44 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. |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 16007 | I assume existence, rather than reasoning towards it [Kierkegaard] |
| Full Idea: I always reason from existence, not towards existence. | |
| From: Søren Kierkegaard (Philosophical Fragments [1844], p.40) | |
| A reaction: Kierkegaard's important premise to help show that theistic proofs for God's existence don't actually prove existence, but develop the content of a conception. [SY] |
| 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] |
| 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 |
| 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 |
| 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 |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 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 |
| 16013 | Nothing necessary can come into existence, since it already 'is' [Kierkegaard] |
| Full Idea: Can the necessary come into existence? That is a change, and everything that comes into existence demonstrates that it is not necessary. The necessary already 'is'. | |
| From: Søren Kierkegaard (Philosophical Fragments [1844], p.74) | |
| A reaction: [SY] |
| 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. |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 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 |
| 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. |
| 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 |