120 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] |
| 14897 | We should abandon intuitions, especially that the world is made of little things, and made of something [Ladyman/Ross] |
| 14905 | The supremacy of science rests on its iterated error filters [Ladyman/Ross] |
| 18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
| 18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| 18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| 18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 10594 | Henkin semantics is more plausible for plural logic than for second-order logic [Maddy] |
| 14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 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] |
| 18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
| 18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
| 18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
| 18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
| 18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
| 18182 | The extension of concepts is not important to me [Maddy] |
| 18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
| 18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
| 18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
| 18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
| 18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
| 18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
| 18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 14948 | To be is to be a real pattern [Ladyman/Ross] |
| 14942 | Only admit into ontology what is explanatory and predictive [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] |
| 18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
| 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] |
| 14915 | The theory of evolution was accepted because it explained, not because of its predictions [Ladyman/Ross] |
| 14916 | What matters is whether a theory can predict - not whether it actually does so [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] |
| 18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
| 14939 | Two versions of quantum theory say that the world is deterministic [Ladyman/Ross] |
| 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] |
| 14901 | Spacetime may well be emergent, rather than basic [Ladyman/Ross] |
| 14924 | If spacetime is substantial, what is the substance? [Ladyman/Ross] |
| 14938 | A fixed foliation theory of quantum gravity could make presentism possible [Ladyman/Ross] |