10 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. |
| 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. |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| Full Idea: Much theorizing about justification conflates issues of justified belief with issues of justified/blameless believers. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.12) | |
| A reaction: [They cite Kent Bach 1985] Presumably the only thing that really justifies a belief is the truth, or the actual facts. You could then say 'p is a justified belief, though no one actually believes it'. E.g. the number of stars is odd. |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| Full Idea: If knowledge is indeed unanalyzable, that could be seen as a liberation of justification to assume importance in its own right. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.11) | |
| A reaction: [They cite Kvanvig 2003:192 and Greco 2010:9-] See Scruton's Idea 3897. I suspect that we should just give up discussing 'knowledge', which is a woolly and uninformative term, and focus on where the real epistemological action is. |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| Full Idea: Entailment is modelled in formal semantics as set inclusion. 'Cat' entails 'mammal' because the cats are a subset of the mammals. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.10) | |
| A reaction: I would have thought that this was only one type of entailment. 'Travelling to Iceland entails flying'. Travelling includes flying, the reverse of cats/mammals, to a very complex set-theoretic account is needed. Interesting. |
| 6000 | The goal is rationality in the selection of things according to nature [Diogenes of Babylon, by Blank] |
| Full Idea: Diogenes of Babylon defined the goal to be rationality in the selection and rejection of the things according to nature. | |
| From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
| A reaction: This captures the central Stoic idea quite nicely. 'Live according to nature', but this always meant 'live according to reason', because that is (as Aristotle had taught) the essence of our nature. This only makes sense if reason and nature coincide. |
| 5999 | The good is what is perfect by nature [Diogenes of Babylon, by Blank] |
| Full Idea: Diogenes of Babylon defined the good as what is perfect by nature. | |
| From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
| A reaction: This might come close to G.E. Moore's Ideal Utilitarianism, but its dependence on the rather uneasy of concept of 'perfection' makes it questionable. Personally I find it appealing. I wish we had Diogenes' explanation. |
| 6001 | Justice is a disposition to distribute according to desert [Diogenes of Babylon, by Blank] |
| Full Idea: Diogenes of Babylon defined justice as the disposition which distributes to everyone what he deserves. | |
| From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
| A reaction: The questions that arise would be 'what does a new-born baby deserve?', and 'what do animals deserve?', and 'does the lowest and worst of criminals deserve anything at all?' |