61 ideas
17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
17928 | Ordinal numbers represent order relations [Colyvan] |
17923 | Intuitionists only accept a few safe infinities [Colyvan] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
7871 | Perceptual concepts can't just refer to what causes classification [Papineau] |
17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
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] |
17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
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] |
7883 | Verificationists tend to infer indefinite answers from undecidable questions [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] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
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] |