53 ideas
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [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] |
| 1618 | We study bound variables not to know reality, but to know what reality language asserts [Quine] |
| 8455 | Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein] |
| 8456 | Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein] |
| 1611 | Names can be converted to descriptions, and Russell showed how to eliminate those [Quine] |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| 1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
| 1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
| 1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
| 10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
| 1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
| 10241 | For Quine, there is only one way to exist [Quine, by Shapiro] |
| 4064 | The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane] |
| 19277 | Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale] |
| 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] |
| 12210 | Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine] |
| 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] |
| 8496 | What actually exists does not, of course, depend on language [Quine] |
| 1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
| 8459 | Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein] |
| 8497 | An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine] |
| 16261 | If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine] |
| 7698 | If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine] |
| 10532 | We can understand universals by studying predication [Dummett] |
| 1612 | Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine] |
| 10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
| 15402 | There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine] |
| 4443 | Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong] |
| 8498 | Treating scattered sensations as single objects simplifies our understanding of experience [Quine] |
| 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] |
| 10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
| 10543 | Abstract objects must have names that fall within the range of some functional expression [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] |
| 10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
| 8856 | Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo] |
| 12443 | Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine] |
| 18209 | We can never translate our whole language of objects into phenomenalism [Quine] |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
| 10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
| 1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
| 1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
| 1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| 19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |
| 467 | A virtue is a combination of intelligence, strength and luck [Ion] |