Combining Philosophers

All the ideas for Archimedes, Diogenes (Apoll) and Mnesarchus

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12 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
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
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
     Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
     From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
     A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.
9. Objects / C. Structure of Objects / 6. Constitution of an Object
If someone squashed a horse to make a dog, something new would now exist [Mnesarchus]
     Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist.
     From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11
     A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance?
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
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.
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
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
12. Knowledge Sources / B. Perception / 6. Inference in Perception
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
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
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.
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
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.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
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.
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-
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
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-
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-