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All the ideas for 'fragments/reports', 'Gorgias' and 'The Nature of Mathematical Knowledge'

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61 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
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.378 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.
2. Reason / C. Styles of Reason / 2. Elenchus
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.378 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.117
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.378 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.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher]
     Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik]
     Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets).
     From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2
     A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist.
Mathematical a priorism is conceptualist, constructivist or realist [Kitcher]
     Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts).
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3)
     A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means.
The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher]
     Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3)
     A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means.
The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher]
     Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4)
     A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers stand to measurement as natural numbers stand to counting [Kitcher]
     Full Idea: The real numbers stand to measurement as the natural numbers stand to counting.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4)
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / j. Complex numbers
Complex numbers were only accepted when a geometrical model for them was found [Kitcher]
     Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
     A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A one-operation is the segregation of a single object [Kitcher]
     Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3)
     A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero).
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
The old view is that mathematics is useful in the world because it describes the world [Kitcher]
     Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
     A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
With infinitesimals, you divide by the time, then set the time to zero [Kitcher]
     Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2)
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
     Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1)
     A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it.
Mathematical intuition is not the type platonism needs [Kitcher]
     Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3)
     A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'.
Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
     Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2)
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Mathematical knowledge arises from basic perception [Kitcher]
     Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
     A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to.
My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
     Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro)
     A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction.
We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
     Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2)
     A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction.
The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
     Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5)
     A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
     Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I)
     A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
     Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics.
Arithmetic is an idealizing theory [Kitcher]
     Full Idea: I construe arithmetic as an idealizing theory.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'.
We develop a language for correlations, and use it to perform higher level operations [Kitcher]
     Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2)
     A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory.
Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
     Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second.
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
     Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1)
     A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them?
If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]
     Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6)
     A reaction: Nice question! He's a fan of getting at the explanatory in mathematics.
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Abstract objects were a bad way of explaining the structure in mathematics [Kitcher]
     Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
     A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
A priori knowledge comes from available a priori warrants that produce truth [Kitcher]
     Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4)
     A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start.
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
In long mathematical proofs we can't remember the original a priori basis [Kitcher]
     Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2)
     A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2.
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher]
     Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3)
     A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view.
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher]
     Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6)
     A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / a. Justification issues
A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher]
     Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2)
     A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention.
13. Knowledge Criteria / A. Justification Problems / 1. Justification / c. Defeasibility
If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo]
     Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence.
     From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3
     A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher]
     Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways.
     From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5)
     A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man.
19. Language / F. Communication / 1. Rhetoric
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.378 BCE], 455a)
     A reaction: Surely there must be good rhetoric (or at least it is an open question)?
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.378 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.
20. Action / B. Preliminaries of Action / 1. Intention to Act / b. Types of intention
All activity aims at the good [Plato]
     Full Idea: All activity aims at the good.
     From: Plato (Gorgias [c.378 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.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / g. Will to power
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.378 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?
22. Metaethics / B. Value / 2. Values / h. Fine deeds
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.378 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.
22. Metaethics / B. Value / 2. Values / i. Self-interest
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.378 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.
22. Metaethics / C. The Good / 1. Goodness / f. Good as pleasure
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.378 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.
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.378 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?
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
Admirable people are happy, and unjust people are miserable [Plato]
     Full Idea: I say that the admirable and good person, man or woman, is happy [eudaimon], but that the one who's unjust and wicked is miserable.
     From: Plato (Gorgias [c.378 BCE], 470e)
     A reaction: This is eudaimonia, which is flourishing. So Socrates might consider them to be flourishing, when they saw themselves as failure. Parents said make money, but instead they lived altruistically, but guiltily. Note 'woman'.
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
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.378 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.
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
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.378 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.
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.378 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.
23. Ethics / A. Egoism / 2. Hedonism
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.378 BCE], 492c)
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
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.378 BCE], 480a)
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
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.378 BCE], 469c)
     A reaction: cf Democritus 68B45
23. Ethics / C. Virtue Theory / 3. Virtues / b. Temperance
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.378 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.
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.378 BCE], 507e)
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
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.378 BCE], 472e)
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.378 BCE], 492a)
23. Ethics / C. Virtue Theory / 4. External Goods / b. Health
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.378 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.
24. Political Theory / B. Nature of a State / 1. Purpose of a State
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.378 BCE], 506e)
24. Political Theory / D. Ideologies / 5. Democracy / c. Direct democracy
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.378 BCE], 517b)
25. Social Practice / B. Equalities / 1. Grounds of equality
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.378 BCE], 483c)
25. Social Practice / B. Equalities / 4. Economic equality
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.378 BCE], 483d)
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
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
27. Natural Reality / G. Biology / 3. Evolution
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.