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All the ideas for 'reports', 'Naturalism in Mathematics' and 'Phaedrus'

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62 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Can we understand an individual soul without knowing the soul in general? [Plato]
     Full Idea: Do you think it possible to form an adequate conception of the nature of an individual soul without considering the nature of soul in general?
     From: Plato (Phaedrus [c.366 BCE], 270c)
     A reaction: Do animals understand anything (as opposed to simply being aware of things)?
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato]
     Full Idea: When I believe that I have found in anyone the ability to discuss unity and plurality as they exist in the nature of things, I follow his footsteps as if he was a god.
     From: Plato (Phaedrus [c.366 BCE], 266b)
     A reaction: This sounds like the problem of identity, which is at the heart of modern metaphysics.
1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
A speaker should be able to divide a subject, right down to the limits of divisibility [Plato]
     Full Idea: A speaker must be able to define a subject generically, and then to divide it into its various specific kinds until he reaches the limits of divisibility.
     From: Plato (Phaedrus [c.366 BCE], 277b)
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
'Forcing' can produce new models of ZFC from old models [Maddy]
     Full Idea: Cohen's method of 'forcing' produces a new model of ZFC from an old model by appending a carefully chosen 'generic' set.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.4)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
     Full Idea: A possible axiom is the Large Cardinal Axiom, which asserts that there are more and more stages in the cumulative hierarchy. Infinity can be seen as the first of these stages, and Replacement pushes further in this direction.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.5)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
     Full Idea: The axiom of infinity: that there are infinite sets is to claim that completed infinite collections can be treated mathematically. In its standard contemporary form, the axioms assert the existence of the set of all finite ordinals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
     Full Idea: In the presence of other axioms, the Axiom of Foundation is equivalent to the claim that every set is a member of some Vα.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
     Full Idea: The Axiom of Reducibility states that every propositional function is extensionally equivalent to some predicative proposition function.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
'Propositional functions' are propositions with a variable as subject or predicate [Maddy]
     Full Idea: A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Completed infinities resulted from giving foundations to calculus [Maddy]
     Full Idea: The line of development that finally led to a coherent foundation for the calculus also led to the explicit introduction of completed infinities: each real number is identified with an infinite collection of rationals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.3)
     A reaction: Effectively, completed infinities just are the real numbers.
Cantor and Dedekind brought completed infinities into mathematics [Maddy]
     Full Idea: Both Cantor's real number (Cauchy sequences of rationals) and Dedekind's cuts involved regarding infinite items (sequences or sets) as completed and subject to further manipulation, bringing the completed infinite into mathematics unambiguously.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1 n39)
     A reaction: So it is the arrival of the real numbers which is the culprit for lumbering us with weird completed infinites, which can then be the subject of addition, multiplication and exponentiation. Maybe this was a silly mistake?
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
     Full Idea: The stunning discovery that infinity comes in different degrees led to the theory of infinite cardinal numbers, the heart of contemporary set theory.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: It occurs to me that these huge cardinals only exist in set theory. If you took away that prop, they would vanish in a puff.
For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
     Full Idea: By the mid 1890s Cantor was aware that there could be no set of all sets, as its cardinal number would have to be the largest cardinal number, while his own theorem shows that for any cardinal there is a larger.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: There is always a larger cardinal because of the power set axiom. Some people regard that with suspicion.
An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
     Full Idea: An 'inaccessible' cardinal is one that cannot be reached by taking unions of small collections of smaller sets or by taking power sets.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.5)
     A reaction: They were introduced by Hausdorff in 1908.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
Theorems about limits could only be proved once the real numbers were understood [Maddy]
     Full Idea: Even the fundamental theorems about limits could not [at first] be proved because the reals themselves were not well understood.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: This refers to the period of about 1850 (Weierstrass) to 1880 (Dedekind and Cantor).
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
The extension of concepts is not important to me [Maddy]
     Full Idea: I attach no decisive importance even to bringing in the extension of the concepts at all.
     From: Penelope Maddy (Naturalism in Mathematics [1997], §107)
     A reaction: He almost seems to equate the concept with its extension, but that seems to raise all sorts of questions, about indeterminate and fluctuating extensions.
In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
     Full Idea: In the ZFC cumulative hierarchy, Frege's candidates for numbers do not exist. For example, new three-element sets are formed at every stage, so there is no stage at which the set of all three-element sets could he formed.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: Ah. This is a very important fact indeed if you are trying to understand contemporary discussions in philosophy of mathematics.
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
Frege solves the Caesar problem by explicitly defining each number [Maddy]
     Full Idea: To solve the Julius Caesar problem, Frege requires explicit definitions of the numbers, and he proposes his well-known solution: the number of Fs = the extension of the concept 'equinumerous with F' (based on one-one correspondence).
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: Why do there have to be Fs before there can be the corresponding number? If there were no F for 523, would that mean that '523' didn't exist (even if 522 and 524 did exist)?
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
     Full Idea: The set theory axioms developed in producing foundations for mathematics also have strong consequences for existing fields, and produce a theory that is immensely fruitful in its own right.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: [compressed] Second of Maddy's three benefits of set theory. This benefit is more questionable than the first, because the axioms may be invented because of their nice fruit, instead of their accurate account of foundations.
Unified set theory gives a final court of appeal for mathematics [Maddy]
     Full Idea: The single unified area of set theory provides a court of final appeal for questions of mathematical existence and proof.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: Maddy's third benefit of set theory. 'Existence' means being modellable in sets, and 'proof' means being derivable from the axioms. The slightly ad hoc character of the axioms makes this a weaker defence.
Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
     Full Idea: Set theoretic foundations bring all mathematical objects and structures into one arena, allowing relations and interactions between them to be clearly displayed and investigated.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: The first of three benefits of set theory which Maddy lists. The advantages of the one arena seem to be indisputable.
Identifying geometric points with real numbers revealed the power of set theory [Maddy]
     Full Idea: The identification of geometric points with real numbers was among the first and most dramatic examples of the power of set theoretic foundations.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: Hence the clear definition of the reals by Dedekind and Cantor was the real trigger for launching set theory.
The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
     Full Idea: The structure of a geometric line by rational points left gaps, which were inconsistent with a continuous line. Set theory provided an ordering that contained no gaps. These reals are constructed from rationals, which come from integers and naturals.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.2)
     A reaction: This completes the reduction of geometry to arithmetic and algebra, which was launch 250 years earlier by Descartes.
Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
     Full Idea: Our much loved mathematical knowledge rests on two supports: inexorable deductive logic (the stuff of proof), and the set theoretic axioms.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I Intro)
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Maybe applications of continuum mathematics are all idealisations [Maddy]
     Full Idea: It could turn out that all applications of continuum mathematics in natural sciences are actually instances of idealisation.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.6)
Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
     Full Idea: Crudely, the scientist posits only those entities without which she cannot account for observations, while the set theorist posits as many entities as she can, short of inconsistency.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.5)
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
     Full Idea: Recent commentators have noted that Frege's versions of the basic propositions of arithmetic can be derived from Hume's Principle alone, that the fatal Law V is only needed to derive Hume's Principle itself from the definition of number.
     From: Penelope Maddy (Naturalism in Mathematics [1997], I.1)
     A reaction: Crispin Wright is the famous exponent of this modern view. Apparently Charles Parsons (1965) first floated the idea.
7. Existence / D. Theories of Reality / 2. Realism
Reasoning needs to cut nature accurately at the joints [Plato]
     Full Idea: In our reasoning we need a clear view of the ability to divide a genus into species, observing the natural joints, not mangling any of the parts, like an unskilful butcher.
     From: Plato (Phaedrus [c.366 BCE], 265d)
     A reaction: In modern times this Platonic idea has become the standard metaphor for realism. I endorse it. I think nature has joints, and we should hunt for them. There are natural sets. The joints may exist in abstract concepts, as well as in objects.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
     Full Idea: The case of atoms makes it clear that the indispensable appearance of an entity in our best scientific theory is not generally enough to convince scientists that it is real.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.6)
     A reaction: She refers to the period between Dalton and Einstein, when theories were full of atoms, but there was strong reluctance to actually say that they existed, until the direct evidence was incontrovertable. Nice point.
7. Existence / E. Categories / 2. Categorisation
I revere anyone who can discern a single thing that encompasses many things [Plato]
     Full Idea: If I believe that someone is capable of discerning a single thing that is also by nature capable of encompassing many, I follow 'straight behind, in his footsteps, as if he were a god'.
     From: Plato (Phaedrus [c.366 BCE], 266b)
     A reaction: [Plato quote Odyssey 2.406] This is the sort of simple but profound general observation which only the early philosophers bothered to make, and no one comments on now. Encompassing many under one is the very essence of thinking.
8. Modes of Existence / D. Universals / 2. Need for Universals
It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato]
     Full Idea: It takes a man to understand by the use of universals, and to collect out of the multiplicity of sense-impressions a unity arrived at by a process of reason.
     From: Plato (Phaedrus [c.366 BCE], 249b)
8. Modes of Existence / D. Universals / 6. Platonic Forms / a. Platonic Forms
We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato]
     Full Idea: What overpowering love knowledge would inspire if it could bring a clear image of itself before our sight, and the same may be said of the other forms.
     From: Plato (Phaedrus [c.366 BCE], 250d)
     A reaction: the motivation in Plato's theory
12. Knowledge Sources / C. Rationalism / 1. Rationalism
True knowledge is of the reality behind sense experience [Plato]
     Full Idea: True knowledge is concerned with the abode of true reality, without colour or shape, intangible but utterly real, apprehensible only to the intellect.
     From: Plato (Phaedrus [c.366 BCE], 247c)
14. Science / A. Basis of Science / 5. Anomalies
If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato]
     Full Idea: There are some occasions when both prosecution and defence should positively suppress the facts in favour of probability, if the facts are improbable.
     From: Plato (Phaedrus [c.366 BCE], 272e)
15. Nature of Minds / A. Nature of Mind / 2. Psuche
The soul is self-motion [Plato]
     Full Idea: Self-motion is of the very nature of the soul.
     From: Plato (Phaedrus [c.366 BCE], 245e)
     A reaction: This culminates a length discussion of the soul. He gives an implausible argument that the soul is immortal, because it could never cease its self-motion. Why are we so unimpressed by motion, when the Greeks were amazed by it?
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy]
     Full Idea: In science we treat the earth's surface as flat, we assume the ocean to be infinitely deep, we use continuous functions for what we know to be quantised, and we take liquids to be continuous despite atomic theory.
     From: Penelope Maddy (Naturalism in Mathematics [1997], II.6)
     A reaction: If fussy people like scientists do this all the time, how much more so must the confused multitude be doing the same thing all day?
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie]
     Full Idea: Plato had a conception of the emotions and our bodily appetites as being like wild horses, to be harnassed and controlled by reason.
     From: report of Plato (Phaedrus [c.366 BCE]) by Peter Goldie - The Emotions 4 'Education'
     A reaction: This seems to make Plato the patriarch of puritanism. See Symposium, as well as Phaedrus. But bringing up children can often seem like taming wild beasts.
19. Language / F. Communication / 1. Rhetoric
Only a good philosopher can be a good speaker [Plato]
     Full Idea: Unless a man becomes an adequate philosopher he will never be an adequate speaker on any subject.
     From: Plato (Phaedrus [c.366 BCE], 261a)
     A reaction: Depends. Hitler showed little sign of clear philosophical thinking, but the addition of lights and uniforms seemed to sweep reasonably intelligent people along with him.
'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato]
     Full Idea: The purpose of the 'Phaedrus' is to pioneer the notion of philosophical rhetoric.
     From: comment on Plato (Phaedrus [c.366 BCE], Ch.10) by Hugh Lawson-Tancred - Plato's Republic and Greek Enlightenment
     A reaction: This is a wonderfully challenging view of what Plato was up to. One might connect it with Rorty's claim that philosophy should move away from epistemology and analysis, towards hermeneutics, which sounds to me like rhetoric. 'Phaedrus' is beautiful.
An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato]
     Full Idea: If a speech is to be classed as excellent, does that not presuppose knowledge of the truth about the subject of the speech in the mind of the speaker.
     From: Plato (Phaedrus [c.366 BCE], 259e)
     A reaction: I like the thought that Plato's main interest was rhetoric, but with the view that the only good rhetoric is truth-speaking. It would be hard to admire a speech if you disagreed with it.
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P]
     Full Idea: Jesus was a learned Jew who said that learning was not necessary, who took the spirit and not the letter as the essence of the Law.
     From: report of Jesus (reports [c.32]) by Paul Johnson - The History of the Jews Pt II
     A reaction: This seems to me the perfect opposite of Socrates's intellectualism, offering the essence of morality as 'purity of heart', rather than careful thought about virtue or principles. On the whole I am with Socrates, but the idea is interesting.
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
Beauty is the clearest and most lovely of the Forms [Plato]
     Full Idea: Only beauty has the privilege of being the most clearly discerned and the most lovely of the forms.
     From: Plato (Phaedrus [c.366 BCE], 250e)
     A reaction: the motivation in Plato's theory
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato]
     Full Idea: In each one of us there are two ruling and impelling principles: a desire for pleasure, which is innate, and an acquired conviction which causes us to aim at excellence.
     From: Plato (Phaedrus [c.366 BCE], 237d)
     A reaction: This division is too neat and simple. An obsession with pleasure I would take to be acquired. If you set out to do something, I think there is an innate desire to do it well.
22. Metaethics / B. Value / 2. Values / g. Love
Love your enemies [Jesus]
     Full Idea: Love your enemies.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.44
     A reaction: The germ of this idea had been around for several hundred years, but this very forceful statement is perhaps Jesus' most distinctive contribution to moral thought. It has the same clarion call as the Stoic demand for pure virtue. What about deserving?
Love thy neighbour as thyself [Jesus]
     Full Idea: Love thy neighbour as thyself.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 19.19
     A reaction: It would be stronger and better to say 'Love your neighbour, even if you don't love yourself'. Self-loathing and vicious hatred often go together. For once Jesus does not attach an instant heavenly reward to obedience of the command.
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
Most pleasure is release from pain, and is therefore not worthwhile [Plato]
     Full Idea: Life is not worth living for pleasures whose enjoyment entirely depends on previous sensation of pain, like almost all physical pleasures.
     From: Plato (Phaedrus [c.366 BCE], 258e)
     A reaction: Eating exotic food which is hard to obtain? (Pay someone to obtain it). Rock climbing. Training for sport.
23. Ethics / B. Contract Ethics / 2. Golden Rule
Treat others as you would have them treat you [Jesus]
     Full Idea: All things whatsoever ye would that men should do to you, so ye even so to them: for this is the law and the prophets.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 07.12
     A reaction: A problem which probably didn't occur to Jesus and the prophets is that of masochists. Personally I like buying philosophy books, but most people have no such desire. The Rule needs restricting to the basics of pleasure and pain.
23. Ethics / B. Contract Ethics / 4. Value of Authority
Blessed are the merciful: for they shall obtain mercy [Jesus]
     Full Idea: Blessed are the merciful: for they shall obtain mercy.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.07
     A reaction: This appears to be a straightforward application of social contract morality, with God playing the role of Hobbes' absolute monarch. It highlights the uncomfortable fact at the heart of Christian morality, that the motivation for altruism is selfish.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
Reason impels us towards excellence, which teaches us self-control [Plato]
     Full Idea: The conviction which impels us towards excellence is rational, and the power by which it masters us we call self-control.
     From: Plato (Phaedrus [c.366 BCE], 237e)
Except ye become as little children, ye shall not enter heaven [Jesus]
     Full Idea: Except ye be converted, and become as little children, ye shall not enter into the kingdom of heaven.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 18.03
     A reaction: The appeal of such purity of heart is undeniable, but essentially I dislike this remark. It is the opponent of education, reason, autonomy, responsibility, democracy and maturity. It confirms the view that religion is the opium of the people.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / h. Right feelings
If you lust after a woman, you have committed adultery [Jesus]
     Full Idea: Whosoever look on a woman to lust after her hath committed adultery with her already in his heart.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.28
     A reaction: Compare Democritus, Idea 503. Literally this idea seems absurd, but it is also at the heart of Greek virtue theory. Aristotle (Idea 34) defines virtue as an activity 'of the soul', not an action in the world. Excellence has become purity of soul.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
Blessed are the meek; for they shall inherit the earth [Jesus]
     Full Idea: Blessed are the meek; for they shall inherit the earth.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.05
     A reaction: If they are truly meek, why would they want to inherit the earth? This is the classic statement of Nietzsche's 'inversion of values', where the qualities of a good slave are elevated above those of the greatest human beings.
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Don't resist evil, but turn the other cheek [Jesus]
     Full Idea: Ye have heard it said, An eye for an eye, and a tooth for a tooth; But I say unto you, That ye resist not evil, but whosoever shall smite thee on thy right cheek, turn to him the other also.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 05.38-9
     A reaction: Compare Socrates, Idea 346. The viciousness of many Hollywood movies is that they set up a character as thoroughly evil so that we can have the pleasure of watching him pulverised. On the whole, Jesus gives bad advice. 'Doormats' in game theory.
23. Ethics / C. Virtue Theory / 4. External Goods / c. Wealth
It is almost impossible for the rich to go to heaven [Jesus]
     Full Idea: It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 19.24
     A reaction: Aristotle and others (Margaret Thatcher) have observed that you cannot practise charity if you are poor. Jesus implies that the human race should remain in poverty. No wonder autocratic medieval rulers taught Christianity to peasants. Cf. Matt 25.30.
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Bad people are never really friends with one another [Plato]
     Full Idea: It is not ordained that bad men should be friends with one another.
     From: Plato (Phaedrus [c.366 BCE], 255b)
27. Natural Reality / E. Cosmology / 3. The Beginning
If the prime origin is destroyed, it will not come into being again out of anything [Plato]
     Full Idea: If the prime origin is destroyed, it will not come into being again out of anything.
     From: Plato (Phaedrus [c.366 BCE], 245d)
     A reaction: This is the essence of Aquinas's Third Way of proving God's existence.
28. God / A. Divine Nature / 3. Divine Perfections
The mind of God is fully satisfied and happy with a vision of reality and truth [Plato]
     Full Idea: The mind of a god, sustained by pure intelligence and knowledge, is satisfied with the vision of reality, and nourished and made happy by the vision of truth.
     From: Plato (Phaedrus [c.366 BCE], 247d)
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
No one is good except God [Jesus]
     Full Idea: Why callest thou me good? There is none good but one, that is, God.
     From: Jesus (reports [c.32]), quoted by St Matthew - 01: Gospel of St Matthew 19.17
     A reaction: This remark raises the problem that if God is good, there must be some separate moral standard by which he can be judged good. What is that standard? It is related to the problem of whether Plato's Form of the Beautiful is itself beautiful.
28. God / C. Attitudes to God / 4. God Reflects Humanity
We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato]
     Full Idea: Because we have never seen or formed an adequate idea of a god, we picture him to ourselves as a being of the same kind as ourselves but immortal.
     From: Plato (Phaedrus [c.366 BCE], 246d)
28. God / C. Attitudes to God / 5. Atheism
There isn't a single reason for positing the existence of immortal beings [Plato]
     Full Idea: There is not a single sound reason for positing the existence of such a being who is immortal
     From: Plato (Phaedrus [c.366 BCE], 246d)
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P]
     Full Idea: Jesus was a member of the school of Hillel the Elder, and may have sat under him. He repeated some of the sayings of Hillel, ...and turned his ideas into a moral theology, stripping the law of all but its moral and ethical elements.
     From: report of Jesus (reports [c.32]) by Paul Johnson - The History of the Jews Pt II
     A reaction: The crucial move, it seems to me, is to strip Judaism of its complexity, and reduce it to very simple moral maxims, which means that ordinary illiterate people no longer need priests to understand and follow it. Jesus was, above all, a great teacher.
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
Soul is always in motion, so it must be self-moving and immortal [Plato]
     Full Idea: All soul is immortal, for what is always in motion is immortal. Only that which moves itself never ceases to be in motion.
     From: Plato (Phaedrus [c.366 BCE], 245c)