56 ideas
| 2956 | There is nothing so obvious that a philosopher cannot be found to deny it [Lockwood] |
| 2963 | There may only be necessary and sufficient conditions (and counterfactuals) because we intervene in the world [Lockwood] |
| 2958 | No one has ever succeeded in producing an acceptable non-trivial analysis of anything [Lockwood] |
| 2959 | If something is described in two different ways, is that two facts, or one fact presented in two ways? [Lockwood] |
| 9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
| 9912 | There are no such things as numbers [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] |
| 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] |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [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] |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [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] |
| 2969 | How does a direct realist distinguish a building from Buckingham Palace? [Lockwood] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 2970 | Dogs seem to have beliefs, and beliefs require concepts [Lockwood] |
| 2961 | Empiricism is a theory of meaning as well as of knowledge [Lockwood] |
| 2960 | Commonsense realism must account for the similarity of genuine perceptions and known illusions [Lockwood] |
| 2952 | A 1988 estimate gave the brain 3 x 10-to-the-14 synaptic junctions [Lockwood] |
| 2964 | How come unconscious states also cause behaviour? [Lockwood] |
| 2951 | Could there be unconscious beliefs and desires? [Lockwood] |
| 2953 | Fish may operate by blindsight [Lockwood] |
| 2967 | We might even learn some fundamental physics from introspection [Lockwood] |
| 2966 | Can phenomenal qualities exist unsensed? [Lockwood] |
| 2955 | If mental events occur in time, then relativity says they are in space [Lockwood] |
| 2950 | Only logical positivists ever believed behaviourism [Lockwood] |
| 2954 | Identity theory likes the identity of lightning and electrical discharges [Lockwood] |
| 16362 | An identity statement aims at getting the hearer to merge two mental files [Lockwood] |
| 2971 | Perhaps logical positivism showed that there is no dividing line between science and metaphysics [Lockwood] |
| 4055 | It isn't obviously wicked to destroy a potential human being (e.g. an ununited egg and sperm) [Lockwood] |
| 4056 | If the soul is held to leave the body at brain-death, it should arrive at the time of brain-creation [Lockwood] |
| 4054 | I may exist before I become a person, just as I exist before I become an adult [Lockwood] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 2962 | Maybe causation is a form of rational explanation, not an observation or a state of mind [Lockwood] |
| 2949 | We have the confused idea that time is a process of change [Lockwood] |