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All the ideas for 'works', 'reports' and 'The Nature of Mathematics'

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57 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb]
     Full Idea: Aristotle takes wisdom to come in two forms, the practical and the theoretical, the former of which is good judgement about how to act, and the latter of which is deep knowledge or understanding.
     From: report of Aristotle (works [c.330 BCE]) by Dennis Whitcomb - Wisdom Intro
     A reaction: The interesting question is then whether the two are connected. One might be thoroughly 'sensible' about action, without counting as 'wise', which seems to require a broader view of what is being done. Whitcomb endorses Aristotle on this idea.
1. Philosophy / G. Scientific Philosophy / 3. Scientism
Philosophy is an experimental science, resting on common experience [Peirce]
     Full Idea: Philosophy, although it uses no microscopes or other apparatus of special observation, is really an experimental science, resting on that experience which is common to us all.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], I)
     A reaction: The 'experimental' either implies that thought-experiments are central to the subject, or that philosophers are discussing the findings of scientists, but at a high level of theory and abstraction. Peirce probably means the latter. I can't disagree.
2. Reason / A. Nature of Reason / 2. Logos
For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
     Full Idea: For Aristotle logos is the ability to speak rationally about, with the hope of attaining knowledge, questions of value.
     From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.26
2. Reason / A. Nature of Reason / 4. Aims of Reason
Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
     Full Idea: Aristotle is the great theoretician who articulates a vision of a world in which natural and stable structures can be rationally discovered. His is the most optimistic and richest view of the possibilities of logos
     From: comment on Aristotle (works [c.330 BCE]) by David Roochnik - The Tragedy of Reason p.95
2. Reason / A. Nature of Reason / 7. Status of Reason
Reason is a more powerful persuader than gold [Democritus (attr)]
     Full Idea: In power of persuasion, reasoning is far stronger than gold.
     From: Democritus (attrib) (reports [c.250 BCE], B051), quoted by John Stobaeus - Anthology 2.04.12
2. Reason / B. Laws of Thought / 3. Non-Contradiction
Self-contradiction doesn't reveal impossibility; it is inductive impossibility which reveals self-contradiction [Peirce]
     Full Idea: It is an anacoluthon to say that a proposition is impossible because it is self-contradictory. It rather is thought so to appear self-contradictory because the ideal induction has shown it to be impossible.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
2. Reason / D. Definition / 4. Real Definition
Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
     Full Idea: A real definition, according to the Aristotelian tradition, gives the essence of the kind of thing defined. Man is defined as a rational animal, and thus rationality and animality are of the essence of each of us.
     From: report of Aristotle (works [c.330 BCE]) by Willard Quine - Vagaries of Definition p.51
     A reaction: Compare Idea 4385. Personally I prefer the Aristotelian approach, but we may have to say 'We cannot identify the essence of x, and so x cannot be defined'. Compare 'his mood was hard to define' with 'his mood was hostile'.
2. Reason / D. Definition / 5. Genus and Differentia
Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
     Full Idea: For Aristotle, to give a definition one must first state the genus and then the differentia of the kind of thing to be defined.
     From: report of Aristotle (works [c.330 BCE]) by J.O. Urmson - Aristotle's Doctrine of the Mean p.157
     A reaction: Presumably a modern definition would just be a list of properties, but Aristotle seeks the substance. How does he define a genus? - by placing it in a further genus?
4. Formal Logic / G. Formal Mereology / 1. Mereology
Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
     Full Idea: Aristotle proposes to relativise unity and plurality, so that a single object can be both one (indivisible) and many (divisible) simultaneously, without contradiction, relative to different measures. Wholeness has degrees, with the strength of the unity.
     From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.12
     A reaction: [see Koslicki's account of Aristotle for details] As always, the Aristotelian approach looks by far the most promising. Simplistic mechanical accounts of how parts make wholes aren't going to work. We must include the conventional and conceptual bit.
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Logic, unlike mathematics, is not hypothetical; it asserts categorical ends from hypothetical means [Peirce]
     Full Idea: Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is a normative science, and not a mere discovery of what really is. It discovers ends from means.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], II)
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
     Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality.
     From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4
     A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Mathematics is close to logic, but is even more abstract [Peirce]
     Full Idea: The whole of the theory of numbers belongs to logic; or rather, it would do so, were it not, as pure mathematics, pre-logical, that is, even more abstract than logic.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], IV)
     A reaction: Peirce seems to flirt with logicism, but rejects in favour of some subtler relationship. I just don't believe that numbers are purely logical entities.
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki]
     Full Idea: Aristotle's discussion of the unmoved mover and of the soul confirms the suspicion that form, when it is not thought of as the object represented in a definition, plays the role of the ultimate mereological atom within his system.
     From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 6.6
     A reaction: Aristotle is concerned with which things are 'divisible', and he cites these two examples as indivisible, but they may be too unusual to offer an actual theory of how Aristotle builds up wholes from atoms. He denies atoms in matter.
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki]
     Full Idea: Thus in Aristotle we may think of an object's formal components as a sort of recipe for how to build wholes of that particular kind.
     From: report of Aristotle (works [c.330 BCE]) by Kathrin Koslicki - The Structure of Objects 7.2.5
     A reaction: In the elusive business of pinning down what Aristotle means by the crucial idea of 'form', this analogy strikes me as being quite illuminating. It would fit DNA in living things, and the design of an artifact.
10. Modality / B. Possibility / 1. Possibility
Some logical possibility concerns single propositions, but there is also compatibility between propositions [Peirce]
     Full Idea: Many say everything is logically possible which involves no contradiction. In this sense two contradictory propositions may be severally possible. In the substantive sense, the contradictory of a possible proposition is impossible (if we were omniscient).
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
11. Knowledge Aims / A. Knowledge / 1. Knowledge
For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code]
     Full Idea: Aristotle thinks that in general we have knowledge or understanding when we grasp causes, and he distinguishes three fundamental types of knowledge - theoretical, practical and productive.
     From: report of Aristotle (works [c.330 BCE]) by Alan D. Code - Aristotle
     A reaction: Productive knowledge we tend to label as 'knowing how'. The centrality of causes for knowledge would get Aristotle nowadays labelled as a 'naturalist'. It is hard to disagree with his three types, though they may overlap.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
The notion of a priori truth is absent in Aristotle [Aristotle, by Politis]
     Full Idea: The notion of a priori truth is conspicuously absent in Aristotle.
     From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5
     A reaction: Cf. Idea 11240.
12. Knowledge Sources / C. Rationalism / 1. Rationalism
Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M]
     Full Idea: Aristotle is a rationalist …but reason for him is a disposition which we only acquire over time. Its acquisition is made possible primarily by perception and experience.
     From: report of Aristotle (works [c.330 BCE]) by Michael Frede - Aristotle's Rationalism p.173
     A reaction: I would describe this process as the gradual acquisition of the skill of objectivity, which needs the right knowledge and concepts to evaluate new experiences.
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Experience is indeed our only source of knowledge, provided we include inner experience [Peirce]
     Full Idea: If Mill says that experience is the only source of any kind of knowledge, I grant it at once, provided only that by experience he means personal history, life. But if he wants me to admit that inner experience is nothing, he asks what cannot be granted.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898])
     A reaction: Notice from Idea 14785 that Peirce has ideas in mind, and not just inner experiences like hunger. Empiricism certainly begins to look more plausible if we expand the notion of experience. It must include what we learned from prior experience.
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
The world is one of experience, but experiences are always located among our ideas [Peirce]
     Full Idea: The real world is the world of sensible experience, and it is part of the process of sensible experience to locate its facts in the world of ideas.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], III)
     A reaction: This is the neatest demolition of the sharp dividing line between empiricism and rationalism that I have ever encountered.
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
     Full Idea: Since Aristotle generally prefers a metaphysical theory that accords with common intuitions, he frequently relies on facts about language to guide his metaphysical claims.
     From: report of Aristotle (works [c.330 BCE]) by Mary Louise Gill - Aristotle on Substance Ch.5
     A reaction: I approve of his procedure. I take intuition to be largely rational justifications too complex for us to enunciate fully, and language embodies folk intuitions in its concepts (especially if the concepts occur in many languages).
14. Science / B. Scientific Theories / 1. Scientific Theory
Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
     Full Idea: Plato's unity of science principle states that all - legitimate - sciences are ultimately about the Forms. Aristotle's principle states that all sciences must be, ultimately, about substances, or aspects of substances.
     From: report of Aristotle (works [c.330 BCE], 1) by Julius Moravcsik - Aristotle on Adequate Explanations 1
14. Science / D. Explanation / 1. Explanation / a. Explanation
Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
     Full Idea: For Aristotle things which explain (the explanantia) are facts, which should not be associated with the modern view that says explanations are dependent on how we conceive and describe the world (where causes are independent of us).
     From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 2.1
     A reaction: There must be some room in modern thought for the Aristotelian view, if some sort of robust scientific realism is being maintained against the highly linguistic view of philosophy found in the twentieth century.
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
     Full Idea: The standard Aristotelian doctrine of species and genus in the theory of anything whatever involves specifying what the thing is in terms of something more general.
     From: report of Aristotle (works [c.330 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.10
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
     Full Idea: The view that essential properties are those in virtue of which other significant properties of the subjects under investigation can be explained is encountered repeatedly in Aristotle's work.
     From: report of Aristotle (works [c.330 BCE]) by Joan Kung - Aristotle on Essence and Explanation IV
     A reaction: What does 'significant' mean here? I take it that the significant properties are the ones which explain the role, function and powers of the object.
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji]
     Full Idea: Aristotle, and also the Stoics, denied rationality to animals. …The Platonists, the Pythagoreans, and some more independent Aristotelians, did grant reason and intellect to animals.
     From: report of Aristotle (works [c.330 BCE]) by Richard Sorabji - Rationality 'Denial'
     A reaction: This is not the same as affirming or denying their consciousness. The debate depends on how rationality is conceived.
19. Language / E. Analyticity / 2. Analytic Truths
The notion of analytic truth is absent in Aristotle [Aristotle, by Politis]
     Full Idea: The notion of analytic truth is conspicuously absent in Aristotle.
     From: report of Aristotle (works [c.330 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.5
     A reaction: Cf. Idea 11239.
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty is merely animal without intelligence [Democritus (attr)]
     Full Idea: Physical beauty is merely animal unless intelligence be present.
     From: Democritus (attrib) (reports [c.250 BCE], B105)
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
Ethics is the science of aims [Peirce]
     Full Idea: Ethics is the science of aims.
     From: Charles Sanders Peirce (The Nature of Mathematics [1898], II)
     A reaction: Intriguing slogan. He is discussing the aims of logic. I think what he means is that ethics is the science of value. 'Science' may be optimistic, but I would sort of agree with his basic idea.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
Behave well when alone, and feel shame in you own eyes [Democritus (attr)]
     Full Idea: Do not say or do what is base, even when you are alone. Learn to feel shame in your own eyes much more than before others.
     From: Democritus (attrib) (reports [c.250 BCE], B244), quoted by John Stobaeus - Anthology 3.31.7
     A reaction: I like this. How you think and behave when unobserved is the true test of who you are. Feeling shame at a very private failing is an interesting phenomenon.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin]
     Full Idea: To the best of my knowledge (and somewhat to my surprise), Aristotle never actually says that man is a rational animal; however, he all but says it.
     From: report of Aristotle (works [c.330 BCE]) by Robert Fogelin - Walking the Tightrope of Reason Ch.1
     A reaction: When I read this I thought that this database would prove Fogelin wrong, but it actually supports him, as I can't find it in Aristotle either. Descartes refers to it in Med.Two. In Idea 5133 Aristotle does say that man is a 'social being'. But 22586!
22. Metaethics / B. Value / 2. Values / d. Health
Good breeding in men means having a good character [Democritus (attr)]
     Full Idea: Good breeding in cattle depends on physical health, but in men on a well-formed character.
     From: Democritus (attrib) (reports [c.250 BCE], B057), quoted by John Stobaeus - Anthology 4.29.18
     A reaction: In our ultra-democratic age (supposedly) it is heresy to talk about good breeding, or some people being superior to others. But surely people should aim to improve their characters?
22. Metaethics / B. Value / 2. Values / g. Love
Virtuous love consists of decorous desire for the beautiful [Democritus (attr)]
     Full Idea: Virtuous love consists of decorous desire for the beautiful.
     From: Democritus (attrib) (reports [c.250 BCE], B073), quoted by John Stobaeus - Anthology 3.5.23
     A reaction: Is it possible to love something without seeing it as beautiful? A badly crippled dog, for example. If not, that seems to reveal something about beauty.
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
We should only choose pleasures which are concerned with the beautiful [Democritus (attr)]
     Full Idea: One should choose not every pleasure, but only that concerned with the beautiful.
     From: Democritus (attrib) (reports [c.250 BCE], B207), quoted by John Stobaeus - Anthology 3.05.22
     A reaction: The pleasures we should prefer are those which involve the whole person, rather than the mere stimulation of one sense. Sez me.
Good and true are the same for everyone, but pleasures differ [Democritus (attr)]
     Full Idea: For all men, good and true are the same; but pleasant differs for different men.
     From: Democritus (attrib) (reports [c.250 BCE], B069)
     A reaction: Truth is not 'for' anyone, but there's good-in-itself, and good-for-me. Are there some pleasures we should all enjoy (such as watching our children flourish)?
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Only accept beneficial pleasures [Democritus (attr)]
     Full Idea: Accept no pleasure unless it is beneficial.
     From: Democritus (attrib) (reports [c.250 BCE], B074)
     A reaction: Maybe all pleasures bestow some benefit - even if they are linked to harm. I struggle to see what is wrong with a harmless and non-beneficial pleasure, and I doubt if anyone could explain it to me.
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
The great pleasures come from the contemplation of noble works [Democritus (attr)]
     Full Idea: The great pleasures come from the contemplation of noble works.
     From: Democritus (attrib) (reports [c.250 BCE], B194), quoted by John Stobaeus - Anthology 3.03.46
     A reaction: Only, of course, for those able to perceive the nobility. In what does the 'nobility' consist, other than in the morally acceptable pleasure? Hard to explain 'noble'. Just 'wow!'?
Moderation brings more pleasures, and so increases pleasure [Democritus (attr)]
     Full Idea: Moderation multiplies pleasures, and increases pleasure.
     From: Democritus (attrib) (reports [c.250 BCE], B211), quoted by John Stobaeus - Anthology 3.05.27
     A reaction: So moderation is a sneaky trick to avoid moderation? I presume the most intense pleasures are mostly unfamiliar, and so add novelty to the mix. Apart from eating chocolate, of course.
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
Immoderate desire is the mark of a child, not an adult [Democritus (attr)]
     Full Idea: Immoderate desire is the mark of a child, not a man.
     From: Democritus (attrib) (reports [c.250 BCE], B070)
     A reaction: Not factually correct, since the world is full of adults who have immoderate desires (notably for money). However, there are plenty of grown ups who don't seem very adult.
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
It is as brave to master pleasure as to overcome the enemy [Democritus (attr)]
     Full Idea: The brave man is not only he who overcomes the enemy, but he who is stronger than pleasures. Some men are masters of cities, but are enslaved by women.
     From: Democritus (attrib) (reports [c.250 BCE], B214), quoted by John Stobaeus - Anthology 3.07.25
     A reaction: I'm not sure if 'bravery' is the relevant virtue here.Sounds like self-control or temperance. I suspect that mastering a city is quite pleasurable, if that's your thing.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)]
     Full Idea: Virtue consists, not in avoiding wrong-doing, but in having no wish thereto.
     From: Democritus (attrib) (reports [c.250 BCE], B062), quoted by John Stobaeus - Anthology 3.17.37
Be virtuous from duty, not from fear [Democritus (attr)]
     Full Idea: Refrain from crimes not through fear but through duty [deon].
     From: Democritus (attrib) (reports [c.250 BCE], B041), quoted by John Stobaeus - Anthology 3.01.95
     A reaction: [not sure about the translation here]
A bad life is just a drawn-out death [Democritus (attr)]
     Full Idea: To live badly is not just to live badly, but to spend a long time dying.
     From: Democritus (attrib) (reports [c.250 BCE], B160), quoted by (who?) - where?
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
Repentance of shameful deeds is salvation [Democritus (attr)]
     Full Idea: Repentance for shameful deeds is salvation in life.
     From: Democritus (attrib) (reports [c.250 BCE], B043)
Virtue comes more from practice than from nature [Democritus (attr)]
     Full Idea: More men become good through practice than by nature.
     From: Democritus (attrib) (reports [c.250 BCE], B242), quoted by John Stobaeus - Anthology 3.29.66
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / i. Absolute virtues
One must avoid even speaking of evil deeds [Democritus (attr)]
     Full Idea: One must avoid even speaking of evil deeds.
     From: Democritus (attrib) (reports [c.250 BCE], B190), quoted by John Stobaeus - Anthology 3.01.91
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
The wrongdoer is more unfortunate than the person wronged [Democritus (attr)]
     Full Idea: The wrongdoer is more unfortunate than the man wronged.
     From: Democritus (attrib) (reports [c.250 BCE], B045)
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
The endless desire for money is a crueller slavery than poverty [Democritus (attr)]
     Full Idea: Unless a point of satiety is reached, the desire for money is far more cruel than the utmost poverty, because the greater the desire, the greater the need
     From: Democritus (attrib) (reports [c.250 BCE], B219), quoted by John Stobaeus - Anthology 3.10.43
Small appetite makes poverty equal to wealth [Democritus (attr)]
     Full Idea: Small appetite makes poverty equivalent to wealth.
     From: Democritus (attrib) (reports [c.250 BCE], B284), quoted by John Stobaeus - Anthology 4.33.24
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
It is better to have one intelligent friend than many unintelligent [Democritus (attr)]
     Full Idea: The friendship of one intelligent man is better than that of all the unintelligent.
     From: Democritus (attrib) (reports [c.250 BCE], B098)
23. Ethics / D. Deontological Ethics / 2. Duty
It is a great thing, when one is in adversity, to think of duty [Democritus (attr)]
     Full Idea: It is a great thing, when one is in adversity, to think of duty.
     From: Democritus (attrib) (reports [c.250 BCE], B042), quoted by John Stobaeus - Anthology 4.44.68
     A reaction: Something wrong with the translation here, if there is no Greek word for 'duty'.
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
It is better to be poor in a democracy than be rich without freedom [Democritus (attr)]
     Full Idea: Poverty in a democracy is as preferable to what is called prosperity under autocracy as freedom is to slavery.
     From: Democritus (attrib) (reports [c.250 BCE], B251), quoted by John Stobaeus - Anthology 3.40.42
25. Social Practice / E. Policies / 5. Education / a. Aims of education
It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle]
     Full Idea: It is the mark of an educated mind to be able to entertain an idea without accepting it.
     From: Aristotle (works [c.330 BCE])
     A reaction: The epigraph on a David Chalmers website. A wonderful remark, and it should be on the wall of every beginners' philosophy class. However, while it is in the spirit of Aristotle, it appears to be a misattribution with no ancient provenance.
25. Social Practice / E. Policies / 5. Education / b. Education principles
Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius]
     Full Idea: Aristotle was asked how much educated men were superior to those uneducated; "As much," he said, "as the living are to the dead."
     From: report of Aristotle (works [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 05.1.11
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
     Full Idea: Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent.
     From: report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3
     A reaction: Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle.
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins]
     Full Idea: Aristotle's conception of matter permits any kind of matter to become any other kind of matter.
     From: report of Aristotle (works [c.330 BCE]) by David Wiggins - Substance 4.11.2
     A reaction: This is obviously crucial background information when we read Aristotle on matter. Our 92+ elements, and fixed fundamental particles, gives a quite different picture. Aristotle would discuss form and matter quite differently now.
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]
     Full Idea: Aristotle said that the conception of gods arose among mankind from two originating causes, namely from events which concern the soul and from celestial phenomena.
     From: report of Aristotle (works [c.330 BCE], Frag 10) by Sextus Empiricus - Against the Physicists (two books) I.20
     A reaction: The cosmos suggests order, and possible creation. What do events of the soul suggest? It doesn't seem to be its non-physical nature, because Aristotle is more of a functionalist. Puzzling. (It says later that gods are like the soul).