104 ideas
| 11912 | Substantive metaphysics says what a property is, not what a predicate means [Molnar] |
| 10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
| 11920 | A real definition gives all the properties that constitute an identity [Molnar] |
| 10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
| 10206 | Modal operators are usually treated as quantifiers [Shapiro] |
| 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] |
| 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] |
| 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] |
| 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] |
| 8978 | Events are made of other things, and are not fundamental to ontology [Bennett] |
| 11919 | Ontological dependence rests on essential connection, not necessary connection [Molnar] |
| 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] |
| 11929 | The three categories in ontology are objects, properties and relations [Molnar] |
| 11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
| 11915 | If atomism is true, then all properties derive from ultimate properties [Molnar] |
| 11916 | 'Being physical' is a second-order property [Molnar] |
| 11956 | 'Categorical properties' are those which are not powers [Molnar] |
| 11928 | Are tropes transferable? If they are, that is a version of Platonism [Molnar] |
| 11933 | A power's type-identity is given by its definitive manifestation [Molnar] |
| 11932 | Powers have Directedness, Independence, Actuality, Intrinsicality and Objectivity [Molnar] |
| 11934 | The physical world has a feature very like mental intentionality [Molnar] |
| 11947 | Dispositions and external powers arise entirely from intrinsic powers in objects [Molnar] |
| 11952 | The Standard Model suggest that particles are entirely dispositional, and hence are powers [Molnar] |
| 11953 | Some powers are ungrounded, and others rest on them, and are derivative [Molnar] |
| 11943 | Dispositions can be causes, so they must be part of the actual world [Molnar] |
| 11939 | If powers only exist when actual, they seem to be nomadic, and indistinguishable from non-powers [Molnar] |
| 11914 | Platonic explanations of universals actually diminish our understanding [Molnar] |
| 11913 | For nominalists, predicate extensions are inexplicable facts [Molnar] |
| 11962 | Nominalists only accept first-order logic [Molnar] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 10275 | A blurry border is still a border [Shapiro] |
| 11917 | Structural properties are derivate properties [Molnar] |
| 11955 | There are no 'structural properties', as properties with parts [Molnar] |
| 11918 | The essence of a thing need not include everything that is necessarily true of it [Molnar] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 11963 | What is the truthmaker for a non-existent possible? [Molnar] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 11951 | Hume allows interpolation, even though it and extrapolation are not actually valid [Molnar] |
| 11936 | The two ways proposed to distinguish mind are intentionality or consciousness [Molnar] |
| 11935 | Physical powers like solubility and charge also have directedness [Molnar] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 11944 | Rule occasionalism says God's actions follow laws, not miracles [Molnar] |
| 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] |
| 11960 | Singular causation is prior to general causation; each aspirin produces the aspirin generalization [Molnar] |
| 11937 | We should analyse causation in terms of powers, not vice versa [Molnar] |
| 11954 | We should analyse causation in terms of powers [Molnar] |
| 10364 | Facts are about the world, not in it, so they can't cause anything [Bennett] |
| 11961 | Causal dependence explains counterfactual dependence, not vice versa [Molnar] |
| 11959 | Science works when we assume natural kinds have essences - because it is true [Molnar] |
| 9448 | Location in space and time are non-power properties [Molnar, by Mumford] |
| 11930 | One essential property of a muon doesn't entail the others [Molnar] |
| 11957 | It is contingent which kinds and powers exist in the world [Molnar] |
| 11921 | The laws of nature depend on the powers, not the other way round [Molnar] |
| 11931 | Energy fields are discontinuous at the very small [Molnar] |