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. |
| 12580 | Experiences have no conceptual content [Evans, by Greco] |
| Full Idea: In Evans's work experiences are conceived of as not having a conceptual content at all. | |
| From: report of Gareth Evans (The Varieties of Reference [1980]) by John Greco - Justification is not Internal | |
| A reaction: I presume it is this view which provoked McDowell's contrary view in 'Mind and World'. I say this is a job for neuroscience, and I struggle to see what philosophical questions hang on the outcome. I think I side with Evans. |
| 7643 | We have far fewer colour concepts than we have discriminations of colour [Evans] |
| Full Idea: Do we really understand the proposal that we have as many colour concepts as there are shades colour that we can sensibly discriminate? | |
| From: Gareth Evans (The Varieties of Reference [1980], 7.5) | |
| A reaction: This is the argument (rejected by McDowell) that experience cannot be conceptual because experience is too rich. We should not confuse lack of concepts with lack of words. I may have a concept of a colour between two shades, but no word for it. |
| 23794 | Some representational states, like perception, may be nonconceptual [Evans, by Schulte] |
| Full Idea: Evans introduced the idea that there are some representational states, for example perceptual experiences, which have content that is nonconceptual. | |
| From: report of Gareth Evans (The Varieties of Reference [1980]) by Peter Schulte - Mental Content 3.4 | |
| A reaction: McDowell famously disagree, and whether all experience is inherently conceptualised is a main debate from that period. Hard to see how it could be settled, but I incline to McDowell, because minimal perception hardly counts as 'experience'. |
| 16366 | The Generality Constraint says if you can think a predicate you can apply it to anything [Evans] |
| Full Idea: If a subject can be credited with the thought that a is F, then he must have the conceptual resources for entertaining the thought that a is G, for every property of being G of which he has conception. This condition I call the 'Generality Constraint'. | |
| From: Gareth Evans (The Varieties of Reference [1980], p.104), quoted by François Recanati - Mental Files 5.3 | |
| A reaction: Recanati endorses the Constraint in his account of mental files. Apparently if I can entertain the thought of a circle being round, I can also entertain the thought of it being square, so I am not too sure about this one. |
| 12575 | Concepts have a 'Generality Constraint', that we must know how predicates apply to them [Evans, by Peacocke] |
| Full Idea: Evans's 'Generality Constraint' says that if a thinker is capable of attitudes to the content Fa and possesses the singular concept b, then he is capable of having attitudes to the content Fb. | |
| From: report of Gareth Evans (The Varieties of Reference [1980], 4.3) by Christopher Peacocke - A Study of Concepts 1.1 | |
| A reaction: So having an attitude becomes the test of whether one possesses a concept. I suppose if one says 'You know you've got a concept when you are capable of thinking about it', that is much the same thing. Sounds fine. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |