19 ideas
| 1542 | Diogenes of Apollonia was the last natural scientist [Diogenes of Apollonia, by Simplicius] |
| Full Idea: Diogenes of Apollonia was more or less the last of those who made a study of natural science. | |
| From: report of Diogenes (Apoll) (fragments/reports [c.440 BCE], A05) by Simplicius - On Aristotle's 'Physics' 9.25.1 | |
| A reaction: He quotes Theophrastus |
| 21695 | The set scheme discredited by paradoxes is actually the most natural one [Quine] |
| Full Idea: Each proposed revision of set theory is unnatural, because the natural scheme is the unrestricted one that the antinomies discredit. | |
| From: Willard Quine (The Ways of Paradox [1961], p.16) | |
| A reaction: You can either takes this free-far-all version of set theory, and gradually restrain it for each specific problem, or start from scratch and build up in safe steps. The latter is (I think) the 'iterated' approach. |
| 21693 | Russell's antinomy challenged the idea that any condition can produce a set [Quine] |
| Full Idea: In the case of Russell's antinomy, the tacit and trusted pattern of reasoning that is found wanting is this: for any condition you can formulate, there is a class whose members are the things meeting the condition. | |
| From: Willard Quine (The Ways of Paradox [1961], p.11) | |
| A reaction: This is why Russell's Paradox is so important for set theory, which in turn makes it important for the foundations of mathematics. |
| 21691 | Antinomies contradict accepted ways of reasoning, and demand revisions [Quine] |
| Full Idea: An 'antinomy' produces a self-contradiction by accepted ways of reasoning. It establishes that some tacit and trusted pattern of reasoning must be made explicit and henceforward be avoided or revised. | |
| From: Willard Quine (The Ways of Paradox [1961], p.05) | |
| A reaction: Quine treats antinomies as of much greater importance than mere paradoxes. It is often possible to give simple explanations of paradoxes, but antinomies go to the root of our belief system. This was presumably Kant's intended meaning. |
| 21690 | Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine] |
| Full Idea: The Achilles argument is that (if the front runner keeps running) each time the pursuer reaches a spot where the pursuer has been, the pursued has moved a bit beyond. | |
| From: Willard Quine (The Ways of Paradox [1961], p.03) | |
| A reaction: Quine is always wonderfully lucid, and this is the clearest simple statement of the paradox. |
| 21689 | A barber shaves only those who do not shave themselves. So does he shave himself? [Quine] |
| Full Idea: In a certain village there is a barber, who shaves all and only those men in the village who do not shave themselves. So does the barber shave himself? The barber shaves himself if and only if he does not shave himself. | |
| From: Willard Quine (The Ways of Paradox [1961], p.02) | |
| A reaction: [Russell himself quoted this version of his paradox, from an unnamed source] Quine treats his as trivial because it only concerns barbers, but the full Russell paradox is a major 'antinomy', because it concerns sets. |
| 21694 | Membership conditions which involve membership and non-membership are paradoxical [Quine] |
| Full Idea: With Russell's antinomy, ...each tie the trouble comes of taking a membership condition that itself talks in turn of membership and non-membership. | |
| From: Willard Quine (The Ways of Paradox [1961], p.13) | |
| A reaction: Hence various stipulations to rule out vicious circles or referring to sets of the 'wrong type' are invoked to cure the problem. The big question is how strong to make the restrictions. |
| 21692 | If we write it as '"this sentence is false" is false', there is no paradox [Quine] |
| Full Idea: If we supplant the sentence 'this sentence is false' with one saying what it refers to, we get '"this sentence is false" is false'. But then the whole outside sentence attributes falsity no longer to itself but to something else, so there is no paradox. | |
| From: Willard Quine (The Ways of Paradox [1961], p.07) | |
| A reaction: Quine is pointing us towards type theory and meta-languages to solve the problem. We now have the Revenge Liar, and the problem has not been fully settled. |
| 489 | Each thing must be in some way unique [Diogenes of Apollonia] |
| Full Idea: No one thing among things subject to change can possibly be exactly like any other thing, without becoming the same thing. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B05), quoted by Simplicius - On Aristotle's 'Physics' 153.8 | |
| A reaction: This is said to be the first ever formulation of the principle of identity of indiscernible. |
| 483 | Start a thesis with something undisputable [Diogenes of Apollonia] |
| Full Idea: In starting any thesis, it seems to me, one should put forward as one's point of departure something incontrovertible. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B01), quoted by Diogenes Laertius - Lives of Eminent Philosophers 09.57 |
| 1544 | Perception must be an internal matter, because we can fail to perceive when we are preoccupied [Diogenes of Apollonia, by Theophrastus] |
| Full Idea: That it is the inner air that perceives, as being a fragment of the god, is shown by the fact that often when our minds are preoccupied with other matters we fail to see or hear. | |
| From: report of Diogenes (Apoll) (fragments/reports [c.440 BCE], A19) by Theophrastus - On the Senses 42 |
| 24042 | The older Diogenes said the soul is air, made of the smallest particles [Diogenes of Apollonia] |
| Full Idea: Diogenes [of Apollonia] took the soul to be air, thnking that of all things air is composed of the smallest particles and is a starting point. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], DK 64), quoted by Aristotle - De Anima 405a21 | |
| A reaction: This suggests that Diogenes of Apollonia was an atomist, if the soul is made of particles. See also Met 984a5, which says Anaxagoras had the same view. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 5995 | Diogenes of Apollonia offered the first teleological account of cosmology [Diogenes of Apollonia, by Robinson,TM] |
| Full Idea: Credit for the first clear assertion of teleological explanation in cosmology goes to Diogenes of Apollonia, for whom air is the divine and intelligent ground of the real and disposes things in the best possible way. | |
| From: report of Diogenes (Apoll) (fragments/reports [c.440 BCE]) by T.M. Robinson - Classical Cosmology (frags) | |
| A reaction: The first teleological explanation seems to be based on a conscious mind. There also emerges the possibility of some sort of non-conscious teleology, closer to the laws of physics than to God. |
| 488 | Air is divine, because it is in and around everything, and arranges everything [Diogenes of Apollonia] |
| Full Idea: Air in itself seems to me to be God and to reach everywhere and to arrange everything and to be in everything. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B05), quoted by Simplicius - On Aristotle's 'Physics' 152.22- | |
| A reaction: So water and fire and air have been offered as the ultimate explanans, though no one seems to offer earth, which is too grubby and miserable (and was denied a Form by Plato). 'Air is God' could ground a nice modern religious sect. |
| 484 | Everything is ultimately a variation of one underlying thing [Diogenes of Apollonia] |
| Full Idea: It seems to me that all existing things are created by the alteration of the same thing, and are the same thing. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 151.31- |
| 486 | Plants and animals can only come into existence if something fixes their species [Diogenes of Apollonia] |
| Full Idea: No plant could grow out of the earth, and no animal or any other thing could come into being, unless it were so compounded as to be the same. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 151.31- |
| 485 | Things must retain their essential nature during change, or mixing would be impossible [Diogenes of Apollonia] |
| Full Idea: If any existing thing were different in its own essential nature, and were not the same thing which was transformed in many ways and changed, in no way could things mix with one another. | |
| From: Diogenes (Apoll) (fragments/reports [c.440 BCE], B02), quoted by Simplicius - On Aristotle's 'Physics' 151.31- |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |