43 ideas
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
14703 | Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter] |
14714 | Contradictory claims about a necessary god both seem apriori coherent [Schroeter] |
14704 | 2D semantics gives us apriori knowledge of our own meanings [Schroeter] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
14706 | Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter] |
14711 | Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter] |
14717 | Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter] |
14720 | Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter] |
14695 | Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter] |
14696 | Simple semantics assigns extensions to names and to predicates [Schroeter] |
14697 | 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter] |
14698 | Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter] |
14699 | Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter] |
14709 | Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter] |
14719 | In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter] |
14701 | Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter] |
14702 | If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter] |
14705 | Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter] |
14715 | 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter] |
14716 | 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter] |