60 ideas
11912 | Substantive metaphysics says what a property is, not what a predicate means [Molnar] |
11920 | A real definition gives all the properties that constitute an identity [Molnar] |
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] |
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] |
11919 | Ontological dependence rests on essential connection, not necessary connection [Molnar] |
11929 | The three categories in ontology are objects, properties and relations [Molnar] |
11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
11915 | If atomism is true, then all properties derive from ultimate properties [Molnar] |
11916 | 'Being physical' is a second-order property [Molnar] |
11956 | 'Categorical properties' are those which are not powers [Molnar] |
11928 | Are tropes transferable? If they are, that is a version of Platonism [Molnar] |
11933 | A power's type-identity is given by its definitive manifestation [Molnar] |
11932 | Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar] |
11934 | The physical world has a feature very like mental intentionality [Molnar] |
11947 | Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar] |
11952 | The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar] |
11953 | Some powers are ungrounded, and others rest on them, and are derivative [Molnar] |
11943 | Dispositions can be causes, so they must be part of the actual world [Molnar] |
11939 | If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar] |
11914 | Platonic explanations of universals actually diminish our understanding [Molnar] |
11913 | For nominalists, predicate extensions are inexplicable facts [Molnar] |
11962 | Nominalists only accept first-order logic [Molnar] |
11917 | Structural properties are derivate properties [Molnar] |
11955 | There are no 'structural properties', as properties with parts [Molnar] |
11918 | The essence of a thing need not include everything that is necessarily true of it [Molnar] |
11963 | What is the truthmaker for a non-existent possible? [Molnar] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
11951 | Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar] |
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] |
11936 | The two ways proposed to distinguish mind are intentionality or consciousness [Molnar] |
11935 | Physical powers like solubility and charge also have directedness [Molnar] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
11944 | Rule occasionalism says God's actions follow laws, not miracles [Molnar] |
11960 | Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar] |
11937 | We should analyse causation in terms of powers, not vice versa [Molnar] |
11954 | We should analyse causation in terms of powers [Molnar] |
11961 | Causal dependence explains counterfactual dependence, not vice versa [Molnar] |
11959 | Science works when we assume natural kinds have essences - because it is true [Molnar] |
9448 | Location in space and time are non-power properties [Molnar, by Mumford] |
11930 | One essential property of a muon doesn't entail the others [Molnar] |
11957 | It is contingent which kinds and powers exist in the world [Molnar] |
11921 | The laws of nature depend on the powers, not the other way round [Molnar] |
11931 | Energy fields are discontinuous at the very small [Molnar] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |