99 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] |
15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
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] |
10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
18176 | Pure mathematics is pure set theory [Cantor] |
8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
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] |
7401 | Heat and colour don't exist, so cannot mislead about the external world [Galileo, by Tuck] |
5454 | Tastes, odours and colours only reside in consciousness, and would disappear with creatures [Galileo] |
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] |
16560 | Galileo introduced geometrico-mechanical explanation, based on Archimedes [Galileo, by Machamer/Darden/Craver] |
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] |
8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
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] |
13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
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] |
3645 | To understand the universe mathematics is essential [Galileo] |
10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
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] |