21 ideas
13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
8751 | Only applicability raises arithmetic from a game to a science [Frege] |
472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
9891 | The first demand of logic is of a sharp boundary [Frege] |
9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
541 | Virtue comes more from habit than character [Critias] |
473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus] |
476 | Self-created numbers make the universe stable [Philolaus] |
1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |
542 | Fear of the gods was invented to discourage secret sin [Critias] |