26 ideas
8820 | Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock] |
8819 | We need the concept of truth for defeasible reasoning [Pollock] |
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] |
8822 | Statements about necessities need not be necessarily true [Pollock] |
8818 | Defeasible reasoning requires us to be able to think about our thoughts [Pollock] |
8811 | What we want to know is - when is it all right to believe something? [Pollock] |
8817 | Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock] |
8814 | Epistemic norms are internalised procedural rules for reasoning [Pollock] |
8823 | Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock] |
8813 | If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock] |
8812 | Norm Externalism says norms must be internal, but their selection is partly external [Pollock] |
8816 | Externalists tend to take a third-person point of view of epistemology [Pollock] |
8815 | Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock] |