99 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| 2512 | Philosophy is a battle against the bewitchment of our intelligence by means of language [Wittgenstein] |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| 4148 | What is your aim in philosophy? - To show the fly the way out of the fly-bottle [Wittgenstein] |
| 22490 | Bring words back from metaphysics to everyday use [Wittgenstein] |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| 6566 | The problem is to explain the role of contradiction in social life [Wittgenstein] |
| 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] |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [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] |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [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] |
| 18743 | Wittgenstein says we want the grammar of problems, not their first-order logical structure [Wittgenstein, by Horsten/Pettigrew] |
| 4139 | Naming is a preparation for description [Wittgenstein] |
| 4946 | A name is not determined by a description, but by a cluster or family [Wittgenstein, by Kripke] |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| 13513 | Models are ways the world might be from a first-order point of view [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] |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| 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] |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [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] |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| 15106 | Essence is expressed by grammar [Wittgenstein] |
| 6600 | The belief that fire burns is like the fear that it burns [Wittgenstein] |
| 4153 | Are sense-data the material of which the universe is made? [Wittgenstein] |
| 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] |
| 6501 | As sense-data are necessarily private, they are attacked by Wittgenstein's objections [Wittgenstein, by Robinson,H] |
| 11079 | How do I decide when to accept or obey an intuition? [Wittgenstein] |
| 4160 | One can mistrust one's own senses, but not one's own beliefs [Wittgenstein] |
| 19273 | I don't have the opinion that people have minds; I just treat them as such [Wittgenstein] |
| 5663 | It is irresponsible to generalise from my own case of pain to other people's [Wittgenstein] |
| 19272 | To imagine another's pain by my own, I must imagine a pain I don't feel, by one I do feel [Wittgenstein] |
| 4161 | If a lion could talk, we could not understand him [Wittgenstein] |
| 7392 | If a lion could talk, it would be nothing like other lions [Dennett on Wittgenstein] |
| 5676 | To say that I 'know' I am in pain means nothing more than that I AM in pain [Wittgenstein] |
| 4154 | Why are we not aware of the huge gap between mind and brain in ordinary life? [Wittgenstein] |
| 6165 | Every course of action can either accord or conflict with a rule, so there is no accord or conflict [Wittgenstein] |
| 4143 | One cannot obey a rule 'privately', because that is a practice, not the same as thinking one is obeying [Wittgenstein] |
| 7092 | If individuals can't tell if they are following a rule, how does a community do it? [Grayling on Wittgenstein] |
| 4158 | An 'inner process' stands in need of outward criteria [Wittgenstein] |
| 4138 | Is white simple, or does it consist of the colours of the rainbow? [Wittgenstein] |
| 7055 | Externalist accounts of mental content begin in Wittgenstein [Wittgenstein, by Heil] |
| 12576 | Possessing a concept is knowing how to go on [Wittgenstein, by Peacocke] |
| 4157 | Concepts direct our interests and investigations, and express those interests [Wittgenstein] |
| 12606 | Man learns the concept of the past by remembering [Wittgenstein] |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| 4141 | Various games have a 'family resemblance', as their similarities overlap and criss-cross [Wittgenstein] |
| 23450 | Wittgenstein rejected his earlier view that the form of language is the form of the world [Wittgenstein, by Morris,M] |
| 4150 | Asking about verification is only one way of asking about the meaning of a proposition [Wittgenstein] |
| 6567 | For Wittgenstein, words are defined by their use, just as chess pieces are [Wittgenstein, by Fogelin] |
| 6169 | We do not achieve meaning and understanding in our heads, but in the world [Wittgenstein, by Rowlands] |
| 4155 | We all seem able to see quite clearly how sentences represent things when we use them [Wittgenstein] |
| 4137 | In the majority of cases the meaning of a word is its use in the language [Wittgenstein] |
| 4142 | To understand a sentence means to understand a language [Wittgenstein] |
| 4149 | We don't have 'meanings' in our minds in addition to verbal expressions [Wittgenstein] |
| 4156 | Make the following experiment: say "It's cold here" and mean "It's warm here" [Wittgenstein] |
| 4145 | How do words refer to sensations? [Wittgenstein] |
| 4140 | The standard metre in Paris is neither one metre long nor not one metre long [Wittgenstein] |
| 4136 | To imagine a language means to imagine a form of life [Wittgenstein] |
| 6166 | Was Wittgenstein's problem between individual and community, or between occasions for an individual? [Rowlands on Wittgenstein] |
| 7875 | If a brilliant child invented a name for a private sensation, it couldn't communicate it [Wittgenstein] |
| 4146 | We cannot doublecheck mental images for correctness (or confirm news with many copies of the paper) [Wittgenstein] |
| 4147 | If we only named pain by our own case, it would be like naming beetles by looking in a private box [Wittgenstein] |
| 5659 | If the reference is private, that is incompatible with the sense being public [Wittgenstein, by Scruton] |
| 4152 | Getting from perceptions to words cannot be a private matter; the rules need an institution of use [Wittgenstein] |
| 4144 | Common human behaviour enables us to interpret an unknown language [Wittgenstein] |
| 11049 | To communicate, language needs agreement in judgment as well as definition [Wittgenstein] |
| 6658 | What is left over if I subtract my arm going up from my raising my arm? [Wittgenstein] |
| 4151 | Grammar tells what kind of object anything is - and theology is a kind of grammar [Wittgenstein] |
| 4159 | The human body is the best picture of the human soul [Wittgenstein] |