97 ideas
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] |
14415 | A ground must be about its truth, and not just necessitate it [Merricks] |
14408 | Truthmaker needs truths to be 'about' something, and that is often unclear [Merricks] |
14395 | If a ball changes from red to white, Truthmaker says some thing must make the change true [Merricks] |
14398 | Truthmaker says if an entity is removed, some nonexistence truthmaker must replace it [Merricks] |
14403 | If Truthmaker says each truth is made by the existence of something, the theory had de re modality at is core [Merricks] |
14397 | Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients [Merricks] |
14396 | If 'truth supervenes on being', worlds with the same entities, properties and relations have the same truths [Merricks] |
14400 | If truth supervenes on being, that won't explain why truth depends on being [Merricks] |
14394 | It is implausible that claims about non-existence are about existing things [Merricks] |
14390 | Truthmaker isn't the correspondence theory, because it offers no analysis of truth [Merricks] |
14412 | Speculations about non-existent things are not about existent things, so Truthmaker is false [Merricks] |
14414 | I am a truthmaker for 'that a human exists', but is it about me? [Merricks] |
14418 | Being true is not a relation, it is a primitive monadic property [Merricks] |
14391 | If the correspondence theory is right, then necessary truths must correspond to something [Merricks] |
14419 | Deflationism just says there is no property of being truth [Merricks] |
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] |
14393 | The totality state is the most plausible truthmaker for negative existential truths [Merricks] |
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] |
14413 | Some properties seem to be primitive, but others can be analysed [Merricks] |
14416 | An object can have a disposition when the revelant conditional is false [Merricks] |
10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
14392 | Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified [Merricks] |
10275 | A blurry border is still a border [Shapiro] |
14410 | You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks] |
10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
14417 | Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks] |
10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
14402 | If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks] |
5163 | Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer] |
5167 | The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer] |
10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
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] |
5164 | A statement is meaningful if observation statements can be deduced from it [Ayer] |
5165 | Directly verifiable statements must entail at least one new observation statement [Ayer] |
5166 | The principle of verification is not an empirical hypothesis, but a definition [Ayer] |
5162 | Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer] |
5168 | Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer] |
14406 | Presentists say that things have existed and will exist, not that they are instantaneous [Merricks] |
14407 | Presentist should deny there is a present time, and just say that things 'exist' [Merricks] |
14411 | Maybe only presentism allows change, by now having a property, and then lacking it [Merricks] |
14405 | How can a presentist explain an object's having existed? [Merricks] |