58 ideas
| 23531 | Philosophers should interpret the world, by expressing its possibilities [Berardi] |
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| 10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
| 10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| 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] |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| 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] |
| 10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
| 23538 | Nothingness only exists in consciousness [Berardi] |
| 10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
| 10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
| 10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
| 10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
| 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] |
| 10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
| 10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
| 10532 | We can understand universals by studying predication [Dummett] |
| 10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| 10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
| 10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| 10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| 10543 | Abstract objects must have names that fall within the range of some functional expression [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] |
| 10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
| 10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| 10531 | There is a modern philosophical notion of 'object', first introduced by Frege [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] |
| 23532 | The delusion of free will brings a sense of guilt [Berardi] |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by 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] |
| 10549 | Since abstract objects cannot be picked out, we must rely on identity statements [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] |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| 23537 | American white men trusted the philosophy of winning, and then discovered losing [Berardi] |
| 23536 | Community is now a nostalgic memory, which no longer exists [Berardi] |
| 23534 | Communism failed to unite western workers with the oppressed of the south [Berardi] |
| 23533 | The economy has replaced medieval theocracy at the centre of our society [Berardi] |
| 23535 | Western workers turn to nationalism, to avert the effects of globalisation [Berardi] |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |