
| 10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
| 13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
| 17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
| 13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
| 13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
| 13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
| 13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
| 13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
| 18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
| 13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
| 9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
| 1860 | Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas] |
| 5987 | Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von] |
| 1855 | If we saw something as totally and utterly good, we would be compelled to will it [Aquinas] |
| 1856 | Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas] |
| 1862 | However habituated you are, given time to ponder you can go against a habit [Aquinas] |
| 1849 | Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas] |
| 1861 | The will is not compelled to move, even if pleasant things are set before it [Aquinas] |
| 1853 | Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas] |
| 1854 | We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas] |
| 1847 | The will must aim at happiness, but can choose the means [Aquinas] |
| 1857 | We don't have to will even perfect good, because we can choose not to think of it [Aquinas] |
| 1846 | The will can only want what it thinks is good [Aquinas] |
| 1850 | Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas] |
| 1851 | Good applies to goals, just as truth applies to ideas in the mind [Aquinas] |
| 1859 | Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas] |
| 24043 | Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle] |