68 ideas
| 8766 | In much wisdom is much grief [Anon (Ecc)] |
| 8767 | Sorrow is better than laughter [Anon (Ecc)] |
| 7494 | Laughter is mad; of mirth, what doeth it? [Anon (Ecc)] |
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| 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] |
| 19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
| 19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
| 19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
| 19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
| 19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
| 19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
| 19172 | To define a class of true sentences is to stipulate a possible language [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] |
| 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] |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| 19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| 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] |
| 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] |
| 8765 | All is vanity, saith the Preacher [Anon (Ecc)] |
| 8768 | Books are endless, and study is wearisome [Anon (Ecc)] |