32 ideas
13734 | Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J] |
13751 | If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J] |
13743 | We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
10751 | Second-order logic needs the sets, and its consequence has epistemological problems [Rossberg] |
10757 | Henkin semantics has a second domain of predicates and relations (in upper case) [Rossberg] |
10759 | There are at least seven possible systems of semantics for second-order logic [Rossberg] |
10753 | Logical consequence is intuitively semantic, and captured by model theory [Rossberg] |
10752 | Γ |- S says S can be deduced from Γ; Γ |= S says a good model for Γ makes S true [Rossberg] |
10754 | In proof-theory, logical form is shown by the logical constants [Rossberg] |
10756 | A model is a domain, and an interpretation assigning objects, predicates, relations etc. [Rossberg] |
10758 | If models of a mathematical theory are all isomorphic, it is 'categorical', with essentially one model [Rossberg] |
10761 | Completeness can always be achieved by cunning model-design [Rossberg] |
10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
13741 | If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J] |
13748 | Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J] |
13747 | Supervenience is just modal correlation [Schaffer,J] |
13744 | The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J] |
13739 | Maybe categories are just the different ways that things depend on basic substances [Schaffer,J] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
13742 | There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J] |
13752 | The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J] |
13749 | Belief in impossible worlds may require dialetheism [Schaffer,J] |
13740 | 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J] |