72 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] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 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] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 7871 | Perceptual concepts can't just refer to what causes classification [Papineau] |
| 7852 | The only serious mind-brain theories now are identity, token identity, realization and supervenience [Papineau] |
| 7864 | Maybe mind and body do overdetermine acts, but are linked (for some reason) [Papineau] |
| 7873 | Young children can see that other individuals sometimes have false beliefs [Papineau] |
| 7874 | Do we understand other minds by simulation-theory, or by theory-theory? [Papineau] |
| 7882 | Researching phenomenal consciousness is peculiar, because the concepts involved are peculiar [Papineau] |
| 7854 | Whether octopuses feel pain is unclear, because our phenomenal concepts are too vague [Papineau] |
| 7889 | Our concept of consciousness is crude, and lacks theoretical articulation [Papineau] |
| 7891 | We can’t decide what 'conscious' means, so it is undecidable whether cats are conscious [Papineau] |
| 7890 | Maybe a creature is conscious if its mental states represent things in a distinct way [Papineau] |
| 7885 | The 'actualist' HOT theory says consciousness comes from actual higher judgements of mental states [Papineau] |
| 7886 | Actualist HOT theories imply that a non-conscious mental event could become conscious when remembered [Papineau] |
| 7887 | States are conscious if they could be the subject of higher-order mental judgements [Papineau] |
| 7888 | Higher-order judgements may be possible where the subject denies having been conscious [Papineau] |
| 7860 | The epiphenomenal relation of mind and brain is a 'causal dangler', unlike anything else [Papineau] |
| 7862 | Maybe minds do not cause actions, but do cause us to report our decisions [Papineau] |
| 7870 | Role concepts either name the realising property, or the higher property constituting the role [Papineau] |
| 7858 | If causes are basic particulars, this doesn't make conscious and physical properties identical [Papineau] |
| 7865 | Supervenience can be replaced by identifying mind with higher-order or disjunctional properties [Papineau] |
| 7892 | The completeness of physics is needed for mind-brain identity [Papineau] |
| 7879 | Mind-brain reduction is less explanatory, because phenomenal concepts lack causal roles [Papineau] |
| 20971 | Weak reduction of mind is to physical causes; strong reduction is also to physical laws [Papineau] |
| 7856 | It is absurd to think that physical effects are caused twice, so conscious causes must be physical [Papineau] |
| 7881 | Accept ontological monism, but conceptual dualism; we think in a different way about phenomenal thought [Papineau] |
| 7866 | Mary acquires new concepts; she previously thought about the same property using material concepts [Papineau] |
| 7850 | Thinking about a thing doesn't require activating it [Papineau] |
| 7851 | Consciousness affects bodily movement, so thoughts must be material states [Papineau] |
| 7884 | Most reductive accounts of representation imply broad content [Papineau] |
| 7863 | If content hinges on matters outside of you, how can it causally influence your actions? [Papineau] |
| 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] |
| 7883 | Verificationists tend to infer indefinite answers from undecidable questions [Papineau] |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| 7872 | Teleosemantics equates meaning with the item the concept is intended to track [Papineau] |
| 7869 | Truth conditions in possible worlds can't handle statements about impossibilities [Papineau] |
| 7868 | Thought content is possible worlds that make the thought true; if that includes the actual world, it's true [Papineau] |
| 7853 | Causation is based on either events, or facts, or states of affairs [Papineau] |
| 7857 | Causes are instantiations of properties by particulars, or they are themselves basic particulars [Papineau] |
| 20976 | The completeness of physics cannot be proved [Papineau] |
| 20970 | Determinism is possible without a complete physics, if mental forces play a role [Papineau] |
| 20974 | Modern biological research, especially into the cell, has revealed no special new natural forces [Papineau] |
| 20975 | Quantum 'wave collapses' seem to violate conservation of energy [Papineau] |