86 ideas
13407 | All worthwhile philosophy is synthetic theorizing, evaluated by experience [Papineau] |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
13412 | Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf] |
13413 | We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf] |
9912 | There are no such things as numbers [Benacerraf] |
9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
13411 | If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf] |
9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
13415 | An adequate account of a number must relate it to its series [Benacerraf] |
9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
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] |
9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
12583 | Belief truth-conditions are normal circumstances where the belief is supposed to occur [Papineau] |
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] |
13408 | Intuition and thought-experiments embody substantial information about the world [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] |
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] |
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] |
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] |