139 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] |
| 20744 | Phenomenologists say all experience is about something and is directed [Aho] |
| 10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
| 10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
| 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] |
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| 8309 | A set is a 'number of things', not a 'collection', because nothing actually collects the members [Lowe] |
| 8322 | I don't believe in the empty set, because (lacking members) it lacks identity-conditions [Lowe] |
| 10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
| 10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
| 10207 | Anti-realists reject set theory [Shapiro] |
| 10259 | The two standard explanations of consequence are semantic (in models) and deductive [Shapiro] |
| 10257 | Intuitionism only sanctions modus ponens if all three components are proved [Shapiro] |
| 10253 | Either logic determines objects, or objects determine logic, or they are separate [Shapiro] |
| 10251 | The law of excluded middle might be seen as a principle of omniscience [Shapiro] |
| 10212 | Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |
| 10268 | Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro] |
| 10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
| 10240 | Model theory deals with relations, reference and extensions [Shapiro] |
| 10239 | The central notion of model theory is the relation of 'satisfaction' [Shapiro] |
| 10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
| 10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
| 10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
| 10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
| 10213 | Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro] |
| 18243 | Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro] |
| 18245 | Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro] |
| 10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
| 10256 | For intuitionists, proof is inherently informal [Shapiro] |
| 10202 | Natural numbers just need an initial object, successors, and an induction principle [Shapiro] |
| 10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
| 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] |
| 10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
| 10218 | Baseball positions and chess pieces depend entirely on context [Shapiro] |
| 10224 | The even numbers have the natural-number structure, with 6 playing the role of 3 [Shapiro] |
| 10228 | Could infinite structures be apprehended by pattern recognition? [Shapiro] |
| 10230 | The 4-pattern is the structure common to all collections of four objects [Shapiro] |
| 10249 | The main mathematical structures are algebraic, ordered, and topological [Shapiro] |
| 10273 | Some structures are exemplified by both abstract and concrete [Shapiro] |
| 10276 | Mathematical structures are defined by axioms, or in set theory [Shapiro] |
| 10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
| 10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
| 10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
| 10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
| 10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
| 8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
| 10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
| 10200 | We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro] |
| 10210 | If mathematical objects are accepted, then a number of standard principles will follow [Shapiro] |
| 10215 | Platonists claim we can state the essence of a number without reference to the others [Shapiro] |
| 10233 | Platonism must accept that the Peano Axioms could all be false [Shapiro] |
| 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] |
| 10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
| 10280 | A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro] |
| 10254 | Can the ideal constructor also destroy objects? [Shapiro] |
| 10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
| 10279 | Can we discover whether a deck is fifty-two cards, or a person is time-slices or molecules? [Shapiro] |
| 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] |
| 10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
| 10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| 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] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 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] |
| 10275 | A blurry border is still a border [Shapiro] |
| 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] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 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] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 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] |
| 20736 | Science has to abstract out the subjective attributes of things, focusing on what is objective [Aho] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 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] |
| 10229 | Simple types can be apprehended through their tokens, via abstraction [Shapiro] |
| 10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
| 9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
| 10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
| 8306 | You can think of a direction without a line, but a direction existing with no lines is inconceivable [Lowe] |
| 20734 | Anxiety, nausea, guilt and absurdity shake us up, revealing our freedom and limits [Aho] |
| 20733 | Our 'existence' is how we create ourselves, unconstrained by any prior 'essence' [Aho] |
| 20753 | The self is constituted by its choices made within a social context [Aho] |
| 20738 | Social contracts and markets have made society seem disconnected and artificial [Aho] |
| 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] |
| 20737 | Protestantism brought the modern emphasis on inner states of the soul [Aho] |
| 20766 | Four Noble Truths: life is suffering, caused by attachment, it is avoidable, there is a path [Aho] |