21 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 |
| 10842 | The fact which is stated by a true sentence is not something in the world [Strawson,P] |
| Full Idea: The fact which is stated by a true sentence is not something in the world. | |
| From: Peter F. Strawson (Truth [1950], §2) | |
| A reaction: Everything is in the world. This may just be a quibble over how we should use the word 'fact'. At some point the substance of what is stated in a sentence must eventually be out there, or we would never act on what we say. |
| 10843 | Facts aren't exactly true statements, but they are what those statements say [Strawson,P] |
| Full Idea: Facts are what statements (when true) state; they are not what statements are about. ..But it would be wrong to identify 'fact' and 'true statement' for these expressions have different roles in our language. | |
| From: Peter F. Strawson (Truth [1950], §2) | |
| A reaction: Personally I like to reserve the word 'facts' for what is out there, independent of any human thought or speech. As a realist, I believe that the facts are quite independent of our attempts to understand the facts. True statements attempt to state facts. |
| 10844 | The statement that it is raining perfectly fits the fact that it is raining [Strawson,P] |
| Full Idea: What could fit more perfectly the fact that it is raining than the statement that it is raining? | |
| From: Peter F. Strawson (Truth [1950], §2) |
| 10841 | The word 'true' always refers to a possible statement [Strawson,P] |
| Full Idea: It is of prime importance to distinguish the fact that the use of 'true' always glances backwards or forwards to the actual or envisaged making of a statement by someone. | |
| From: Peter F. Strawson (Truth [1950], §1) | |
| A reaction: 'The truth of this matter will never be known'. Strawson is largely right, but it is crazy for any philosopher to use the word 'always' if they can possibly avoid it. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 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. |
| 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- |