74 ideas
| 2512 | Philosophy is a battle against the bewitchment of our intelligence by means of language [Wittgenstein] |
| 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] |
| 6566 | The problem is to explain the role of contradiction in social life [Wittgenstein] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 13522 | Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS] |
| 13521 | Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 13534 | In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS] |
| 13535 | First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS] |
| 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] |
| 13532 | Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS] |
| 13519 | Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS] |
| 13533 | First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS] |
| 13531 | Model theory reveals the structures of mathematics [Wolf,RS] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 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] |
| 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] |
| 4158 | An 'inner process' stands in need of outward criteria [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] |
| 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] |
| 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] |
| 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] |
| 4136 | To imagine a language means to imagine a form of life [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] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 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] |