13 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. |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 6012 | We must choose in which of the virtues we wish to excel [Panaetius] |
| Full Idea: Humans have four roles in life, of which the fourth involves choices, of career, and of the virtue in which one wishes to excel. | |
| From: Panaetius (fragments/reports [c.145 BCE]), quoted by Elizabeth Asmis - Panaetius | |
| A reaction: Panaetius strikes me as exceptionally wise. A big gap in Aristotle is the fact that we cannot excel in all virtues, and that therefore some choice is required. By what criteria? We have the Gauguin problem (excel in one, disgraceful in the others). |
| 6013 | Panaetius said we should live according to our natural starting-points [Panaetius, by Asmis] |
| Full Idea: Panaetius reformulated the Stoic goal as living in accordance with the starting-points given to us by nature. | |
| From: report of Panaetius (fragments/reports [c.145 BCE]) by Elizabeth Asmis - Panaetius | |
| A reaction: This sounds remarkably like the substitution of meritocratic equality of opportunity for communistic actual equality. In other words, it doesn't sound very Stoic. 'Live according to nature' implies more restraint than this ambitious version. |
| 6014 | Panaetius identified courage with great-mindedness, preferring civic courage to military [Panaetius, by Asmis] |
| Full Idea: Panaetius recast the virtue of courage as 'greatmindedness' (Aristotle's paramount virtue), he demoted military valour and gave priority to courage displayed in civic life. | |
| From: report of Panaetius (fragments/reports [c.145 BCE]) by Elizabeth Asmis - Panaetius | |
| A reaction: I find this very appealing, as I am increasingly horrified by our denigration of the people who implement our democracy for us. We urgently need to get back to the Greek idea of civic virtue, and this idea of Panaetius should be widely promulgated. |
| 5888 | Souls are born, since they are sensitive and inherited, so they must perish [Panaetius, by Cicero] |
| Full Idea: Panaetius says that whatever is born must perish, and souls are clearly born, as shown by the resemblance of children to their parents in disposition as well as body; also, anything sensible of pain is susceptible to sickness, and hence perishes. | |
| From: report of Panaetius (fragments/reports [c.145 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xxxii | |
| A reaction: These seem to be rather good arguments. If we actually observe what someone's soul is like (through character) it seems rooted in a family and culture, and it certainly seems susceptible to disease. An empirical approach. |