107 ideas
| 12644 | Who cares what 'philosophy' is? Most pre-1950 thought doesn't now count as philosophy [Fodor] |
| 12633 | Definitions often give necessary but not sufficient conditions for an extension [Fodor] |
| 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] |
| 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] |
| 12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
| 10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
| 12648 | Names in thought afford a primitive way to bring John before the mind [Fodor] |
| 12650 | 'Paderewski' has two names in mentalese, for his pianist file and his politician file [Fodor] |
| 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] |
| 10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
| 10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
| 10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
| 12656 | P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor] |
| 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] |
| 10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
| 14797 | Vagueness is a neglected but important part of mathematical thought [Peirce] |
| 14798 | All communication is vague, and is outside the principle of non-contradiction [Peirce] |
| 10275 | A blurry border is still a border [Shapiro] |
| 10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
| 12653 | There's statistical, logical, nomological, conceptual and metaphysical possibility [Fodor] |
| 10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
| 12651 | Some beliefs are only inferred when needed, like 'Shakespeare had not telephone' [Fodor] |
| 12628 | Knowing that must come before knowing how [Fodor] |
| 12625 | Pragmatism is the worst idea ever [Fodor] |
| 12636 | Mental states have causal powers [Fodor] |
| 10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
| 12661 | The different types of resemblance don't resemble one another [Fodor] |
| 12632 | In the Representational view, concepts play the key linking role [Fodor] |
| 12624 | Only the labels of nodes have semantic content in connectionism, and they play no role [Fodor] |
| 12641 | Connectionism gives no account of how constituents make complex concepts [Fodor] |
| 12640 | Associative thinking avoids syntax, but can't preserve sense, reference or truth [Fodor] |
| 12643 | Ambiguities in English are the classic reason for claiming that we don't think in English [Fodor] |
| 12649 | We think in file names [Fodor] |
| 12647 | Mental representations name things in the world, but also files in our memory [Fodor] |
| 12655 | Frame Problem: how to eliminate most beliefs as irrelevant, without searching them? [Fodor] |
| 12630 | If concept content is reference, then my Twin and I are referring to the same stuff [Fodor] |
| 12658 | Nobody knows how concepts are acquired [Fodor] |
| 12662 | We have an innate capacity to form a concept, once we have grasped the stereotype [Fodor] |
| 12635 | Having a concept isn't a pragmatic matter, but being able to think about the concept [Fodor] |
| 12652 | Concepts have two sides; they are files that face thought, and also face subject-matter [Fodor] |
| 12626 | Cartesians put concept individuation before concept possession [Fodor] |
| 12637 | Frege's puzzles suggest to many that concepts have sense as well as reference [Fodor] |
| 12638 | If concepts have sense, we can't see the connection to their causal powers [Fodor] |
| 12639 | Belief in 'senses' may explain intentionality, but not mental processes [Fodor] |
| 12654 | You can't think 'brown dog' without thinking 'brown' and 'dog' [Fodor] |
| 12659 | Maybe stereotypes are a stage in concept acquisition (rather than a by-product) [Fodor] |
| 12660 | One stereotype might be a paradigm for two difference concepts [Fodor] |
| 12629 | For the referential view of thought, the content of a concept is just its reference [Fodor] |
| 12631 | Compositionality requires that concepts be atomic [Fodor] |
| 12657 | Abstractionism claims that instances provide criteria for what is shared [Fodor] |
| 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] |
| 12634 | 'Inferential-role semantics' says meaning is determined by role in inference [Fodor] |
| 12642 | Co-referring terms differ if they have different causal powers [Fodor] |
| 12663 | We refer to individuals and to properties, and we use singular terms and predicates [Fodor] |
| 12645 | Semantics (esp. referential semantics) allows inferences from utterances to the world [Fodor] |
| 12646 | Semantics relates to the world, so it is never just psychological [Fodor] |
| 12627 | Before you can plan action, you must decide on the truth of your estimate of success [Fodor] |