59 ideas
18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein] |
18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
18735 | Talking nonsense is not following the rules [Wittgenstein] |
18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
18707 | All thought has the logical form of reality [Wittgenstein] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
18724 | In logic nothing is hidden [Wittgenstein] |
18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
18726 | For each necessity in the world there is an arbitrary rule of language [Wittgenstein] |
18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
18721 | Explanation and understanding are the same [Wittgenstein] |
18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
21932 | 'Différance' is the interwoven history of each sign [Derrida, by Glendinning] |
18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |