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 |
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| Full Idea: Normal propositional modal logics derive from the minimal system K: wffs of PC are axioms; □(p⊃q)⊃(□p⊃□q); uniform substitution; modus ponens; necessitation (α→□α). | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1) |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| Full Idea: If a frame contains any dead end or blind world, then D is not valid on that frame, ...but D is valid on every serial frame. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.1) |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| Full Idea: In S4 there are exactly 14 distinct modalities, and any modality may be reduced to one containing no more than three modal operators in sequence. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: The significance of this may be unclear, but it illustrates one of the rewards of using formal systems to think about modal problems. There is at least an appearance of precision, even if it is only conditional precision. |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| Full Idea: S5 contains the four main reduction laws, so the first of any pair of operators may be deleted. Hence all but the last modal operator may be deleted. This leaves six modalities: p, ◊p, □p, and their negations. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |
| Full Idea: If one wants the quantifiers in each world to range only over the things that exist in that world, and one doesn't believe that the same things exist in every world, one would probably not want the Barcan formula. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.2) | |
| A reaction: I haven't quite got this, but it sounds to me like I should reject the Barcan formula (but Idea 9449!). I like a metaphysics to rest on the actual world (with modal properties). I assume different things could have existed, but don't. |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| Full Idea: A relation is 'Euclidean' if aRb and aRc imply bRc. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: If a thing has a relation to two separate things, then those two things will also have that relation between them. If I am in the same family as Jim and as Jill, then Jim and Jill are in the same family. |
| 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. |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| Full Idea: A de dicto necessary truth says that something is φ, that this proposition is a necessary truth, i.e. that in every accessible world something (but not necessarily the same thing in each world) is φ. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.1) | |
| A reaction: At last, a really clear and illuminating account of this term! The question is then invited of what is the truthmaker for a de dicto truth, assuming that the objects themselves are truthmakers for de re truths. |
| 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. |
| 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. |
| 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 |
| 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- |
| 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. |