101 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] |
17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
17751 | Gödel proved the completeness of first order predicate logic in 1930 [Gödel, by Walicki] |
8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
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] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
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] |
14922 | The Ramsey sentence describes theoretical entities; it skips reference, but doesn't eliminate it [Ladyman/Ross] |
14921 | The Ramsey-sentence approach preserves observations, but eliminates unobservables [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] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
14911 | Science is opposed to downward causation [Ladyman/Ross] |
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] |
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] |