93 ideas
| 13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| 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] |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 7508 | Good reductionism connects fields of knowledge, but doesn't replace one with another [Pinker] |
| 3509 | Externalism may be the key idea in philosophical naturalism [Papineau] |
| 13409 | Our best theories may commit us to mathematical abstracta, but that doesn't justify the commitment [Papineau] |
| 12583 | Belief truth-conditions are normal circumstances where the belief is supposed to occur [Papineau] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 13406 | A priori knowledge is analytic - the structure of our concepts - and hence unimportant [Papineau] |
| 7871 | Perceptual concepts can't just refer to what causes classification [Papineau] |
| 7510 | Connectionists say the mind is a general purpose learning device [Pinker] |
| 13408 | Intuition and thought-experiments embody substantial information about the world [Papineau] |
| 7513 | Is memory stored in protein sequences, neurons, synapses, or synapse-strengths? [Pinker] |
| 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] |
| 7509 | Roundworms live successfully with 302 neurons, so human freedom comes from our trillions [Pinker] |
| 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] |
| 3513 | How does a dualist mind represent, exist outside space, and be transparent to itself? [Papineau] |
| 3514 | Functionalism needs causation and intentionality to explain actions [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] |
| 3510 | Epiphenomenalism is supervenience without physicalism [Papineau] |
| 3511 | Supervenience requires all mental events to have physical effects [Papineau] |
| 7865 | Supervenience can be replaced by identifying mind with higher-order or disjunctional properties [Papineau] |
| 3515 | Knowing what it is like to be something only involves being (physically) that thing [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] |
| 7511 | Neural networks can generalise their training, e.g. truths about tigers apply mostly to lions [Pinker] |
| 7512 | There are five types of reasoning that seem beyond connectionist systems [Pinker, by PG] |
| 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] |
| 3512 | If a mental state is multiply realisable, why does it lead to similar behaviour? [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] |
| 16369 | There is a single file per object, memorised, reactivated, consolidated and expanded [Papineau, by Recanati] |
| 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] |
| 7883 | Verificationists tend to infer indefinite answers from undecidable questions [Papineau] |
| 13410 | Verificationism about concepts means you can't deny a theory, because you can't have the concept [Papineau] |
| 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] |
| 3516 | The Private Language argument only means people may misjudge their experiences [Papineau] |
| 7505 | Many think that accepting human nature is to accept innumerable evils [Pinker] |
| 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] |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| 20974 | Modern biological research, especially into the cell, has revealed no special new natural forces [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] |
| 20975 | Quantum 'wave collapses' seem to violate conservation of energy [Papineau] |
| 7516 | In 1828, the stuff of life was shown to be ordinary chemistry, not a magic gel [Pinker] |
| 7515 | All the evidence says evolution is cruel and wasteful, not intelligent [Pinker] |
| 7514 | Intelligent Design says that every unexplained phenomenon must be design, by default [Pinker] |