37 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] |
| 10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
| 10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
| 10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
| 10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
| 10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
| 10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
| 10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
| 10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
| 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] |
| 10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
| 22180 | Multiple realisability is said to make reduction impossible [Okasha] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 10789 | Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)] |
| 10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
| 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] |
| 10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 22172 | Not all sciences are experimental; astronomy relies on careful observation [Okasha] |
| 22177 | Randomised Control Trials have a treatment and a control group, chosen at random [Okasha] |
| 22174 | The discoverers of Neptune didn't change their theory because of an anomaly [Okasha] |
| 22175 | Science mostly aims at confirming theories, rather than falsifying them [Okasha] |
| 22182 | Theories with unobservables are underdetermined by the evidence [Okasha] |
| 22185 | Two things can't be incompatible if they are incommensurable [Okasha] |
| 22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
| 22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
| 22173 | Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha] |