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. |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
| From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
| A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
| A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
| A reaction: [compressed] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
| A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
| A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
| A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
| 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 |
| 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 |
| 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. |
| 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. |