28 ideas
| 23250 | Desired responsible actions result either from rational or from irrational desire [Aristotle] |
| Full Idea: And of responsible actions, some are done through habit, some through desire, and of these some through rational and some through irrational desire. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1369a01) | |
| A reaction: Identified by Michael Frede, to illustrate reason having its own distinctive type of desire ('Boulesis'). I suspect that the rational desires are the morally good desires. |
| 5847 | It is the role of dialectic to survey syllogisms [Aristotle] |
| Full Idea: It belongs to dialectic to survey equally all kinds of syllogism. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1355a08) | |
| A reaction: Since dialectic is central to philosophy, this implies that philosophers ought to be students of logic. This duty seems to me to be taken more seriously in the analytical tradition than in the 'continental' tradition. |
| 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. |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| Full Idea: Maddy dispenses with pure sets, by sketching a strong set theory in which everything is either a physical object or a set of sets of ...physical objects. Eventually a physiological story of perception will extend to sets of physical objects. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: This doesn't seem to find many supporters, but if we accept the perception of resemblances as innate (as in Hume and Quine), it is isn't adding much to see that we intrinsically see things in groups. |
| 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. |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| Full Idea: Maddy takes a natural number to be a certain property of sui generis sets, the property of having a certain number of members. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990], 3 §2) by Alex Oliver - The Metaphysics of Properties | |
| A reaction: [I believe Maddy has shifted since then] Presumably this will make room for zero and infinities as natural numbers. Personally I want my natural numbers to count things. |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| Full Idea: Maddy says that intuition alone does not support very much mathematics; more importantly, a naturalist cannot accept intuition at face value, but must ask why we are justified in relying on intuition. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Stewart Shapiro - Thinking About Mathematics 8.3 | |
| A reaction: It depends what you mean by 'intuition', but I identify with her second objection, that every faculty must ultimately be subject to criticism, which seems to point to a fairly rationalist view of things. |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| Full Idea: Maddy proposes that we can know (some) mind-independent mathematical truths through knowing about sets, and that we can obtain knowledge of sets through experience. | |
| From: report of Penelope Maddy (Realism in Mathematics [1990]) by Carrie Jenkins - Grounding Concepts 6.5 | |
| A reaction: Maddy has since backed off from this, and now tries to merely defend 'objectivity' about sets (2011:114). My amateurish view is that she is overrating the importance of sets, which merely model mathematics. Look at category theory. |
| 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. |
| 5862 | A single counterexample is enough to prove that a truth is not necessary [Aristotle] |
| Full Idea: If we have a single counter-instance, the argument is refuted as not necessary, even if more cases are otherwise or more often otherwise. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1403a07) | |
| A reaction: This is Aristotle (pioneering hero) pointing out what we now tend to think of as Karl Popper's falsification, the certain way to demonstrate the falseness of a supposed law of nature, by finding one anomaly from it. |
| 5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
| Full Idea: Nobody is on his guard against a disease that nobody has yet caught. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1372a27) | |
| A reaction: A beautifully simple indication of one problem with induction. In a dangerous situation, you can't wait around for a few experiences in order to learn the regularities and rules. Either you are doomed, or you must explain using related experiences. |
| 5849 | Rhetoric is a political offshoot of dialectic and ethics [Aristotle] |
| Full Idea: Rhetoric is a kind of offshoot of dialectic and of the study of ethics, and is quite properly categorized as political. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1356a25) | |
| A reaction: Aristotle gives a higher status to rhetoric than Socrates and Plato did - and rightly, in my view. We have lost sight of it as a vital part of politics, and philosophers must fight for virtue in rhetoric, which requires right reason and fine principles. |
| 5851 | Pentathletes look the most beautiful, because they combine speed and strength [Aristotle] |
| Full Idea: The pentathletes are the most beautiful, being at the same time naturally suited to both speed and force. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1361b09) | |
| A reaction: This is still true. Watch the Olympics. The bodies we envy most belong to those who do a variety of disciplines. The most beautiful music fulfils a variety of functions (structure, as well as melody, drama, rhythm, harmony, novelty). |
| 5858 | Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle] |
| Full Idea: The body is in its prime from the ages of thirty to thirty-five, and the soul around the age of forty-nine. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1390b09) | |
| A reaction: Wonderfully specific! It is important that Aristotle is interested in these questions. The good for man follows the path laid out by nature, in which a man rises to his highest good in maturity, and then declines from it into old age. |
| 5855 | We all feel universal right and wrong, independent of any community or contracts [Aristotle] |
| Full Idea: There is something of which we all have an inkling, being a naturally universal right and wrong, even if there should be no community between the parties or contract. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1373b07) | |
| A reaction: This is the strongest assertion I know of in Aristotle of an absolute moral standard, independent of natural function. It makes Aristotle an intuitionist, and is strikingly opposed to contracts as the most basic aspect of morality. |
| 5850 | Happiness is composed of a catalogue of internal and external benefits [Aristotle] |
| Full Idea: The elements of happiness are: gentle birth, many virtuous friends, wealth, creditable and extensive offspring, a comfortable old age; also health, beauty, strength, size and competitiveness, reputation, status, luck and the virtues. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1360b18) | |
| A reaction: This is Aristotle's pluralism, and his commitment to 'external goods' (rather than the inner good of pure virtue, which the Stoics preferred). 'Gentle birth' might turn out to mean good upbringing and education. Who was the most 'beautiful' philosopher? |
| 5856 | Self-interest is a relative good, but nobility an absolute good [Aristotle] |
| Full Idea: One's own interest is a relative good, nobility a good absolutely. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1389b37) | |
| A reaction: The key idea in the whole of Greek moral theory is the concept of what we can call a 'beautiful' action. Such things, or course, tend to be visible in great actions, such as sparing an enemy, rather than the minutiae of well-mannered daily life. |
| 5853 | The best virtues are the most useful to others [Aristotle] |
| Full Idea: The greatest virtues must be those most useful to others. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1366b02) | |
| A reaction: I wonder if this applies to the intellectual virtues, as well as to the social virtues? Is this virtue theory's answer to utilitarianism, or utilitarianism's answer to virtue theory? Personally I think good persons are prior to benefits. |
| 5848 | All good things can be misused, except virtue [Aristotle] |
| Full Idea: If one used strength, health, wealth and strategic expertise well, one might do the greatest possible good and if badly the greatest possible harm; this is a problem common to all good things, except virtue. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1355b04) | |
| A reaction: Of course, this may just be a tautology about virtue, rather than an empirical observation. However, in 'Ethics' he tries to describe a state of mind (essentially one of harmony) which could never result in misuse. |
| 5857 | The young feel pity from philanthropy, but the old from self-concern [Aristotle] |
| Full Idea: Old men are prone to pity, but where the young are so from philanthropy, the old are so from weakness, for they think all these things are near for themselves to suffer. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1390a18) | |
| A reaction: I am shocked to find Aristotle being so cynical. I see no reason why the old should not be as philanthropic as anyone else, and they clearly are so, as when they plant trees for future generations to enjoy. |
| 5859 | Rich people are mindlessly happy [Aristotle] |
| Full Idea: The character of the rich man is that of the mindlessly happy one. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1391a12) | |
| A reaction: Very nice. It is hard to deny that the rich tend to be happy (in some sense of the word), and recent sociological research has tended to demonstrate this, but the pursuit of wealth must inevitably take the focus away from key intellectual pursuits. Yeh? |
| 5852 | The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle] |
| Full Idea: There are four types of constitution: democracy (whose purpose is freedom), oligarchy (for wealth), aristocracy (for education and customs), and monarch or tyranny (for security). | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1365b28-37) | |
| A reaction: An aristocracy seems to be the guardians of tradition and culture (as in an English public school education). The tyranny of Hitler and Stalin did not exactly lead to security. Democracy and aristocracy are the front-runners. Compare Idea 2821. |
| 1660 | It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle] |
| Full Idea: It is noble to avenge oneself on one's enemies and not to come to terms with them. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1367a19), quoted by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.189 |
| 5861 | People assume events cause what follows them [Aristotle] |
| Full Idea: Men take its occurring after as its occurring because. | |
| From: Aristotle (The Art of Rhetoric [c.350 BCE], 1401b30) | |
| A reaction: The Latin is 'post hoc propter hoc' - after this so because of this. It is quite a good inductive rule, but obviously open to abuse, as in legal cases, as when someone happens to acquire a lot of money just after a crime. |