63 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
7871 | Perceptual concepts can't just refer to what causes classification [Papineau] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
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] |
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] |