42 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] |
| 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] |
| 12747 | Monads are not extended, but have a kind of situation in extension [Leibniz] |
| 12748 | Only monads are substances, and bodies are collections of them [Leibniz] |
| 13184 | The division of nature into matter makes distinct appearances, and that presupposes substances [Leibniz] |
| 13188 | The only indications of reality are agreement among phenomena, and their agreement with necessities [Leibniz] |
| 12752 | Only unities have any reality [Leibniz] |
| 13187 | In actual things nothing is indefinite [Leibniz] |
| 19383 | A man's distant wife dying is a real change in him [Leibniz] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 13179 | A complete monad is a substance with primitive active and passive power [Leibniz] |
| 12749 | Derivate forces are in phenomena, but primitive forces are in the internal strivings of substances [Leibniz] |
| 12722 | Thought terminates in force, rather than extension [Leibniz] |
| 19379 | The law of the series, which determines future states of a substance, is what individuates it [Leibniz] |
| 14082 | No sortal could ever exactly pin down which set of particles count as this 'cup' [Schaffer,J] |
| 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] |
| 13182 | Changeable accidents are modifications of unchanging essences [Leibniz] |
| 14081 | Identities can be true despite indeterminate reference, if true under all interpretations [Schaffer,J] |
| 13178 | Things in different locations are different because they 'express' those locations [Leibniz] |
| 19411 | In nature there aren't even two identical straight lines, so no two bodies are alike [Leibniz] |
| 19412 | If two bodies only seem to differ in their position, those different environments will matter [Leibniz] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 19410 | Scientific truths are supported by mutual agreement, as well as agreement with the phenomena [Leibniz] |
| 13183 | Primitive forces are internal strivings of substances, acting according to their internal laws [Leibniz] |
| 19409 | Soul represents body, but soul remains unchanged, while body continuously changes [Leibniz] |
| 11873 | Our notions may be formed from concepts, but concepts are formed from things [Leibniz] |
| 13186 | Universals are just abstractions by concealing some of the circumstances [Leibniz] |
| 13185 | Even if extension is impenetrable, this still offers no explanation for motion and its laws [Leibniz] |
| 13177 | An entelechy is a law of the series of its event within some entity [Leibniz] |
| 13093 | The only permanence in things, constituting their substance, is a law of continuity [Leibniz] |
| 13096 | The force behind motion is like a soul, with its own laws of continual change [Leibniz] |
| 13180 | Space is the order of coexisting possibles [Leibniz] |
| 13181 | Time is the order of inconsistent possibilities [Leibniz] |