52 ideas
| 21360 | Unobservant thinkers tend to dogmatise using insufficient facts [Aristotle] |
| 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] |
| 13212 | Infinity is only potential, never actual [Aristotle] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 13221 | Existence is either potential or actual [Aristotle] |
| 10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
| 16100 | True change is in a thing's logos or its matter, not in its qualities [Aristotle] |
| 16101 | A change in qualities is mere alteration, not true change [Aristotle] |
| 12133 | If the substratum persists, it is 'alteration'; if it doesn't, it is 'coming-to-be' or 'passing-away' [Aristotle] |
| 13213 | All comings-to-be are passings-away, and vice versa [Aristotle] |
| 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] |
| 12134 | Matter is the substratum, which supports both coming-to-be and alteration [Aristotle] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 16572 | Does the pure 'this' come to be, or the 'this-such', or 'so-great', or 'somewhere'? [Aristotle] |
| 16573 | Philosophers have worried about coming-to-be from nothing pre-existing [Aristotle] |
| 13214 | The substratum changing to a contrary is the material cause of coming-to-be [Aristotle] |
| 13215 | If a perceptible substratum persists, it is 'alteration'; coming-to-be is a complete change [Aristotle] |
| 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] |
| 16717 | Which of the contrary features of a body are basic to it? [Aristotle] |
| 13216 | Matter is the limit of points and lines, and must always have quality and form [Aristotle] |
| 17994 | The primary matter is the substratum for the contraries like hot and cold [Aristotle] |
| 13224 | There couldn't be just one element, which was both water and air at the same time [Aristotle] |
| 16594 | The Four Elements must change into one another, or else alteration is impossible [Aristotle] |
| 13223 | Fire is hot and dry; Air is hot and moist; Water is cold and moist; Earth is cold and dry [Aristotle] |
| 13210 | Wood is potentially divided through and through, so what is there in the wood besides the division? [Aristotle] |
| 13220 | Bodies are endlessly divisible [Aristotle] |
| 13211 | If a body is endlessly divided, is it reduced to nothing - then reassembled from nothing? [Aristotle] |
| 13228 | There is no time without movement [Aristotle] |
| 16595 | If each thing can cease to be, why hasn't absolutely everything ceased to be long ago? [Aristotle] |
| 13227 | Being is better than not-being [Aristotle] |
| 13226 | An Order controls all things [Aristotle] |