11 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. |
| 9312 | Consciousness is reductively explained either by how it represents, or how it is represented [Kriegel/Williford] |
| Full Idea: The two main competitors for reductive theories of consciousness are the representational theory (conscious if it represents in the right way), and higher-order monitoring (conscious if it is represented in the right way). | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], Intro) | |
| A reaction: Presumably there are also neuroscientists hunting for physical functions which might generate consciousness. The two mentioned here are rivals at one level of discourse. Both views may be simplistic, if complex teams of activities are involved. |
| 9313 | Experiences can be represented consciously or unconsciously, so representation won't explain consciousness [Kriegel/Williford] |
| Full Idea: On the assumption that any environmental feature can be represented either consciously or unconsciously, it is unclear how the mere representation of such a feature can render the representing state conscious. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §1) | |
| A reaction: The authors are rejecting simple representation as the key, in favour of a distinctive sort of self-representation. I'm inclined to think that consciousness results from multiple co-ordinated layers of representation etc., which has no simple account. |
| 9315 | Red tomato experiences are conscious if the state represents the tomato and itself [Kriegel/Williford] |
| Full Idea: The self-representational theory of consciousness says that when one has a conscious experience as of a red tomato, one is in an internal state that represents both a red tomato and itself. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §1) | |
| A reaction: This seems to be avoiding the concept of 'higher-order', and yet that seems the only way to describe it - thought steps outside of itself, generating a level of meta-thought. I think that's the way to go. Philosophy is about-fifth level. |
| 9316 | How is self-representation possible, does it produce a regress, and is experience like that? [Kriegel/Williford] |
| Full Idea: The difficulties with a self-representational view of consciousness are how self-representation of mental states could be possible, whether it leads to an infinite regress, and whether it can capture the actual phenomenology of experience. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §3) | |
| A reaction: [compressed] All of these objections strike me as persuasive, especially the first one. I'm not sure I know what self-representation is. Mirrors externally represent, and they can't represent themselves. Two mirrors together achieve something.. |
| 9314 | Unfortunately, higher-order representations could involve error [Kriegel/Williford] |
| Full Idea: A problem for explaining consciousness by higher-order representations is that, like their first-order counterparts, they can misrepresent; there could be a subjective impression of being in a conscious state without actually being in any conscious state. | |
| From: U Kriegel / K Williford (Intro to 'Self-Representational Consciousness' [2006], §1) | |
| A reaction: It sounds plausible that this is a logical possibility, but how do you assess whether it is an actual or natural possibility? Are we saying that higher-order representations are judgments, which could be true or false? Hm. |
| 541 | Virtue comes more from habit than character [Critias] |
| Full Idea: More men are good through habit than through character. | |
| From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41 |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |
| Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret. | |
| From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54 |