48 ideas
22285 | Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter] |
22301 | The Identity Theory says a proposition is true if it coincides with what makes it true [Potter] |
22324 | It has been unfortunate that externalism about truth is equated with correspondence [Potter] |
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] |
22279 | Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter] |
22291 | Deductivism can't explain how the world supports unconditional conclusions [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
22295 | Modern logical truths are true under all interpretations of the non-logical words [Potter] |
17867 | If a concept is not compact, it will not be presentable to finite minds [Almog] |
17877 | The number series is primitive, not the result of some set theoretic axioms [Almog] |
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] |
22310 | The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter] |
22298 | Why is fictional arithmetic applicable to the real world? [Potter] |
22287 | If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
22284 | 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
16065 | Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman] |
16067 | Constitution is not identity, because it is an asymmetric dependence relation [Wasserman] |
16069 | There are three main objections to seeing constitution as different from identity [Wasserman] |
16068 | The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
17871 | Fregean meanings are analogous to conceptual essence, defining a kind [Almog] |
17866 | Essential definition aims at existence conditions and structural truths [Almog] |
17868 | Surface accounts aren't exhaustive as they always allow unintended twin cases [Almog] |
17872 | Definitionalists rely on snapshot-concepts, instead of on the real processes [Almog] |
17870 | Alien 'tigers' can't be tigers if they are not related to our tigers [Almog] |
17869 | Kripke and Putnam offer an intermediary between real and nominal essences [Almog] |
17876 | Individual essences are just cobbled together classificatory predicates [Almog] |
16074 | Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman] |
10709 | Priority is a modality, arising from collections and members [Potter] |
22281 | A material conditional cannot capture counterfactual reasoning [Potter] |
22327 | Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter] |
22273 | Traditionally there are twelve categories of judgement, in groups of three [Potter] |
17873 | Water must be related to water, just as tigers must be related to tigers [Almog] |
22290 | The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter] |
22283 | Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter] |
22282 | 'Direct compositonality' says the components wholly explain a sentence meaning [Potter] |
22296 | Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter] |
17864 | Defining an essence comes no where near giving a thing's nature [Almog] |
17863 | Essences promise to reveal reality, but actually drive us away from it [Almog] |