6 ideas
| 18256 | Quantity is inconceivable without the idea of addition [Frege] |
| Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
| A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
| 9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
| Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |
| 541 | Virtue comes more from habit than character [Critias] |
| Full Idea: More men are good through habit than through character. | |
| From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41 |
| 22439 | There are only duties if there are rights, so truth is only for those with a right to it [Constant] |
| Full Idea: A duty is that on the part of one being which corresponds to the rights of another. Where there are no rights there are no duties. To tell the truth is therefore a duty, but only to the one who has the right to the truth. | |
| From: Benjamin Constant (On Political Reactions [1797], p.123), quoted by Immanuel Kant - On a supposed right to lie p.28 | |
| A reaction: We can't claim a right to have all questions answered truthfully (because there is a right to privacy), but we might claim a right not to be lied to (as long as we accept a refusal to answer). Kant rejected this idea. |
| 22440 | Unconditional truth-telling makes a society impossible [Constant] |
| Full Idea: The moral principle 'it is a duty to tell the truth' would, if taken unconditionally and singly, make any society impossible. | |
| From: Benjamin Constant (On Political Reactions [1797], p.124), quoted by Immanuel Kant - On a supposed right to lie p.28 | |
| A reaction: He gives the well known example of the murderer at the door asking if your friend is inside. Compare everyone becoming perfectly telepathic. Our society would collapse, but a new society would learn to live with it. |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |
| Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret. | |
| From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54 |