117 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] |
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| 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] |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| 8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| 8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| 8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| 8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| 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] |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| 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] |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| 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] |
| 16131 | The metaphysically possible is what acceptable principles and categories will permit [Lowe] |
| 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] |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| 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] |