88 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 12644 | Who cares what 'philosophy' is? Most pre-1950 thought doesn't now count as philosophy [Fodor] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 12633 | Definitions often give necessary but not sufficient conditions for an extension [Fodor] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| 12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
| 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] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| 12656 | P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor] |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| 12653 | There's statistical, logical, nomological, conceptual and metaphysical possibility [Fodor] |
| 12651 | Some beliefs are only inferred when needed, like 'Shakespeare had not telephone' [Fodor] |
| 12628 | Knowing that must come before knowing how [Fodor] |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| 12625 | Pragmatism is the worst idea ever [Fodor] |
| 12636 | Mental states have causal powers [Fodor] |
| 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] |
| 12640 | Associative thinking avoids syntax, but can't preserve sense, reference or truth [Fodor] |
| 12641 | Connectionism gives no account of how constituents make complex concepts [Fodor] |
| 12643 | Ambiguities in English are the classic reason for claiming that we don't think in English [Fodor] |
| 12647 | Mental representations name things in the world, but also files in our memory [Fodor] |
| 12649 | We think in file names [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] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 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] |
| 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] |
| 22381 | Being a good father seems to depend on intentions, rather than actual abilities [Foot] |
| 22380 | Some words, such as 'knife', have a meaning which involves its function [Foot] |