25 ideas
| 14179 | The finest branch of wisdom is justice and moderation in ordering states and families [Plato] |
| Full Idea: By far the greatest and fairest branch of wisdom is that which is concerned with the due ordering of states and families, whose name is moderation and justice. | |
| From: Plato (The Symposium [c.373 BCE], 209a) | |
| A reaction: ['Justice' is probably 'dikaiosune'] It is hard to disagree with this, and it relegates ivory tower philosophical contemplation to second place, unlike the late books of Aristotle's Ethics. |
| 13949 | All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano] |
| Full Idea: Peano's axioms are categorical (any two models are isomorphic). Some conclude that the concept of natural number is adequately represented by them, but we cannot identify natural numbers with one rather than another of the isomorphic models. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 11) by Richard Cartwright - Propositions 11 | |
| A reaction: This is a striking anticipation of Benacerraf's famous point about different set theory accounts of numbers, where all models seem to work equally well. Cartwright is saying that others have pointed this out. |
| 18113 | PA concerns any entities which satisfy the axioms [Peano, by Bostock] |
| Full Idea: Peano Arithmetic is about any system of entities that satisfies the Peano axioms. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 6.3) by David Bostock - Philosophy of Mathematics 6.3 | |
| A reaction: This doesn't sound like numbers in the fullest sense, since those should facilitate counting objects. '3' should mean that number of rose petals, and not just a position in a well-ordered series. |
| 17634 | Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell] |
| Full Idea: Peano's premises are recommended not only by the fact that arithmetic follows from them, but also by their inherent obviousness. | |
| From: report of Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 15653 | We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano] |
| Full Idea: Peano Arithmetic cannot derive its own consistency from within itself. But it can be strengthened by adding this consistency statement or by stronger axioms (particularly ones partially expressing soundness). These are known as Reflexion Principles. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], 1.2) by Volker Halbach - Axiomatic Theories of Truth (2005 ver) 1.2 |
| 17635 | Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano] |
| Full Idea: Peano's premises are not the ultimate logical premises of arithmetic. Simpler premises and simpler primitive ideas are to be had by carrying our analysis on into symbolic logic. | |
| From: comment on Giuseppe Peano (Principles of Arithmetic, by a new method [1889], p.276) by Bertrand Russell - Regressive Method for Premises in Mathematics p.276 |
| 1607 | Diotima said the Forms are the objects of desire in philosophical discourse [Plato, by Roochnik] |
| Full Idea: According to Diotima, the Forms are the objects of desire operative in philosophical discourse. | |
| From: report of Plato (The Symposium [c.373 BCE], 210a4-) by David Roochnik - The Tragedy of Reason p.199 |
| 174 | True opinion without reason is midway between wisdom and ignorance [Plato] |
| Full Idea: There is a state of mind half-way between wisdom and ignorance - having true opinions without being able to give reasons for them. | |
| From: Plato (The Symposium [c.373 BCE], 202a) | |
| A reaction: Compare Idea 2140, where Plato scorns this state of mind. What he describes could be split into two - purely lucky true beliefs, and 'externalist knowledge', with non-conscious justification. |
| 181 | Only the gods stay unchanged; we replace our losses with similar acquisitions [Plato] |
| Full Idea: We retain identity not by staying the same (the preserve of gods) but by replacing losses with new similar acquisitions. | |
| From: Plato (The Symposium [c.373 BCE], 208b) | |
| A reaction: Any modern student of personal identity should be intrigued by this remark! It appears to take a rather physical view of the matter, and to be aware of human biology as a process. Are my continuing desires token-identical, or just 'similar'? |
| 180 | We call a person the same throughout life, but all their attributes change [Plato] |
| Full Idea: During the period from boyhood to old age, man does not retain the same attributes, though he is called the same person. | |
| From: Plato (The Symposium [c.373 BCE], 207d) | |
| A reaction: This precisely identifies the basic problem of personal identity over time. If this is the problem, DNA looks more and more significant for the answer, though it would be an awful mistake to think a pattern of DNA was a person. |
| 172 | Love of ugliness is impossible [Plato] |
| Full Idea: There cannot be such a thing as love of ugliness. | |
| From: Plato (The Symposium [c.373 BCE], 201a) |
| 4026 | Beauty is harmony with what is divine, and ugliness is lack of such harmony [Plato] |
| Full Idea: Ugliness is out of harmony with everything that is godly; beauty, however, is in harmony with the divine. | |
| From: Plato (The Symposium [c.373 BCE], 206d) | |
| A reaction: This remark shows how the concept of 'harmony' is at the centre of Greek thought (and is a potential bridge of the is/ought gap). |
| 173 | Beauty and goodness are the same [Plato] |
| Full Idea: What is good is the same as what is beautiful. | |
| From: Plato (The Symposium [c.373 BCE], 201c) |
| 184 | Progress goes from physical beauty, to moral beauty, to the beauty of knowledge, and reaches absolute beauty [Plato] |
| Full Idea: One should step up from physical beauty, to moral beauty, to the beauty of knowledge, until at last one knows what absolute beauty is. | |
| From: Plato (The Symposium [c.373 BCE], 211c) | |
| A reaction: Presumably this is why Socrates refused sexual favours to Alcibiades. The idea is inspiring, and yet it is a rejection of humanity. |
| 183 | Stage two is the realisation that beauty of soul is of more value than beauty of body [Plato] |
| Full Idea: The second stage of progress is to realise that beauty of soul is more valuable than beauty of body. | |
| From: Plato (The Symposium [c.373 BCE], 210b) |
| 171 | Music is a knowledge of love in the realm of harmony and rhythm [Plato] |
| Full Idea: Music may be called a knowledge of the principles of love in the realm of harmony and rhythm. | |
| From: Plato (The Symposium [c.373 BCE], 187c) |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 176 | Love follows beauty, wisdom is exceptionally beautiful, so love follows wisdom [Plato] |
| Full Idea: Wisdom is one of the most beautiful of things, and Love is love of beauty, so it follows that Love must be a love of wisdom. | |
| From: Plato (The Symposium [c.373 BCE], 204b) | |
| A reaction: Good, but wisdom isn't the only exceptionally beautiful thing. Music is beautiful partly because it is devoid of ideas. |
| 179 | Love is desire for perpetual possession of the good [Plato] |
| Full Idea: Love is desire for perpetual possession of the good. | |
| From: Plato (The Symposium [c.373 BCE], 206a) | |
| A reaction: Even the worst human beings often have lovers. 'Perpetual' is a nice observation. |
| 14177 | Love assists men in achieving merit and happiness [Plato] |
| Full Idea: Phaedrus: Love is not only the oldest and most honourable of the gods, but also the most powerful to assist men in the acquisition of merit and happiness, both here and hereafter. | |
| From: Plato (The Symposium [c.373 BCE], 180b) | |
| A reaction: Maybe we should talk less of love as a feeling, and more as a motivation, not just in human relationships, but in activities like gardening and database compilation. |
| 177 | If a person is good they will automatically become happy [Plato] |
| Full Idea: 'What will be gained by a man who is good?' 'That is easy - he will be happy'. | |
| From: Plato (The Symposium [c.373 BCE], 205a) | |
| A reaction: Suppose you tried to assassinate Hitler in 1944 (a good deed), but failed. Happiness presumably results from success, rather than mere good intentions. |
| 14178 | Happiness is secure enjoyment of what is good and beautiful [Plato] |
| Full Idea: By happy you mean in secure enjoyment of what is good and beautiful? - Certainly. | |
| From: Plato (The Symposium [c.373 BCE], 202c) | |
| A reaction: We seem to have lost track of the idea that beauty might be an essential ingredient of happiness. |
| 182 | The first step on the right path is the contemplation of physical beauty when young [Plato] |
| Full Idea: The man who would pursue the right way to his goal must begin, when he is young, by contemplating physical beauty. | |
| From: Plato (The Symposium [c.373 BCE], 210a) |
| 170 | The only slavery which is not dishonourable is slavery to excellence [Plato] |
| Full Idea: The only form of servitude which has no dishonour has for its object the acquisition of excellence. | |
| From: Plato (The Symposium [c.373 BCE], 184c) |
| 175 | Gods are not lovers of wisdom, because they are already wise [Plato] |
| Full Idea: No god is a lover of wisdom or desires to be wise, for he is wise already. | |
| From: Plato (The Symposium [c.373 BCE], 204a) |