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] |
1852 | For the mind Good is one truth among many, and Truth is one good among many [Aquinas] |
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
1860 | Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas] |
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] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
1859 | Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |