42 ideas
| 14767 | The demonstrations of the metaphysicians are all moonshine [Peirce] |
| 14764 | I am saturated with the spirit of physical science [Peirce] |
| 19342 | Reason avoids multiplying hypotheses or principles [Leibniz] |
| 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] |
| 12711 | The immediate cause of movements is more real [than geometry] [Leibniz] |
| 19349 | The complete notion of a substance implies all of its predicates or attributes [Leibniz] |
| 7558 | Substances mirror God or the universe, each from its own viewpoint [Leibniz] |
| 16761 | Forms are of no value in physics, but are indispensable in metaphysics [Leibniz] |
| 13088 | Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz] |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| 13085 | Leibniz is some form of haecceitist [Leibniz, by Cover/O'Leary-Hawthorne] |
| 14768 | Infallibility in science is just a joke [Peirce] |
| 14765 | Association of ideas is the best philosophical idea of the prescientific age [Peirce] |
| 5024 | Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz] |
| 14766 | Duns Scotus offers perhaps the best logic and metaphysics for modern physical science [Peirce] |
| 5027 | If a person's memories became totally those of the King of China, he would be the King of China [Leibniz] |
| 5023 | Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz] |
| 2119 | People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason [Leibniz] |
| 5025 | Mind and body can't influence one another, but God wouldn't intervene in the daily routine [Leibniz] |
| 5026 | Animals lack morality because they lack self-reflection [Leibniz] |