18 ideas
| 22396 | We take courage, temperance, wisdom and justice as moral, but Aristotle takes wisdom as intellectual [Foot] |
| Full Idea: For us there are four cardinal moral virtues: courage, temperance, wisdom and justice. But Aristotle and Aquinas call only three of these virtues moral virtues; practical wisdom (phronesis, prudentia) they class with the intellectual virtues. | |
| From: Philippa Foot (Virtues and Vices [1978], p.2) | |
| A reaction: I'm not sure about 'for us'. How many of us rank temperance as a supreme virtue? Aristotle ranks phronesis (which I think of as 'common sense') as the key enabler of the moral virtues, making it unlike the other intellectual virtues. |
| 22397 | Wisdom is open to all, and not just to the clever or well trained [Foot] |
| Full Idea: Knowledge that can be acquired only by someone who is clever or who has access to special training is not counted as part of wisdom. | |
| From: Philippa Foot (Virtues and Vices [1978], p.6) | |
| A reaction: Consider Pierre's peasant friend Platon Karatayev in 'War and Peace'. I assume 'special training' rules out anyone with a philosophy degree. |
| 16415 | Esoteric metaphysics aims to be top science, investigating ultimate reality [Hofweber] |
| Full Idea: Esoteric metaphysics appeals to those, I conjecture, who deep down hold that philosophy is the queen of sciences after all, since it investigates what the world is REALLY like. | |
| From: Thomas Hofweber (Ambitious, yet modest, Metaphysics [2009], 2) | |
| A reaction: He mentions Kit Fine and Jonathan Schaffer as esoteric metaphysicians. I see a pyramid of increasing generality and abstraction, with metaphysics at the top. This doesn't make it 'queen', though, because uncertainties multiply higher up. |
| 16413 | Science has discovered properties of things, so there are properties - so who needs metaphysics? [Hofweber] |
| Full Idea: Material science has found that some features of metals make them more susceptible to corrosion but more resistant to fracture. Thus this immediately implies that there are features, i.e. properties. What is left for metaphysics to do? | |
| From: Thomas Hofweber (Ambitious, yet modest, Metaphysics [2009], 1.1) | |
| A reaction: Presumably economists have discovered 'features' of economies that cause unemployment, and literary critics have discovered 'features' of novels that make them good. |
| 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. |
| 16416 | The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber] |
| Full Idea: The inferential role of the existential quantifier in first order logic does not carry over to the existential quantifier in English (we have empty names, singular terms that are not even in the business of denoting, and so on). | |
| From: Thomas Hofweber (Ambitious, yet modest, Metaphysics [2009], 2) |
| 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. |
| 22402 | Most people think virtues can be displayed in bad actions [Foot] |
| Full Idea: Hardly anyone sees any difficulty in the thought that virtues may sometimes be displayed in bad actions. The courage of the villain can be spoken of as quite unproblematic. | |
| From: Philippa Foot (Virtues and Vices [1978], III) | |
| A reaction: She cites Peter Geach as a sole opponent of this view. The courage of the entire German army in WWII seems to fall into this category. The boldness of villains has to impress the virtuous but timid. |
| 23145 | Virtues are intended to correct design flaws in human beings [Foot, by Driver] |
| Full Idea: A popular view (expressed by Philippa Foot) is that the virtues work to 'correct' for the baser human impulses and motives. …Virtues are solutions to design flaws in human beings. | |
| From: report of Philippa Foot (Virtues and Vices [1978]) by Julia Driver - The Virtues and Human Nature 1 | |
| A reaction: Quite a plausible thought. Not so much design flaws, though, as natural traits of character that suited hunter gatherers but not modern cosmopolitan capitalists. Driver disagrees. |
| 22401 | Actions can be in accordance with virtue, but without actually being virtuous [Foot] |
| Full Idea: Some actions are in accordance with virtue without requiring virtue for their performance, whereas others are both in accordance with virtue and such as to show possession of a virtue. | |
| From: Philippa Foot (Virtues and Vices [1978], p.13) | |
| A reaction: She cites the case of an honest trader, who is honest because of self-interest. She is disentangling Kant from his daft idea that only dutiful (and reluctant) actions are virtuous. Kant was only thinking of 'in accordance' cases. |
| 22398 | Virtues are corrective, to resist temptation or strengthen motivation [Foot] |
| Full Idea: The virtues are corrective, each one standing at a point at which there is some temptation to be resisted or deficiency of motivation to be made good. | |
| From: Philippa Foot (Virtues and Vices [1978], II) | |
| A reaction: A beautifully simple and accurate observation, which I don't remember meeting in Aristotle (...though she cites him as saying that virtues concern what is difficult for us). Justice and charity are given as examples of inadequate motivation. |
| 22403 | Temperance is not a virtue if it results from timidity or excessive puritanism [Foot] |
| Full Idea: In some people temperance is not a virtue, but is rather connected with timidity or with a grudging attitude to the acceptance of good things. | |
| From: Philippa Foot (Virtues and Vices [1978], III) | |
| A reaction: Timidity seems right. The grudging attitude may result from some larger doubts about pleasure, which could be plausible. |
| 22400 | Courage overcomes the fears which should be overcome, and doesn't overvalue personal safety [Foot] |
| Full Idea: The fears that count against a man's courage are those that we think he should overcome, and among them, in a special class, those that reflect the fact that he values his safety too much. | |
| From: Philippa Foot (Virtues and Vices [1978], II) | |
| A reaction: I think that sentence tells us more accurately what courage is than anything in Aristotle's discussion. Ask yourself which of your fears really ought to be overcome, and particularly beware of over-valuing your own safety. But stay safe if you can! |