36 ideas
| 125 | Is a gifted philosopher unmanly if he avoids the strife of the communal world? [Plato] |
| Full Idea: Callicles: Even a naturally gifted philosopher isn't going to develop into a real man, because he's avoiding the heart of his community and the thick of the agora. | |
| From: Plato (Gorgias [c.387 BCE], 485d) | |
| A reaction: A serious charge against philosophy. An attraction of the subject is its purity, its necessity, its timelessness, and in some ways these are just nicer and easier and more understandable than the hard mess of real life. But understanding has to be good. |
| 1654 | In "Gorgias" Socrates is confident that his 'elenchus' will decide moral truth [Vlastos on Plato] |
| Full Idea: In the 'Gorgias' Socrates is still supremely confident that the elenchus is the final arbiter of moral truth. | |
| From: comment on Plato (Gorgias [c.387 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.117 |
| 4321 | We should test one another, by asking and answering questions [Plato] |
| Full Idea: Test me, and let yourself be tested as well, by asking and answering questions. | |
| From: Plato (Gorgias [c.387 BCE], 462a) | |
| A reaction: The idea must be to avoid wild speculation, by continually filtering ideas through rival critical intelligences. The best philosophical method ever devised. |
| 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. |
| 116 | Rhetoric is irrational about its means and its ends [Plato] |
| Full Idea: Rhetoric is a knack, because it lacks rational understanding of its object or what it dispenses (and can't explain the reason anything happens). | |
| From: Plato (Gorgias [c.387 BCE], 465a) | |
| A reaction: If there are cunning people who have the wrong sort of intelligence for morality, there must be cunning users of rhetoric who know exactly what they are doing. |
| 114 | Rhetoric can produce conviction, but not educate people about right and wrong [Plato] |
| Full Idea: Rhetoric is an agent of the kind of persuasion which is designed to produce conviction, but not to educate people about right and wrong. | |
| From: Plato (Gorgias [c.387 BCE], 455a) | |
| A reaction: Surely there must be good rhetoric (or at least it is an open question)? |
| 135 | All activity aims at the good [Plato] |
| Full Idea: All activity aims at the good. | |
| From: Plato (Gorgias [c.387 BCE], 499e) | |
| A reaction: He includes non-conscious activity, so this is the 'teleological' view of nature, which seems a bit optimistic to the modern mind. |
| 122 | Moral rules are made by the weak members of humanity [Plato] |
| Full Idea: Callicles: It's the weaklings who constitute the majority of the human race who make the rules. | |
| From: Plato (Gorgias [c.387 BCE], 483b) | |
| A reaction: An aristocrat bemoans democracy. Presumably the qualification for being a 'weakling' is shortage of money. How strong are the scions of the aristocrats? |
| 139 | A good person is bound to act well, and this brings happiness [Plato] |
| Full Idea: A good person is bound to do whatever he does well and successfully, and success brings fulfilment and happiness. | |
| From: Plato (Gorgias [c.387 BCE], 507c) | |
| A reaction: Not how we would see it, I guess, but this is the Greek idea that a good person is one who functions well. Anyone who functions well is probably having a good time. |
| 128 | Is it natural to simply indulge our selfish desires? [Plato] |
| Full Idea: Callicles: Nature says the only authentic way of life is to do nothing to hinder or restrain the expansion of one's desires. | |
| From: Plato (Gorgias [c.387 BCE], 491e) | |
| A reaction: Sounds like the natural desires of a young single man. Parents and spouses have natural desires that focus on other people's desires. |
| 4322 | In slaking our thirst the goodness of the action and the pleasure are clearly separate [Plato] |
| Full Idea: When we drink to quench thirst, we lose the distress of the thirst and the pleasure of drinking at the same moment, but one loss is good and the other bad, so the pleasure and the goodness must be separate. | |
| From: Plato (Gorgias [c.387 BCE], 497d) | |
| A reaction: This is open to the objection that the good of slaking one's thirst is a long-term pleasure, where the drinking is short-term, so pleasure is still the good. |
| 136 | Good should be the aim of pleasant activity, not the other way round [Plato] |
| Full Idea: Good should be the goal of pleasant activities, rather than pleasure being the goal of good activities. | |
| From: Plato (Gorgias [c.387 BCE], 500a) | |
| A reaction: Nice. Not far off what Aristotle says on the topic. So what activities should we seek out? Narrow the pleasures down to the good ones, or narrow the good ones down to the pleasurable? |
| 134 | Good and bad people seem to experience equal amounts of pleasure and pain [Plato] |
| Full Idea: There is little to tell between good and bad people (e.g. cowards) in terms of how much pleasure and distress they experience. | |
| From: Plato (Gorgias [c.387 BCE], 498c) | |
| A reaction: A very perceptive remark. If the good are people with empathy for others, then they may suffer more distress than the insensitive wicked. |
| 132 | If happiness is the satisfaction of desires, then a life of scratching itches should be happiness [Plato] |
| Full Idea: Socrates: I want to ask whether a lifetime spent scratching, itching and scratching, no end of scratching, is also a life of happiness. | |
| From: Plato (Gorgias [c.387 BCE], 494c) | |
| A reaction: There are plenty of people who think 'fun' is the main aim of life, and who fit what Socrates is referring to. We don't admire such a life, but not many people can be admired. |
| 4319 | In a fool's mind desire is like a leaky jar, insatiable in its desires, and order and contentment are better [Plato] |
| Full Idea: In a fool's mind desire is a leaky jar, …which is an analogy for the mind's insatiability, showing we should prefer an orderly life, in which one is content with whatever is to hand, to a self-indulgent life of insatiable desire. | |
| From: Plato (Gorgias [c.387 BCE], 493b) | |
| A reaction: This points to an interesting paradox, that pleasure requires the misery of desire. And yet absence of desire is like death. An Aristotelian mean, of living according to nature, seems the escape route. |
| 130 | Is the happiest state one of sensual, self-indulgent freedom? [Plato] |
| Full Idea: Callicles: If a person has the means to live a life of sensual, self-indulgent freedom, there's no better or happier state of existence. | |
| From: Plato (Gorgias [c.387 BCE], 492c) |
| 467 | A virtue is a combination of intelligence, strength and luck [Ion] |
| Full Idea: The virtue of each thing is a Triad: intelligence, strength, luck. | |
| From: Ion (fragments/reports [c.435 BCE], B1), quoted by (who?) - where? |
| 120 | Should we avoid evil because it will bring us bad consequences? [Plato] |
| Full Idea: Socrates: We should avoid doing wrong because of all the bad consequences it will bring us. | |
| From: Plato (Gorgias [c.387 BCE], 480a) |
| 118 | I would rather be a victim of crime than a criminal [Plato] |
| Full Idea: Socrates: If I had to choose between doing wrong and having wrong done to me, I'd prefer the latter to the former. | |
| From: Plato (Gorgias [c.387 BCE], 469c) | |
| A reaction: cf Democritus 68B45 |
| 140 | Self-indulgent desire makes friendship impossible, because it makes a person incapable of co-operation [Plato] |
| Full Idea: Self-indulgent desire makes a person incapable of co-operation, which is a prerequisite of friendship. | |
| From: Plato (Gorgias [c.387 BCE], 507e) |
| 131 | If absence of desire is happiness, then nothing is happier than a stone or a corpse [Plato] |
| Full Idea: Callicles: If people who need nothing are happy, there would be nothing happier than a stone or a corpse. | |
| From: Plato (Gorgias [c.387 BCE], 492e) | |
| A reaction: We aren't really supposed to approve of Callicles, but to me this is a splendidly crushing western response to many of the ideals found in eastern philosophy. |
| 119 | A criminal is worse off if he avoids punishment [Plato] |
| Full Idea: Socrates: A criminal is worse off if he doesn't pay the penalty, and continues to do wrong without getting punished. | |
| From: Plato (Gorgias [c.387 BCE], 472e) |
| 129 | Do most people praise self-discipline and justice because they are too timid to gain their own pleasure? [Plato] |
| Full Idea: Callicles: Why do most people praise self-discipline and justice? Because their own timidity makes them incapable of satisfying their pleasures. | |
| From: Plato (Gorgias [c.387 BCE], 492a) |
| 4320 | The popular view is that health is first, good looks second, and honest wealth third [Plato] |
| Full Idea: I'm sure you know the list of human advantages in the party song: 'The very best is health, Second good looks, and third honest wealth'. | |
| From: Plato (Gorgias [c.387 BCE], 451e) | |
| A reaction: This invites the obvious question of why anyone wants these three things, with the implied answer of 'pleasure'. But we might want them even if we couldn't use them, implying pluralism. |
| 137 | As with other things, a good state is organised and orderly [Plato] |
| Full Idea: As in every case (an artefact, a body, a mind, a creature), a good state is an organised and orderly state. | |
| From: Plato (Gorgias [c.387 BCE], 506e) |
| 141 | A good citizen won't be passive, but will redirect the needs of the state [Plato] |
| Full Idea: The only responsibility of a good member of a community is altering the community's needs rather than going along with them. | |
| From: Plato (Gorgias [c.387 BCE], 517b) |
| 123 | Do most people like equality because they are second-rate? [Plato] |
| Full Idea: Callicles: It's because most people are second-rate that they are happy for things to be distributed equally. | |
| From: Plato (Gorgias [c.387 BCE], 483c) |
| 124 | Does nature imply that it is right for better people to have greater benefits? [Plato] |
| Full Idea: Callicles: We only have to look at nature to find evidence that it is right for better to have a greater share than worse. | |
| From: Plato (Gorgias [c.387 BCE], 483d) |