64 ideas
| 22611 | Metaphysics can criticise interpretations of science theories, and give good feedback [Ingthorsson] |
| 22609 | Philosophers accepted first-order logic, because they took science to be descriptive, not explanatory [Ingthorsson] |
| 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] |
| 22629 | Basic processes are said to be either physical, or organic, or psychological [Ingthorsson] |
| 22633 | Indirect realists are cautious about the manifest image, and prefer the scientific image [Ingthorsson] |
| 22606 | Neo-Humeans say there are no substantial connections between anything [Ingthorsson] |
| 22631 | Properties are said to be categorical qualities or non-qualitative dispositions [Ingthorsson] |
| 22632 | Physics understands the charge of an electron as a power, not as a quality [Ingthorsson] |
| 22627 | Compound objects are processes, insofar as change is essential to them [Ingthorsson] |
| 22613 | Most materialist views postulate smallest indivisible components which are permanent [Ingthorsson] |
| 22612 | Endurance and perdurance just show the consequences of A or B series time [Ingthorsson] |
| 22625 | Science suggests causal aspects of the constitution and persistance of objects [Ingthorsson] |
| 22620 | If causation involves production, that needs persisting objects [Ingthorsson] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 22636 | Every philosophical theory must be true in some possible world, so the ontology is hopeless [Ingthorsson] |
| 22638 | Worlds may differ in various respects, but no overall similarity of worlds is implied [Ingthorsson] |
| 22605 | Humeans describe the surface of causation, while powers accounts aim at deeper explanations [Ingthorsson] |
| 22607 | Time and space are not causal, but they determine natural phenomena [Ingthorsson] |
| 22608 | Casuation is the transmission of conserved quantities between causal processes [Ingthorsson] |
| 22621 | Causation as transfer only works for asymmetric interactions [Ingthorsson] |
| 22614 | Interventionist causal theory says it gets a reliable result whenever you manipulate it [Ingthorsson] |
| 22639 | Causal events are always reciprocal, and there is no distinction of action and reaction [Ingthorsson] |
| 22615 | One effect cannot act on a second effect in causation, because the second doesn't yet exist [Ingthorsson] |
| 22616 | Empiricists preferred events to objects as the relata, because they have observable motions [Ingthorsson] |
| 22617 | Science now says all actions are reciprocal, not unidirectional [Ingthorsson] |
| 22619 | Causes are not agents; the whole interaction is the cause, and the changed compound is the effect [Ingthorsson] |
| 22635 | People only accept the counterfactual when they know the underlying cause [Ingthorsson] |
| 22634 | Counterfactuals don't explain causation, but causation can explain counterfactuals [Ingthorsson] |
| 22637 | Counterfactual theories are false in possible worlds where causation is actual [Ingthorsson] |
| 22624 | A cause can fail to produce its normal effect, by prevention, pre-emption, finks or antidotes [Ingthorsson] |
| 22622 | Any process can go backwards or forwards in time without violating the basic laws of physics [Ingthorsson] |
| 22618 | In modern physics the first and second laws of motion (unlike the third) fail at extremes [Ingthorsson] |
| 22630 | If particles have decay rates, they can't really be elementary, in the sense of indivisible [Ingthorsson] |
| 22610 | It is difficult to handle presentism in first-order logic [Ingthorsson] |