66 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| 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] |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| 15682 | Even fairly simple animals make judgements based on categories [Gelman] |
| 15691 | Children accept real stable categories, with nonobvious potential that gives causal explanations [Gelman] |
| 15700 | In India, upper-castes essentialize caste more than lower-castes do [Gelman] |
| 15685 | Essentialism is either natural to us, or an accident of our culture, or a necessary result of language [Gelman] |
| 15684 | Children's concepts include nonobvious features, like internal parts, functions and causes [Gelman] |
| 15681 | Essentialism: real or representational? sortal, causal or ideal? real particulars, or placeholders? [Gelman] |
| 15678 | Essentialism says categories have a true hidden nature which gives an object its identity [Gelman] |
| 15683 | Sortals are needed for determining essence - the thing must be categorised first [Gelman] |
| 15697 | Kind (unlike individual) essentialism assumes preexisting natural categories [Gelman] |
| 15687 | Kinship is essence that comes in degrees, and age groups are essences that change over time [Gelman] |
| 15679 | Essentialism comes from the cognitive need to categorise [Gelman] |
| 15698 | We found no evidence that mothers teach essentialism to their children [Gelman] |
| 15709 | Essentialism is useful for predictions, but it is not the actual structure of reality [Gelman] |
| 15696 | Peope favor historical paths over outward properties when determining what something is [Gelman] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 15707 | There is intentional, mechanical, teleological, essentialist, vitalist and deontological understanding [Gelman] |
| 15703 | Memories often conform to a theory, rather than being neutral [Gelman] |
| 15708 | Inductive success is rewarded with more induction [Gelman] |
| 15694 | Children overestimate the power of a single example [Gelman] |
| 15695 | Children make errors in induction by focusing too much on categories [Gelman] |
| 15692 | People tend to be satisfied with shallow explanations [Gelman] |
| 15680 | Folk essentialism rests on belief in natural kinds, in hidden properties, and on words indicating structures [Gelman] |
| 15686 | Labels may indicate categories which embody an essence [Gelman] |
| 15690 | Causal properties are seen as more central to category concepts [Gelman] |
| 15688 | Categories are characterized by distance from a prototype [Gelman] |
| 15689 | Theory-based concepts use rich models to show which similarities really matter [Gelman] |
| 15699 | Prelinguistic infants acquire and use many categories [Gelman] |
| 15693 | One sample of gold is enough, but one tree doesn't give the height of trees [Gelman] |
| 15701 | Nouns seem to invoke stable kinds more than predicates do [Gelman] |
| 15705 | Essentialism encourages us to think about the world scientifically [Gelman] |
| 15702 | Essentialism doesn't mean we know the essences [Gelman] |
| 15704 | Essentialism starts from richly structured categories, leading to a search for underlying properties [Gelman] |
| 15706 | A major objection to real essences is the essentialising of social categories like race, caste and occupation [Gelman] |