49 ideas
| 9408 | Science studies phenomena, but only metaphysics tells us what exists [Mumford] |
| 9429 | Many forms of reasoning, such as extrapolation and analogy, are useful but deductively invalid [Mumford] |
| 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] |
| 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] |
| 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] |
| 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] |
| 9427 | For Humeans the world is a world primarily of events [Mumford] |
| 9446 | Properties are just natural clusters of powers [Mumford] |
| 9435 | A 'porridge' nominalist thinks we just divide reality in any way that suits us [Mumford] |
| 9447 | If properties are clusters of powers, this can explain why properties resemble in degrees [Mumford] |
| 12248 | How can we show that a universally possessed property is an essential property? [Mumford] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 20959 | Concepts are only analytic once the predicate is absorbed into the subject [Schleiermacher] |
| 9430 | Singular causes, and identities, might be necessary without falling under a law [Mumford] |
| 9445 | We can give up the counterfactual account if we take causal language at face value [Mumford] |
| 9443 | It is only properties which are the source of necessity in the world [Mumford] |
| 9444 | There are four candidates for the logical form of law statements [Mumford] |
| 9416 | Regularities are more likely with few instances, and guaranteed with no instances! [Mumford] |
| 9431 | Pure regularities are rare, usually only found in idealized conditions [Mumford] |
| 9441 | Regularity laws don't explain, because they have no governing role [Mumford] |
| 9415 | Would it count as a regularity if the only five As were also B? [Mumford] |
| 9422 | If the best system describes a nomological system, the laws are in nature, not in the description [Mumford] |
| 9421 | The best systems theory says regularities derive from laws, rather than constituting them [Mumford] |
| 9432 | Laws of nature are necessary relations between universal properties, rather than about particulars [Mumford] |
| 9433 | If laws can be uninstantiated, this favours the view of them as connecting universals [Mumford] |
| 9434 | Laws of nature are just the possession of essential properties by natural kinds [Mumford] |
| 9437 | To distinguish accidental from essential properties, we must include possible members of kinds [Mumford] |
| 9439 | The Central Dilemma is how to explain an internal or external view of laws which govern [Mumford] |
| 9412 | You only need laws if you (erroneously) think the world is otherwise inert [Mumford] |
| 9411 | There are no laws of nature in Aristotle; they became standard with Descartes and Newton [Mumford] |