17 ideas
| 7893 | Our life is the creation of our mind [Anon (Dham)] |
| Full Idea: What we are today comes from our thoughts of yesterday, and our present thoughts build our life of tomorrow: our life is the creation of our mind. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.1) | |
| A reaction: I may adopt this as a second epigraph for the database. This idea records the subjective view, which now comes up against evolutionary psychology. Maybe philosophy is opposed to science, because it is committed to exploring the subjective view? |
| 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. |
| 7898 | The world is just the illusion of an appearance [Anon (Dham)] |
| Full Idea: When a man considers this world as a bubble of froth, and as the illusion of an appearance, then the king of death has no power over him. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §13.170) | |
| A reaction: Strictly, of course, this says you can 'consider' things this way. Perhaps we could substitute 'pretends', but the world's great religions don't go in for that sort of thing. Berkeley would be shocked to learn he was approaching Buddhism. |
| 7894 | Hate is conquered by love [Anon (Dham)] |
| Full Idea: Hate is not conquered by hate: hate is conquered by love. This is the law eternal. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §1.5) | |
| A reaction: [N.B. This thought was not invented by Jesus] The challenge to this view might be the tit-for-tat strategy of game theory, which says that hate is actually conquered by a combination of hate and love, judiciously applied. |
| 7899 | Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)] |
| Full Idea: Since a shower of gold coins could not satisfy craving desires and the end of all pleasure is pain, how could a wise man find satisfaction even in the pleasures of the gods? | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §14.186) | |
| A reaction: I'm never sure how so many ancient thinkers arrived at this implausible view. They seem to think that no one knows when to stop, and that every drink leads to hangover. What is actually wrong with moderate sensible pleasure? |
| 7896 | The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)] |
| Full Idea: The falling of drops of water will in time fill a water-jar. Even so the foolish man becomes full of evil, although he gather it little by little. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.121) | |
| A reaction: This coincides closely with Aristotle's view of moral education. Maybe a wise man can maintain one small vice. Not all slopes are slippery. |
| 7897 | The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)] |
| Full Idea: The falling of drops of water will in time fill a water-jar. Even so the wise man becomes full of good, although he gather it little by little. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §9.122) | |
| A reaction: Again, this is like Aristotle's proposal of how to educate people in virtue. In my experience, there is no guarantee that small acts of politeness and charity will eventually guarantee goodness of character. Thought is also needed. |
| 7895 | Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)] |
| Full Idea: If on the great journey of life a man cannot find one who is better or at least as good as himself, let him joyfully travel alone: a fool cannot help him on his journey. | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §5.61) | |
| A reaction: This is a slightly disturbing aspect of Buddhism, possibly leading to contradiction. It urges friendship and love, but the finest people will have virtually no friends, and solitude is presented as a finer state than friendship. |
| 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 |
| 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. |
| 7900 | Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)] |
| Full Idea: Speak the truth, yield not to anger, give what you can to him who asks: these three steps lead you to the gods | |
| From: Anon (Dham) (The DhammaPada [c.250 BCE], §17.224) | |
| A reaction: I don't recall either the Old or New Testament, or the Koran, placing great emphasis on speaking the truth. The injunction to give is not so simple. Give to greedy children, to alcoholics, to criminals, to the rich, to fools, to yourself? |