7 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. |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 23366 | We see nature's will in the ways all people are the same [Epictetus] |
| Full Idea: The will of nature may be learned from those things in which we do not differ from one another. | |
| From: Epictetus (The Handbook [Encheiridion] [c.58], 26) | |
| A reaction: There you go! This is the rule for anthropologists on field trips. And it guides us towards a core of essential human nature. But it neglects the way that nature is expressed in different cultures, which is also important. |
| 23365 | If someone is weeping, you should sympathise and help, but not share his suffering [Epictetus] |
| Full Idea: When you see someone weeping is sorrow …do not shrink from sympathising with him, and even groaning with him, but be careful not to groan inwardly too. | |
| From: Epictetus (The Handbook [Encheiridion] [c.58], 16) | |
| A reaction: The point is that the person's suffering is an 'indifferent' because nothing can be done about it, and we should only really care about what we are able to choose. He is not opposed to the man's suffering, or his need for support. |
| 4022 | Epictetus says we should console others for misfortune, but not be moved by pity [Epictetus, by Taylor,C] |
| Full Idea: The injunction of Epictetus is well known, that in commiserating with another for his misfortune, we ought to talk consolingly, but not be moved by pity. | |
| From: report of Epictetus (The Handbook [Encheiridion] [c.58], §16) by Charles Taylor - Sources of the Self §15.1 | |
| A reaction: This goes strongly against the grain of the Christian tradition, but strikes me as an appealing attitude (even if I am the sufferer). |
| 23368 | Perhaps we should persuade culprits that their punishment is just? [Epictetus] |
| Full Idea: The governor Agrippinus would try to persuade those whom he sentenced that it was proper for them to be sentenced, …just as the physician persuades a patient to accept their treatment. | |
| From: Epictetus (The Handbook [Encheiridion] [c.58], 22) | |
| A reaction: This resembles the Contractualism of T.H. Scanlon (that actions are good if you can justify them to those involved). It may be possible to persuade people by the use of sophistry and lies. Nevertheless, a fairly civilise proposal. |