11 ideas
| 3067 | A philosopher should have principles ready for understanding, like a surgeon with instruments [Aurelius] |
| Full Idea: As physicians have always their instruments and knives ready for cases which suddenly require their skill, so should you have principles ready for the understanding of things divine and human. | |
| From: Marcus Aurelius (The Meditations (To Himself) [c.170], 3.13) | |
| A reaction: Nice. Philosophy is the training ground where wisdom and good living are made possible, but it cannot be a substitute for living. |
| 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. |
| 3072 | Everything is changing, including yourself and the whole universe [Aurelius] |
| Full Idea: All things are changing; and you yourself are in continuous mutation and in a manner in continuous destruction, and the whole universe too. | |
| From: Marcus Aurelius (The Meditations (To Himself) [c.170], 9.19) |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist. | |
| From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11 | |
| A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance? |
| 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. |
| 3066 | Nothing is evil which is according to nature [Aurelius] |
| Full Idea: Nothing is evil which is according to nature. | |
| From: Marcus Aurelius (The Meditations (To Himself) [c.170], 2.17) | |
| A reaction: A bit hopeful. Sounds tautological. I.e. anything which is agreed to be evil is probably immediately labelled as 'unnatural'. What would he agree was evil? |
| 3071 | Justice has no virtue opposed to it, but pleasure has temperance opposed to it [Aurelius] |
| Full Idea: In the constitution of the rational animal I see no virtue which is opposed to justice; but I see a virtue which is opposed to pleasure, and that is temperance. | |
| From: Marcus Aurelius (The Meditations (To Himself) [c.170], 8.39) | |
| A reaction: There are plenty of hideous things opposed to justice, but presumably that immediately disqualifies them from being virtues. |
| 3069 | The art of life is more like the wrestler's than the dancer's [Aurelius] |
| Full Idea: The art of life is more like the wrestler's than the dancer's. | |
| From: Marcus Aurelius (The Meditations (To Himself) [c.170], 7.61) |
| 3065 | Humans are naturally made for co-operation [Aurelius] |
| Full Idea: We are made for cooperation, like feet, like hands, like eyelids, like the rows of upper and lower teeth. To act against one another, then, is contrary to nature. | |
| From: Marcus Aurelius (The Meditations (To Himself) [c.170], 2.1) |