11 ideas
| 3338 | Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn] |
| Full Idea: Dedekind and Peano define the number series as the series of successors to the number zero, according to five postulates. | |
| From: report of Giuseppe Peano (works [1890]) by Simon Blackburn - Oxford Dictionary of Philosophy p.279 |
| 5897 | 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew] |
| Full Idea: 1) 0 is a number; 2) The successor of any number is a number; 3) No two numbers have the same successor; 4) 0 is not the successor of any number; 5) If P is true of 0, and if P is true of any number n and of its successor, P is true of every number. | |
| From: report of Giuseppe Peano (works [1890]) by Antony Flew - Pan Dictionary of Philosophy 'Peano' | |
| A reaction: Devised by Dedekind and proposed by Peano, these postulates were intended to avoid references to intuition in specifying the natural numbers. I wonder if they could define 'successor' without reference to 'number'. |
| 7127 | If men are good you should keep promises, but they aren't, so you needn't [Machiavelli] |
| Full Idea: If all men were good, promising-breaking would not be good, but because they are bad and do not keep their promises to you, you likewise do not have to keep yours to them. | |
| From: Niccolo Machiavelli (The Prince [1513], Ch.18) | |
| A reaction: A rather depressing proposal to get your promise-breaking in first, based on the pessimistic view that people cannot be improved. The subsequent history of ethics in Europe showed Machiavelli to be wrong. Gentlemen began to keep their word. |
| 6309 | The principle foundations of all states are good laws and good armies [Machiavelli] |
| Full Idea: The principle foundations of all states are good laws and good armies. | |
| From: Niccolo Machiavelli (The Prince [1513], Ch.11) | |
| A reaction: We may be wondering, since 1945, whether a good army is any longer essential, but it would be a foolish modern state which didn't at least form a strong alliance with a state which had a strong army. Fertile land is a huge benefit to a state. |
| 6305 | To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli] |
| Full Idea: If a ruler acquires a state and is determined to keep it, he observes two cautions: he wipes out the family of their long-established princes; and he does not change either their laws or their taxes; in a short time they will unite with his old princedom. | |
| From: Niccolo Machiavelli (The Prince [1513], Ch.3) | |
| A reaction: This nicely illustrates the firmness of purpose for which Machiavelli has become a byword. The question is whether Machiavelli had enough empirical evidence to support this induction. The British in India seem to have been successful without it. |
| 6306 | People are vengeful, so be generous to them, or destroy them [Machiavelli] |
| Full Idea: Men should be either treated generously or destroyed, because they take revenge for slight injuries. | |
| From: Niccolo Machiavelli (The Prince [1513], Ch.3) | |
| A reaction: This sounds like good advice, and works quite well in school teaching too. It seems like advice drawn from the growth of the Roman Empire, rather than from dealing with sophisticated and educated people. |
| 6308 | A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli] |
| Full Idea: A prudent conqueror makes a list of all the harmful deeds he must do, and does them all at once, so that he need not repeat them every day, which then makes men feel secure, and gains their support by treating them well. | |
| From: Niccolo Machiavelli (The Prince [1513], Ch.8) | |
| A reaction: This might work for a new government in a democracy, or a new boss in a business. It sounds horribly true; dreadful deeds done a long time ago can be completely forgotten, as when reformed criminals become celebrities. |
| 6307 | A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli] |
| Full Idea: It is very natural and normal to wish to conquer, and when men do it who can, they always will be praised, or not blamed. | |
| From: Niccolo Machiavelli (The Prince [1513], Ch.3) | |
| A reaction: This view seems shocking to us, but it seems to me that this was a widely held view up until the time of Nietzsche, but came to a swift end with the invention of the machine gun in about 1885, followed by the heavy bomber and atomic bomb. |
| 7486 | Machiavelli emancipated politics from religion [Machiavelli, by Watson] |
| Full Idea: Machiavelli emancipated politics from religion. | |
| From: report of Niccolo Machiavelli (The Prince [1513]) by Peter Watson - Ideas Ch.24 | |
| A reaction: Interestingly, he seems to have done it by saying that ideals are irrelevant to politics, but gradually secular ideals crept back in (sometimes disastrously). A balance needs to be struck on idealism. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |