54 ideas
| 12772 | Philosophy is a value- and attitude-driven enterprise [Fraassen] |
| 12771 | Is it likely that a successful, coherent, explanatory ontological hypothesis is true? [Fraassen] |
| 12773 | Analytic philosophy has an exceptional arsenal of critical tools [Fraassen] |
| 12770 | We may end up with a huge theory of carefully constructed falsehoods [Fraassen] |
| 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] |
| 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] |
| 17292 | Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P] |
| 17295 | Ground relations depend on the properties [Audi,P] |
| 17297 | A ball's being spherical non-causally determines its power to roll [Audi,P] |
| 17302 | Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P] |
| 17303 | The best critique of grounding says it is actually either identity or elimination [Audi,P] |
| 17294 | Grounding is a singular relation between worldly facts [Audi,P] |
| 17300 | If grounding relates facts, properties must be included, as well as objects [Audi,P] |
| 17296 | We must accept grounding, for our important explanations [Audi,P] |
| 17301 | Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P] |
| 17293 | Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 14919 | Empiricists deny what is unobservable, and reject objective modality [Fraassen] |
| 6783 | To 'accept' a theory is not to believe it, but to believe it empirically adequate [Fraassen, by Bird] |
| 14917 | To accept a scientific theory, we only need to believe that it is empirically adequate [Fraassen] |
| 17298 | Two things being identical (like water and H2O) is not an explanation [Audi,P] |
| 17299 | There are plenty of examples of non-causal explanation [Audi,P] |
| 6784 | Why should the true explanation be one of the few we have actually thought of? [Fraassen, by Bird] |
| 12769 | Inference to best explanation contains all sorts of hidden values [Fraassen] |
| 13066 | An explanation is just descriptive information answering a particular question [Fraassen, by Salmon] |
| 12768 | We accept many scientific theories without endorsing them as true [Fraassen] |