18 ideas
| 1765 | Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: When a man said that he was not suited to philosophy, Diogenes said to him, 'Why then do you live, if you have no desire to live properly.' | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: Meaning philosophy is already more practice than theory. |
| 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. |
| 2614 | Modern phenomenalism holds that objects are logical constructions out of sense-data [Ayer] |
| Full Idea: Nowadays phenomenalism is held to be a theory of perception which says that physical objects are logical constructions out of sense-data. | |
| From: A.J. Ayer (Phenomenalism [1947], §1) |
| 2615 | The concept of sense-data allows us to discuss appearances without worrying about reality [Ayer] |
| Full Idea: The introduction of the term 'sense-datum' is a means of referring to appearances without prejudging the question of what it is, if anything, that they are appearances of. | |
| From: A.J. Ayer (Phenomenalism [1947], §1) |
| 1762 | When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes replied to one who asserted that there was no such thing as motion by getting up and walking away. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 7813 | Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling] |
| Full Idea: An advantage of Cynicism was that it was open to anyone who could grasp its simple teachings. Understanding it required neither education nor sophistication. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: This was the source of the well-known opposition of Diogenes to Plato's Academy, and it makes him a key predecessor of the teachings of Jesus. Personally I think the really good life is difficult, and it needs education and careful rational thought. |
| 1763 | Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Plato defined man as a two-footed featherless animal, so Diogenes plucked a cock and brought it into the school, and said, 'This is Plato's man'. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 | |
| A reaction: You have to be very serious about your philosophy to enact your counterexamples, rather than just suggest them. Which university will actually reconstruct the Trolley Problem? |
| 5071 | The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.] |
| Full Idea: The Cynics were convinced of the purely conventional foundation of Athenian values, which meant they had no rational foundation at all. They therefore rejected them in favour of what is correct and worthwhile by nature. | |
| From: comment on Diogenes (Sin) (reports [c.360 BCE]) by Richard Taylor - Virtue Ethics: an Introduction Ch.8 | |
| A reaction: This shows how the Cynics are key players in the progress of the nomos-physis debate, which keeps resurfacing as relativism vs absolutism, cognitivism vs non-cognitivism, and even romanticism vs classicism. The trouble is, convention is natural! |
| 7812 | For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.] |
| Full Idea: There are three essential conditions for peace of mind: autarchy, apathy and freedom. Autarchy is self-government and self-sufficiency; apathy is indifference to what the world can do to you; the freedom is from dependence and possessions. | |
| From: Diogenes (Sin) (reports [c.360 BCE]), quoted by A.C. Grayling - What is Good? Ch.3 | |
| A reaction: Quite good advice, but I don't see 'peace of mind' as the highest human ideal. The basic suggestion here is live alone and do nothing. Certainly don't get married, or have children, or try to achieve anything. |
| 1764 | Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said he was a citizen of no country, but of the world. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |
| 5968 | Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch] |
| Full Idea: Chrysippus praises Diogenes for saying to bystanders as he masturbated in public, "Would that I could thus rub the hunger too out of my belly". | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Plutarch - 70: Stoic Self-contradictions 1044b | |
| A reaction: So it is not quite true that people only need corn and water. Diogenes' remark doesn't explain why he did it in public. Was it to defy local convention (as befits a citizen of the world), or was it to teach? |
| 1766 | Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius] |
| Full Idea: Diogenes said that the most excellent thing among men was freedom of speech. | |
| From: report of Diogenes (Sin) (reports [c.360 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.Di.6 |