28 ideas
| 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] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| 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] |
| 19682 | Internalists are much more interested in evidence than externalists are [McGrew] |
| 19684 | Does spotting a new possibility count as evidence? [McGrew] |
| 19687 | Absence of evidence proves nothing, and weird claims need special evidence [McGrew] |
| 19688 | Every event is highly unlikely (in detail), but may be perfectly plausible [McGrew] |
| 19686 | Criminal law needs two separate witnesses, but historians will accept one witness [McGrew] |
| 19680 | Maybe all evidence consists of beliefs, rather than of facts [McGrew] |
| 19681 | If all evidence is propositional, what is the evidence for the proposition? Do we face a regress? [McGrew] |
| 19689 | Several unreliable witnesses can give good support, if they all say the same thing [McGrew] |
| 19683 | Narrow evidentialism relies wholly on propositions; the wider form includes other items [McGrew] |
| 19685 | Falsificationism would be naive if even a slight discrepancy in evidence killed a theory [McGrew] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |