107 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] |
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 14905 | The supremacy of science rests on its iterated error filters [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] |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 9984 | We can have a series with identical members [Tait] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| 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] |
| 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] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 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] |
| 14939 | Two versions of quantum theory say that the world is deterministic [Ladyman/Ross] |
| 14911 | Science is opposed to downward causation [Ladyman/Ross] |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| 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] |