48 ideas
| 16512 | Semantic facts are preferable to transcendental philosophical fiction [Wiggins] |
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| 17529 | Maybe the concept needed under which things coincide must also yield a principle of counting [Wiggins] |
| 17530 | The sortal needed for identities may not always be sufficient to support counting [Wiggins] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 16523 | Realist Conceptualists accept that our interests affect our concepts [Wiggins] |
| 16524 | Conceptualism says we must use our individuating concepts to grasp reality [Wiggins] |
| 16526 | Animal classifications: the Emperor's, fabulous, innumerable, like flies, stray dogs, embalmed…. [Wiggins] |
| 16492 | Individuation needs accounts of identity, of change, and of singling out [Wiggins] |
| 16493 | Individuation can only be understood by the relation between things and thinkers [Wiggins] |
| 16496 | Singling out extends back and forward in time [Wiggins] |
| 16495 | The only singling out is singling out 'as' something [Wiggins] |
| 16501 | In Aristotle's sense, saying x falls under f is to say what x is [Wiggins] |
| 16506 | Every determinate thing falls under a sortal, which fixes its persistence [Wiggins] |
| 16509 | Natural kinds are well suited to be the sortals which fix substances [Wiggins] |
| 16514 | Artefacts are individuated by some matter having a certain function [Wiggins] |
| 16510 | Nominal essences don't fix membership, ignore evolution, and aren't contextual [Wiggins] |
| 16503 | 'What is it?' gives the kind, nature, persistence conditions and identity over time of a thing [Wiggins] |
| 16499 | A restored church is the same 'church', but not the same 'building' or 'brickwork' [Wiggins] |
| 16515 | A thing begins only once; for a clock, it is when its making is first completed [Wiggins] |
| 16517 | Priests prefer the working ship; antiquarians prefer the reconstruction [Wiggins] |
| 16498 | Identity cannot be defined, because definitions are identities [Wiggins] |
| 16497 | Leibniz's Law (not transitivity, symmetry, reflexivity) marks what is peculiar to identity [Wiggins] |
| 16502 | Identity is primitive [Wiggins] |
| 16521 | A is necessarily A, so if B is A, then B is also necessarily A [Wiggins] |
| 16505 | By the principle of Indiscernibility, a symmetrical object could only be half of itself! [Wiggins] |
| 16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |
| 16522 | It is hard or impossible to think of Caesar as not human [Wiggins] |
| 16525 | Our sortal concepts fix what we find in experience [Wiggins] |
| 16518 | We conceptualise objects, but they impinge on us [Wiggins] |
| 16511 | A 'conception' of a horse is a full theory of what it is (and not just the 'concept') [Wiggins] |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |