32 ideas
| 162 | 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)? |
| 160 | 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. |
| 166 | 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) |
| 23248 | Early empiricists said reason was just a useless concept introduced by philosophers [Galen, by Frede,M] |
| Full Idea: The so-called Empiricists in Hellenistic times [as cited by Galen] denied the existence of reason, treating it as a useless theoretical postulate introduced by some philosophers | |
| From: report of Galen (An Outline of Empiricism [c.170], 87.4-9.28ff) by Michael Frede - Intro to 'Rationality in Greek Thought' p.3 | |
| A reaction: I think 'be sensible' is understood by everyone, but 'use your reason' is far from obvious. The main role of reason seems to be as an identifier for human exceptionalism. Animals obviously make good judgements. Frede thinks the empiricists were right. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 7953 | 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. |
| 16121 | 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. |
| 153 | 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) |
| 154 | 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 |
| 151 | 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) |
| 165 | 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) |
| 9296 | 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? |
| 23997 | 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. |
| 159 | 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. |
| 5946 | '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. |
| 158 | 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. |
| 155 | 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 |
| 143 | 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. |
| 157 | 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. |
| 144 | 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) |
| 156 | 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) |
| 148 | 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. |
| 152 | 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) |
| 150 | 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) |
| 149 | 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) |
| 146 | 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) |