86 ideas
| 21634 | Metaphysics is (supposedly) first the ontology, then in general what things are like [Hofweber] |
| 16415 | Esoteric metaphysics aims to be top science, investigating ultimate reality [Hofweber] |
| 16413 | Science has discovered properties of things, so there are properties - so who needs metaphysics? [Hofweber] |
| 21666 | 'Fundamentality' is either a superficial idea, or much too obscure [Hofweber] |
| 21640 | 'It's true that Fido is a dog' conjures up a contrast class, of 'it's false' or 'it's unlikely' [Hofweber] |
| 17990 | Instances of minimal truth miss out propositions inexpressible in current English [Hofweber] |
| 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] |
| 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] |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| 21657 | Since properties can have properties, some theorists rank them in 'types' [Hofweber] |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| 21653 | Maybe not even names are referential, but are just by used by speakers to refer [Hofweber] |
| 10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
| 21636 | 'Singular terms' are not found in modern linguistics, and are not the same as noun phrases [Hofweber] |
| 21637 | If two processes are said to be identical, that doesn't make their terms refer to entities [Hofweber] |
| 16416 | The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber] |
| 21643 | The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber] |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
| 17988 | Quantification can't all be substitutional; some reference is obviously to objects [Hofweber] |
| 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] |
| 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] |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| 21644 | Numbers are used as singular terms, as adjectives, and as symbols [Hofweber] |
| 21646 | The Amazonian Piraha language is said to have no number words [Hofweber] |
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| 21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |
| 21649 | How can words be used for counting if they are objects? [Hofweber] |
| 10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
| 10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
| 10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
| 10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
| 21647 | Logicism makes sense of our ability to know arithmetic just by thought [Hofweber] |
| 21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |
| 10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
| 21664 | Supervenience offers little explanation for things which necessarily go together [Hofweber] |
| 21660 | Reality can be seen as the totality of facts, or as the totality of things [Hofweber] |
| 21661 | There are probably ineffable facts, systematically hidden from us [Hofweber] |
| 17989 | Since properties have properties, there can be a typed or a type-free theory of them [Hofweber] |
| 21652 | Our perceptual beliefs are about ordinary objects, not about simples arranged chair-wise [Hofweber] |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| 21663 | Counterfactuals are essential for planning, and learning from mistakes [Hofweber] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 10004 | Our minds are at their best when reasoning about objects [Hofweber] |
| 21654 | The "Fido"-Fido theory of meaning says every expression in a language has a referent [Hofweber] |
| 21641 | Inferential role semantics is an alternative to semantics that connects to the world [Hofweber] |
| 21638 | Syntactic form concerns the focus of the sentence, as well as the truth-conditions [Hofweber] |
| 21658 | Properties can be expressed in a language despite the absence of a single word for them [Hofweber] |
| 21659 | 'Being taller than this' is a predicate which can express many different properties [Hofweber] |
| 21655 | Compositonality is a way to build up the truth-conditions of a sentence [Hofweber] |
| 21656 | Proposition have no content, because they are content [Hofweber] |
| 21635 | Without propositions there can be no beliefs or desires [Hofweber] |
| 21662 | Do there exist thoughts which we are incapable of thinking? [Hofweber] |
| 21645 | 'Semantic type coercion' is selecting the reading of a word to make the best sense [Hofweber] |
| 21639 | 'Background deletion' is appropriately omitting background from an answer [Hofweber] |
| 17991 | Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber] |