98 ideas
9414 | Metaphysics is the mapping of possibilities [Lowe, by Mumford] |
16414 | Science needs metaphysics to weed out its presuppositions [Lowe, by Hofweber] |
8282 | Only metaphysics can decide whether identity survives through change [Lowe] |
16127 | Metaphysics tells us what there could be, rather than what there is [Lowe] |
8262 | How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe] |
8315 | Maybe facts are just true propositions [Lowe] |
8319 | One-to-one correspondence would need countable, individuable items [Lowe] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
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] |
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] |
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] |
8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
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] |
8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
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] |
8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
8266 | Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe] |
8302 | Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe] |
8298 | Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe] |
8311 | If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe] |
8310 | Does the existence of numbers matter, in the way space, time and persons do? [Lowe] |
8321 | All possible worlds contain abstracta (e.g. numbers), which means they contain concrete objects [Lowe] |
8300 | Perhaps possession of causal power is the hallmark of existence (and a reason to deny the void) [Lowe] |
8281 | Heraclitus says change is new creation, and Spinoza that it is just phases of the one substance [Lowe] |
8270 | Events are changes or non-changes in properties and relations of persisting objects [Lowe] |
8308 | Events are ontologically indispensable for singular causal explanations [Lowe] |
8314 | Are facts wholly abstract, or can they contain some concrete constituents? [Lowe] |
8316 | Facts cannot be wholly abstract if they enter into causal relations [Lowe] |
8318 | The problem with the structured complex view of facts is what binds the constituents [Lowe] |
8323 | It is whimsical to try to count facts - how many facts did I learn before breakfast? [Lowe] |
8313 | Facts are needed for truth-making and causation, but they seem to lack identity criteria [Lowe] |
8258 | Two of the main rivals for the foundations of ontology are substances, and facts or states-of-affairs [Lowe] |
8301 | Some abstractions exist despite lacking causal powers, because explanation needs them [Lowe] |
8283 | Ontological categories are not natural kinds: the latter can only be distinguished using the former [Lowe] |
8284 | The top division of categories is either abstract/concrete, or universal/particular, or necessary/contingent [Lowe] |
13122 | Lowe divides things into universals and particulars, then kinds and properties, and abstract/concrete [Lowe, by Westerhoff] |
8273 | Is 'the Thames is broad in London' relational, or adverbial, or segmental? [Lowe] |
8285 | I prefer 'modes' to 'tropes', because it emphasises their dependence [Lowe] |
8295 | Why cannot a trope float off and join another bundle? [Lowe] |
8286 | Tropes cannot have clear identity-conditions, so they are not objects [Lowe] |
8294 | How can tropes depend on objects for their identity, if objects are just bundles of tropes? [Lowe] |
8296 | Does a ball snug in plaster have one trope, or two which coincide? [Lowe] |
8288 | Sortal terms for universals involve a substance, whereas adjectival terms do not [Lowe] |
8293 | Real universals are needed to explain laws of nature [Lowe] |
8307 | Particulars are instantiations, and universals are instantiables [Lowe] |
16130 | To be an object at all requires identity-conditions [Lowe] |
8265 | Our commitment to the existence of objects should depend on their explanatory value [Lowe] |
8275 | Objects are entities with full identity-conditions, but there are entities other than objects [Lowe] |
8267 | Perhaps concrete objects are entities which are in space-time and subject to causality [Lowe] |
8263 | An object is an entity which has identity-conditions [Lowe] |
8268 | Some things (such as electrons) can be countable, while lacking proper identity [Lowe] |
8303 | Criteria of identity cannot individuate objects, because they are shared among different types [Lowe] |
8292 | Diversity of two tigers is their difference in space-time; difference of matter is a consequence [Lowe] |
8291 | Individuation principles identify what kind it is; identity criteria distinguish items of the same kind [Lowe] |
16128 | A 'substance' is an object which doesn't depend for existence on other objects [Lowe] |
8279 | The identity of composite objects isn't fixed by original composition, because how do you identify the origin? [Lowe] |
8271 | An object 'endures' if it is always wholly present, and 'perdures' if different parts exist at different times [Lowe] |
8272 | How can you identify temporal parts of tomatoes without referring to tomatoes? [Lowe] |
8305 | A clear idea of the kind of an object must precede a criterion of identity for it [Lowe] |
8290 | One view is that two objects of the same type are only distinguished by differing in matter [Lowe] |
15079 | 'Conceptual' necessity is narrow logical necessity, true because of concepts and logical laws [Lowe] |
16063 | Metaphysical necessity is logical necessity 'broadly construed' [Lowe, by Lynch/Glasgow] |
8260 | Logical necessity can be 'strict' (laws), or 'narrow' (laws and definitions), or 'broad' (all logical worlds) [Lowe] |
490 | Everything happens by reason and necessity [Leucippus] |
16131 | The metaphysically possible is what acceptable principles and categories will permit [Lowe] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
8320 | Does every abstract possible world exist in every possible world? [Lowe] |
8280 | While space may just be appearance, time and change can't be, because the appearances change [Lowe] |
8276 | Properties or qualities are essentially adjectival, not objectual [Lowe] |
8289 | The idea that Cartesian souls are made of some ghostly 'immaterial' stuff is quite unwarranted [Lowe] |
8299 | Abstractions are non-spatial, or dependent, or derived from concepts [Lowe] |
8306 | You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe] |
8317 | To cite facts as the elements in causation is to confuse states of affairs with states of objects [Lowe] |
8269 | Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe] |