56 ideas
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
19160 | A comprehensive theory of truth probably includes a theory of predication [Davidson] |
19151 | Antirealism about truth prevents its use as an intersubjective standard [Davidson] |
19144 | 'Epistemic' truth depends what rational creatures can verify [Davidson] |
19148 | There is nothing interesting or instructive for truths to correspond to [Davidson] |
19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
19136 | Many say that Tarski's definitions fail to connect truth to meaning [Davidson] |
19139 | Tarski does not tell us what his various truth predicates have in common [Davidson] |
19147 | Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson] |
19172 | To define a class of true sentences is to stipulate a possible language [Davidson] |
19153 | Truth is basic and clear, so don't try to replace it with something simpler [Davidson] |
19170 | Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson] |
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] |
19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
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] |
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] |
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] |
19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
19169 | Predicates are a source of generality in sentences [Davidson] |
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] |
19149 | If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson] |
19163 | You only understand an order if you know what it is to obey it [Davidson] |
19152 | Utterances have the truth conditions intended by the speaker [Davidson] |
19162 | Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson] |
19131 | We recognise sentences at once as linguistic units; we then figure out their parts [Davidson] |
19156 | Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson] |
19176 | The concept of truth can explain predication [Davidson] |
19133 | If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson] |
19132 | Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson] |
19158 | 'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson] |
19154 | The principle of charity says an interpreter must assume the logical constants [Davidson] |
19161 | We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson] |
6017 | Nomos is king [Pindar] |