111 ideas
14912 | There is no test for metaphysics, except devising alternative theories [Ladyman/Ross] |
14904 | Metaphysics builds consilience networks across science [Ladyman/Ross] |
14907 | Progress in metaphysics must be tied to progress in science [Ladyman/Ross] |
14908 | Metaphysics must involve at least two scientific hypotheses, one fundamental, and add to explanation [Ladyman/Ross] |
14910 | Some science is so general that it is metaphysical [Ladyman/Ross] |
14940 | Cutting-edge physics has little to offer metaphysics [Ladyman/Ross] |
14945 | The aim of metaphysics is to unite the special sciences with physics [Ladyman/Ross] |
14898 | Modern metaphysics pursues aesthetic criteria like story-writing, and abandons scientific truth [Ladyman/Ross] |
14899 | Why think that conceptual analysis reveals reality, rather than just how people think? [Ladyman/Ross] |
14936 | A metaphysics based on quantum gravity could result in almost anything [Ladyman/Ross] |
14905 | The supremacy of science rests on its iterated error filters [Ladyman/Ross] |
14897 | We should abandon intuitions, especially that the world is made of little things, and made of something [Ladyman/Ross] |
15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
18176 | Pure mathematics is pure set theory [Cantor] |
8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
14942 | Only admit into ontology what is explanatory and predictive [Ladyman/Ross] |
14948 | To be is to be a real pattern [Ladyman/Ross] |
14947 | Any process can be described as transfer of measurable information [Ladyman/Ross] |
14941 | We say there is no fundamental level to ontology, and reality is just patterns [Ladyman/Ross] |
10493 | If concrete is spatio-temporal and causal, and abstract isn't, the distinction doesn't suit physics [Ladyman/Ross] |
14934 | Concrete and abstract are too crude for modern physics [Ladyman/Ross] |
14909 | Physicalism is 'part-whole' (all parts are physical), or 'supervenience/levels' (dependence on physical) [Ladyman/Ross] |
14926 | Relations without relata must be treated as universals, with their own formal properties [Ladyman/Ross] |
14929 | A belief in relations must be a belief in things that are related [Ladyman/Ross] |
14925 | The normal assumption is that relations depend on properties of the relata [Ladyman/Ross] |
14931 | That there are existent structures not made of entities is no stranger than the theory of universals [Ladyman/Ross] |
14932 | Causal essentialism says properties are nothing but causal relations [Ladyman/Ross] |
14920 | If science captures the modal structure of things, that explains why its predictions work [Ladyman/Ross] |
14952 | Things are constructs for tracking patterns (and not linguistic, because animals do it) [Ladyman/Ross] |
14950 | Maybe individuation can be explained by thermodynamic depth [Ladyman/Ross] |
14927 | Physics seems to imply that we must give up self-subsistent individuals [Ladyman/Ross] |
14944 | There is no single view of individuals, because different sciences operate on different scales [Ladyman/Ross] |
14946 | There are no cats in quantum theory, and no mountains in astrophysics [Ladyman/Ross] |
14928 | Things are abstractions from structures [Ladyman/Ross] |
14892 | The idea of composition, that parts of the world are 'made of' something, is no longer helpful [Ladyman/Ross] |
14949 | A sum of things is not a whole if the whole does not support some new generalisation [Ladyman/Ross] |
14951 | We treat the core of a pattern as an essence, in order to keep track of it [Ladyman/Ross] |
14958 | A continuous object might be a type, with instances at each time [Ladyman/Ross] |
14903 | Quantum mechanics seems to imply single-case probabilities [Ladyman/Ross] |
14923 | In quantum statistics, two separate classical states of affairs are treated as one [Ladyman/Ross] |
14955 | Rats find some obvious associations easier to learn than less obvious ones [Ladyman/Ross] |
14918 | The doctrine of empiricism does not itself seem to be empirically justified [Ladyman/Ross] |
14891 | There is no reason to think our intuitions are good for science or metaphysics [Ladyman/Ross] |
8836 | Must all justification be inferential? [Ginet] |
8837 | Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet] |
14916 | What matters is whether a theory can predict - not whether it actually does so [Ladyman/Ross] |
14915 | The theory of evolution was accepted because it explained, not because of its predictions [Ladyman/Ross] |
14921 | The Ramsey-sentence approach preserves observations, but eliminates unobservables [Ladyman/Ross] |
14922 | The Ramsey sentence describes theoretical entities; it skips reference, but doesn't eliminate it [Ladyman/Ross] |
14953 | Induction is reasoning from the observed to the unobserved [Ladyman/Ross] |
14914 | Inductive defences of induction may be rule-circular, but not viciously premise-circular [Ladyman/Ross] |
14913 | We explain by deriving the properties of a phenomenon by embedding it in a large abstract theory [Ladyman/Ross] |
14930 | Maybe the only way we can think about a domain is by dividing it up into objects [Ladyman/Ross] |
14939 | Two versions of quantum theory say that the world is deterministic [Ladyman/Ross] |
14911 | Science is opposed to downward causation [Ladyman/Ross] |
8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
14956 | Explanation by kinds and by clusters of properties just express the stability of reality [Ladyman/Ross] |
14957 | There is nothing more to a natural kind than a real pattern in nature [Ladyman/Ross] |
14954 | Causation is found in the special sciences, but may have no role in fundamental physics [Ladyman/Ross] |
14902 | Science may have uninstantiated laws, inferred from approaching some unrealised limit [Ladyman/Ross] |
14937 | That the universe must be 'made of' something is just obsolete physics [Ladyman/Ross] |
14900 | In physics, matter is an emergent phenomenon, not part of fundamental ontology [Ladyman/Ross] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
14924 | If spacetime is substantial, what is the substance? [Ladyman/Ross] |
14901 | Spacetime may well be emergent, rather than basic [Ladyman/Ross] |
14938 | A fixed foliation theory of quantum gravity could make presentism possible [Ladyman/Ross] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |