113 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] |
| 13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
| 13643 | Aristotelian logic is complete [Shapiro] |
| 13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
| 13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| 13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
| 13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
| 13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
| 13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
| 13627 | There is no 'correct' logic for natural languages [Shapiro] |
| 13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
| 13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
| 13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
| 13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
| 13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
| 13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
| 13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
| 13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
| 15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
| 13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
| 13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
| 13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
| 13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
| 13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
| 13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
| 14943 | Maybe mathematical logic rests on information-processing [Ladyman/Ross] |
| 13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
| 13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
| 13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
| 13644 | Semantics for models uses set-theory [Shapiro] |
| 13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
| 13670 | Categoricity can't be reached in a first-order language [Shapiro] |
| 13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
| 13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
| 13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
| 13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
| 13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
| 13628 | We can live well without completeness in logic [Shapiro] |
| 13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
| 13646 | Compactness is derived from soundness and completeness [Shapiro] |
| 13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
| 13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
| 13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
| 13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
| 13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
| 13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
| 13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| 13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
| 13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
| 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] |
| 13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
| 8526 | We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly] |
| 8527 | More than one trope (even identical ones!) can occupy the same location [Daly] |
| 8528 | If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly] |
| 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] |
| 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] |