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] |
| 19160 | A comprehensive theory of truth probably includes a theory of predication [Davidson] |
| 19151 | Antirealism about truth prevents its use as an intersubjective standard [Davidson] |
| 19144 | 'Epistemic' truth depends what rational creatures can verify [Davidson] |
| 19148 | There is nothing interesting or instructive for truths to correspond to [Davidson] |
| 19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
| 19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
| 19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
| 19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
| 19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
| 19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
| 19136 | Many say that Tarski's definitions fail to connect truth to meaning [Davidson] |
| 19139 | Tarski does not tell us what his various truth predicates have in common [Davidson] |
| 19147 | Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson] |
| 19172 | To define a class of true sentences is to stipulate a possible language [Davidson] |
| 19153 | Truth is basic and clear, so don't try to replace it with something simpler [Davidson] |
| 19170 | Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson] |
| 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] |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| 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] |
| 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] |
| 19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 10275 | A blurry border is still a border [Shapiro] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 12742 | A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 19169 | Predicates are a source of generality in sentences [Davidson] |
| 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] |
| 19149 | If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson] |
| 19163 | You only understand an order if you know what it is to obey it [Davidson] |
| 19152 | Utterances have the truth conditions intended by the speaker [Davidson] |
| 19162 | Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson] |
| 19131 | We recognise sentences at once as linguistic units; we then figure out their parts [Davidson] |
| 19156 | Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson] |
| 19176 | The concept of truth can explain predication [Davidson] |
| 19133 | If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson] |
| 19132 | Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson] |
| 19158 | 'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson] |
| 19154 | The principle of charity says an interpreter must assume the logical constants [Davidson] |
| 19161 | We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson] |