74 ideas
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| 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] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 9895 | A number is a multitude composed of units [Dummett] |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| 19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| 19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19169 | Predicates are a source of generality in sentences [Davidson] |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| 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] |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| 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] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |