36 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] |
18851 | Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen] |
10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [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] |
10540 | We can't say that light is concrete but radio waves abstract [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] |
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] |
18852 | A Meinongian principle might say that there is an object for any modest class of properties [Rosen] |
18849 | Metaphysical necessity is absolute and universal; metaphysical possibility is very tolerant [Rosen] |
18850 | 'Metaphysical' modality is the one that makes the necessity or contingency of laws of nature interesting [Rosen] |
18858 | Sets, universals and aggregates may be metaphysically necessary in one sense, but not another [Rosen] |
18857 | Standard Metaphysical Necessity: P holds wherever the actual form of the world holds [Rosen] |
18856 | Non-Standard Metaphysical Necessity: when ¬P is incompatible with the nature of things [Rosen] |
18848 | Something may be necessary because of logic, but is that therefore a special sort of necessity? [Rosen] |
18855 | Combinatorial theories of possibility assume the principles of combination don't change across worlds [Rosen] |
18853 | A proposition is 'correctly' conceivable if an ominiscient being could conceive it [Rosen] |
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] |
10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
18854 | The MRL view says laws are the theorems of the simplest and strongest account of the world [Rosen] |
20696 | We can approach knowledge of God by negative attributes [Maimonides] |
19085 | Thinking of God as resembling humans results from a bad translation of Genesis 1:26 [Maimonides] |