43 ideas
23890 | For Plato true wisdom is supernatural [Plato, by Weil] |
Full Idea: It is evident that Plato regards true wisdom as something supernatural. | |
From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.61 | |
A reaction: Taken literally, I assume this is wrong, but we can empathise with the thought. Wisdom has the feeling of rising above the level of mere knowledge, to achieve the overview I associate with philosophy. |
3060 | Plato never mentions Democritus, and wished to burn his books [Plato, by Diog. Laertius] |
Full Idea: Plato, who mentions nearly all the ancient philosophers, nowhere speaks of Democritus; he wished to burn all of his books, but was persuaded that it was futile. | |
From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.7.8 |
23891 | Two contradictories force us to find a relation which will correlate them [Plato, by Weil] |
Full Idea: Where contradictions appear there is a correlation of contraries, which is relation. If a contradiction is imposed on the intelligence, it is forced to think of a relation to transform the contradiction into a correlation, which draws the soul higher. | |
From: report of Plato (works [c.375 BCE]) by Simone Weil - God in Plato p.70 | |
A reaction: A much better account of the dialectic than anything I have yet seen in Hegel. For the first time I see some sense in it. A contradiction is not a falsehood, and it must be addressed rather than side-stepped. A kink in the system, that needs ironing. |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
From: David Hilbert (On the Infinite [1925], p.184) | |
A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
12461 | We believe all mathematical problems are solvable [Hilbert] |
Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
From: David Hilbert (On the Infinite [1925], p.200) | |
A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
From: David Hilbert (On the Infinite [1925], p.195) | |
A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
Full Idea: Operating with the infinite can be made certain only by the finitary. | |
From: David Hilbert (On the Infinite [1925], p.201) | |
A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
From: David Hilbert (On the Infinite [1925], p.184) | |
A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
From: David Hilbert (On the Infinite [1925], p.186) | |
A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
From: David Hilbert (On the Infinite [1925], p.192) | |
A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
14502 | Plato's idea of 'structure' tends to be mathematically expressed [Plato, by Koslicki] |
Full Idea: 'Structure' tends to be characterized by Plato as something that is mathematically expressed. | |
From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects V.3 iv | |
A reaction: [Koslicki is drawing on Verity Harte here] |
17948 | Plato's Forms meant that the sophists only taught the appearance of wisdom and virtue [Plato, by Nehamas] |
Full Idea: Plato's theory of Forms allowed him to claim that the sophists and other opponents were trapped in the world of appearance. What they therefore taught was only apparent wisdom and virtue. | |
From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.118 |
20906 | Platonists argue for the indivisible triangle-in-itself [Plato, by Aristotle] |
Full Idea: The Platonists, on the basis of purely logical arguments, posit the existence of an indivisible 'triangle in itself'. | |
From: report of Plato (works [c.375 BCE]) by Aristotle - Coming-to-be and Passing-away (Gen/Corr) 316a15 | |
A reaction: A helpful confirmation that geometrical figures really are among the Forms (bearing in mind that numbers are not, because they contain one another). What shape is the Form of the triangle? |
3039 | When Diogenes said he could only see objects but not their forms, Plato said it was because he had eyes but no intellect [Plato, by Diog. Laertius] |
Full Idea: When Diogenes told Plato he saw tables and cups, but not 'tableness' and 'cupness', Plato replied that this was because Diogenes had eyes but no intellect. | |
From: report of Plato (works [c.375 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 06.2.6 |
556 | If there is one Form for both the Form and its participants, they must have something in common [Aristotle on Plato] |
Full Idea: If there is the same Form for the Forms and for their participants, then they must have something in common. | |
From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a |
563 | If gods are like men, they are just eternal men; similarly, Forms must differ from particulars [Aristotle on Plato] |
Full Idea: We say there is the form of man, horse and health, but nothing else, making the same mistake as those who say that there are gods but that they are in the form of men. They just posit eternal men, and here we are not positing forms but eternal sensibles. | |
From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 997b |
557 | A Form is a cause of things only in the way that white mixed with white is a cause [Aristotle on Plato] |
Full Idea: A Form is a cause of things only in the way that white mixed with white is a cause. | |
From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 991a |
565 | The Forms cannot be changeless if they are in changing things [Aristotle on Plato] |
Full Idea: The Forms could not be changeless if they were in changing things. | |
From: comment on Plato (works [c.375 BCE]) by Aristotle - Metaphysics 998a |
9607 | The greatest discovery in human thought is Plato's discovery of abstract objects [Brown,JR on Plato] |
Full Idea: The greatest discovery in the history of human thought is Plato's discovery of abstract objects. | |
From: comment on Plato (works [c.375 BCE]) by James Robert Brown - Philosophy of Mathematics Ch. 2 | |
A reaction: Compare Idea 2860! Given the diametrically opposed views, it is clearly likely that Plato's central view is the most important idea in the history of human thought, even if it is wrong. |
13263 | We can grasp whole things in science, because they have a mathematics and a teleology [Plato, by Koslicki] |
Full Idea: Due to the mathematical nature of structure and the teleological cause underlying the creation of Platonic wholes, these wholes are intelligible, and are in fact the proper objects of science. | |
From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
A reaction: I like this idea, because it pays attention to the connection between how we conceive objects to be, and how we are able to think about objects. Only examining these two together enables us to grasp metaphysics. |
13261 | Plato sees an object's structure as expressible in mathematics [Plato, by Koslicki] |
Full Idea: The 'structure' of an object tends to be characterised by Plato as something that is mathematically expressible. | |
From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.3 | |
A reaction: This seems to be pure Pythagoreanism (see Idea 644). Plato is pursuing Pythagoras's research programme, of trying to find mathematics buried in every aspect of reality. |
13265 | Plato was less concerned than Aristotle with the source of unity in a complex object [Plato, by Koslicki] |
Full Idea: Plato was less concerned than Aristotle with the project of how to account, in completely general terms, for the source of unity within a mereologically complex object. | |
From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.5 | |
A reaction: Plato seems to have simply asserted that some sort of harmony held things together. Aristotles puts the forms [eidos] within objects, rather than external, so he has to give a fuller account of what is going on in an object. He never managed it! |
593 | Plato's holds that there are three substances: Forms, mathematical entities, and perceptible bodies [Plato, by Aristotle] |
Full Idea: Plato's doctrine was that the Forms and mathematicals are two substances and that the third substance is that of perceptible bodies. | |
From: report of Plato (works [c.375 BCE]) by Aristotle - Metaphysics 1028b |
13260 | Plato says wholes are either containers, or they're atomic, or they don't exist [Plato, by Koslicki] |
Full Idea: Plato considers a 'container' model for wholes (which are disjoint from their parts) [Parm 144e3-], and a 'nihilist' model, in which only wholes are mereological atoms, and a 'bare pluralities' view, in which wholes are not really one at all. | |
From: report of Plato (works [c.375 BCE]) by Kathrin Koslicki - The Structure of Objects 5.2 | |
A reaction: [She cites Verity Harte for this analysis of Plato] The fourth, and best, seems to be that wholes are parts which fall under some unifying force or structure or principle. |
11237 | Only universals have essence [Plato, by Politis] |
Full Idea: Plato argues that only universals have essence. | |
From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4 |
11238 | Plato and Aristotle take essence to make a thing what it is [Plato, by Politis] |
Full Idea: Plato and Aristotle have a shared general conception of essence: the essence of a thing is what that thing is simply in virtue of itself and in virtue of being the very thing it is. It answers the question 'What is this very thing?' | |
From: report of Plato (works [c.375 BCE]) by Vassilis Politis - Aristotle and the Metaphysics 1.4 |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
17085 | A good explanation totally rules out the opposite explanation (so Forms are required) [Plato, by Ruben] |
Full Idea: For Plato, an acceptable explanation is one such that there is no possibility of there being the opposite explanation at all, and he thought that only explanations in terms of the Forms, but never physical explanations, could meet this requirement. | |
From: report of Plato (works [c.375 BCE]) by David-Hillel Ruben - Explaining Explanation Ch 2 | |
A reaction: [Republic 436c is cited] |
1651 | Plato wanted to somehow control and purify the passions [Vlastos on Plato] |
Full Idea: Plato put high on his agenda a project which did not figure in Socrates' programme at all: the hygienic conditioning of the passions. This cannot be an intellectual process, as argument cannot touch them. | |
From: comment on Plato (works [c.375 BCE]) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.88 | |
A reaction: This is the standard traditional view of any thinker who exaggerates the importance and potential of reason in our lives. |
3324 | Plato's whole philosophy may be based on being duped by reification - a figure of speech [Benardete,JA on Plato] |
Full Idea: Plato is liable to the charge of having been duped by a figure of speech, albeit the most profound of all, the trope of reification. | |
From: comment on Plato (works [c.375 BCE]) by José A. Benardete - Metaphysics: the logical approach Ch.12 | |
A reaction: That might be a plausible account if his view was ridiculous, but given how many powerful friends Plato has, especially in the philosophy of mathematics, we should assume he was cleverer than that. |
7503 | Plato never refers to examining the conscience [Plato, by Foucault] |
Full Idea: Plato never speaks of the examination of conscience - never! | |
From: report of Plato (works [c.375 BCE]) by Michel Foucault - On the Genealogy of Ethics p.276 | |
A reaction: Plato does imply some sort of self-evident direct knowledge about that nature of a healthy soul. Presumably the full-blown concept of conscience is something given from outside, from God. In 'Euthyphro', Plato asserts the primacy of morality (Idea 337). |
2173 | As religion and convention collapsed, Plato sought morals not just in knowledge, but in the soul [Williams,B on Plato] |
Full Idea: Once gods and fate and social expectation were no longer there, Plato felt it necessary to discover ethics inside human nature, not just as ethical knowledge (Socrates' view), but in the structure of the soul. | |
From: comment on Plato (works [c.375 BCE]) by Bernard Williams - Shame and Necessity II - p.43 | |
A reaction: anti Charles Taylor |
6000 | The goal is rationality in the selection of things according to nature [Diogenes of Babylon, by Blank] |
Full Idea: Diogenes of Babylon defined the goal to be rationality in the selection and rejection of the things according to nature. | |
From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
A reaction: This captures the central Stoic idea quite nicely. 'Live according to nature', but this always meant 'live according to reason', because that is (as Aristotle had taught) the essence of our nature. This only makes sense if reason and nature coincide. |
5999 | The good is what is perfect by nature [Diogenes of Babylon, by Blank] |
Full Idea: Diogenes of Babylon defined the good as what is perfect by nature. | |
From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
A reaction: This might come close to G.E. Moore's Ideal Utilitarianism, but its dependence on the rather uneasy of concept of 'perfection' makes it questionable. Personally I find it appealing. I wish we had Diogenes' explanation. |
9274 | Plato's legacy to European thought was the Good, the Beautiful and the True [Plato, by Gray] |
Full Idea: Plato's legacy to European thought was a trio of capital letters - the Good, the Beautiful and the True. | |
From: report of Plato (works [c.375 BCE]) by John Gray - Straw Dogs 2.8 | |
A reaction: It seems to have been Baumgarten who turned this into a slogan (Idea 8117). Gray says these ideals are lethal, but I identify with them very strongly, and am quite happy to see the good life as an attempt to find the right balance between them. |
94 | Pleasure is better with the addition of intelligence, so pleasure is not the good [Plato, by Aristotle] |
Full Idea: Plato says the life of pleasure is more desirable with the addition of intelligence, and if the combination is better, pleasure is not the good. | |
From: report of Plato (works [c.375 BCE]) by Aristotle - Nicomachean Ethics 1172b27 | |
A reaction: It is obvious why we like pleasure, but not why intelligence makes it 'better'. Maybe it is just because we enjoy intelligence? |
17947 | Plato decided that the virtuous and happy life was the philosophical life [Plato, by Nehamas] |
Full Idea: Plato came to the conclusion that virtue and happiness consist in the life of philosophy itself. | |
From: report of Plato (works [c.375 BCE]) by Alexander Nehamas - Eristic,Antilogic,Sophistic,Dialectic p.117 | |
A reaction: This view is obviously ridiculous, because it largely excludes almost the entire human race, which sees philosophy as a cul-de-sac, even if it is good. But virtue and happiness need some serious thought. |
6015 | Plato, unusually, said that theoretical and practical wisdom are inseparable [Plato, by Kraut] |
Full Idea: Two virtues that are ordinarily kept distinct - theoretical and practical wisdom - are joined by Plato; he thinks that neither one can be fully possessed unless it is combined with the other. | |
From: report of Plato (works [c.375 BCE]) by Richard Kraut - Plato | |
A reaction: I get the impression that this doctrine comes from Socrates, whose position is widely reported as 'intellectualist'. Aristotle certainly held the opposite view. |
6001 | Justice is a disposition to distribute according to desert [Diogenes of Babylon, by Blank] |
Full Idea: Diogenes of Babylon defined justice as the disposition which distributes to everyone what he deserves. | |
From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon | |
A reaction: The questions that arise would be 'what does a new-born baby deserve?', and 'what do animals deserve?', and 'does the lowest and worst of criminals deserve anything at all?' |
2912 | Plato is boring [Nietzsche on Plato] |
Full Idea: Plato is boring. | |
From: comment on Plato (works [c.375 BCE]) by Friedrich Nietzsche - Twilight of the Idols 9.2 |
1526 | Almost everyone except Plato thinks that time could not have been generated [Plato, by Aristotle] |
Full Idea: With a single exception (Plato) everyone agrees about time - that it is not generated. Democritus says time is an obvious example of something not generated. | |
From: report of Plato (works [c.375 BCE]) by Aristotle - Physics 251b14 |