15 ideas
| 7557 | To solve Zeno's paradox, reject the axiom that the whole has more terms than the parts [Russell] |
| Full Idea: Presumably Zeno appealed to the axiom that the whole has more terms than the parts; so if Achilles were to overtake the tortoise, he would have been in more places than the tortoise, which he can't be; but the conclusion is absurd, so reject the axiom. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.89) | |
| A reaction: The point is that the axiom is normally acceptable (a statue contains more particles than the arm of the statue), but it breaks down when discussing infinity (Idea 7556). Modern theories of infinity are needed to solve Zeno's Paradoxes. |
| 10059 | In mathematic we are ignorant of both subject-matter and truth [Russell] |
| Full Idea: Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.76) | |
| A reaction: A famous remark, though Musgrave is rather disparaging about Russell's underlying reasoning here. |
| 7556 | A collection is infinite if you can remove some terms without diminishing its number [Russell] |
| Full Idea: A collection of terms is infinite if it contains as parts other collections which have as many terms as it has; that is, you can take away some terms of the collection without diminishing its number; there are as many even numbers as numbers all together. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.86) | |
| A reaction: He cites Dedekind and Cantor as source for these ideas. If it won't obey the rule that subtraction makes it smaller, then it clearly isn't a number, and really it should be banned from all mathematics. |
| 5953 | For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch] |
| Full Idea: The Cyrenaics, placing all experience within themselves, thought such evidence was insufficient warrant for certainty about reality, and withdrew as in a siege from the world, admitting that objects 'appear', but refusing to pronounce the word 'are'. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Plutarch - 74: Reply to Colotes §1120 | |
| A reaction: This seems to be the most extreme position found in ancient thought. It accompanies their extreme hedonism, based on the reality of experience and lack of interest in anything external. A bit daft, really. |
| 7554 | Self-evidence is often a mere will-o'-the-wisp [Russell] |
| Full Idea: Self-evidence is often a mere will-o'-the-wisp, which is sure to lead us astray if we take it as our guide. | |
| From: Bertrand Russell (Mathematics and the Metaphysicians [1901], p.78) | |
| A reaction: The sort of nice crisp remark you would expect from a good empiricist philosopher. Compare Idea 4948. However Russell qualifies it with the word 'often', and all philosophers eventually realise that you have to start somewhere. |
| 3023 | Even the foolish may have some virtues [Aristippus young, by Diog. Laertius] |
| Full Idea: The Cyrenaics say that some of the virtues may exist even in the foolish. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 |
| 3026 | Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius] |
| Full Idea: Cyrenaics say errors should be pardoned, because men do not err intentionally but are influenced by circumstances; one should not hate a person, but only teach him better. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.9 | |
| A reaction: A very appealing suggestion, and rather wonderful for its time. There is still implied agreement about what is 'error', and what counts as 'better'. |
| 3024 | Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius] |
| Full Idea: The Cyrenaics taught that there was nothing naturally and intrinsically just, or honourable, or disgraceful; but that things were considered so because of law and fashion. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 | |
| A reaction: As we would say now, values and virtues are 'cultural constructs'. This obviously contains a lot of truth, but I don't think our opposition of genocide is just 'fashion'. |
| 3025 | For a Cyrenaic no one is of equal importance to himself [Aristippus young, by Diog. Laertius] |
| Full Idea: A Cyrenaic will not consider anyone else of equal importance with himself. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.9 |
| 3019 | No one pleasure is different from or more pleasant than another [Aristippus young, by Diog. Laertius] |
| Full Idea: No one pleasure is different from or more pleasant than another. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 |
| 3021 | The Cyrenaics asserted that corporeal pleasures were superior to mental ones [Aristippus young, by Diog. Laertius] |
| Full Idea: The Cyrenaics asserted that corporeal pleasures were superior to mental ones. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 |
| 3027 | Cyrenaics say wise men are self-sufficient, needing no friends [Aristippus young, by Diog. Laertius] |
| Full Idea: Cyrenaics say wise men are sufficient to themselves, and so have no need of friends. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.13 |
| 23104 | Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes] |
| Full Idea: Egalitarians believe that most often it is by promoting equality that autonomy is increased; this is the egalitarianism of such liberals as Ronald Dworkin. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by John Kekes - Against Liberalism 05.1 | |
| A reaction: Not my idea of equality. The whole point is to ascribe reasonable equality to everyone, including those with a limited capacity for autonomy. Equality is a consequence of universal respect. |
| 23257 | We can treat people as equals, or actually treat them equally [Dworkin, by Grayling] |
| Full Idea: Dworkin distinguishes between treating people as equals, that is, 'with equal concern and respect', and treating them equally. This latter can be unjust. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by A.C. Grayling - The Good State 2 | |
| A reaction: The big difference I see between them is that the first is mere words, and the second is actions. Cf. 'thoughts and prayers' after US school shootings. How about equal entitlements, all things being equal? |
| 18621 | Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka] |
| Full Idea: Dworkin suggests that every plausible political theory has the same ultimate value, which is equality - in the more abstract and fundamental sense of treating people 'as equals'. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977], 179-83) by Will Kymlicka - Contemporary Political Philosophy (1st edn) | |
| A reaction: I associate this idea with Kant (who says they are equal by virtue of their rationality), so that's a pretty influential idea. I would associate the main challenge to this with Nietzsche. |