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. |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| Full Idea: The master science can be thought of as the theory of sets with the entire range of physical objects as ur-elements. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: This sounds like Quine's view, since we have to add sets to our naturalistic ontology of objects. It seems to involve unrestricted mereology to create normal objects. |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| Full Idea: In present-day mathematics, it is set theory that serves as the background theory in which other branches of mathematics are developed. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: [He cites Bourbaki as an authority for this] See Benacerraf for a famous difficulty here, when you actually try to derive an ontology from the mathematicians' working practices. |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| Full Idea: If you wonder why multiplication is commutative, you could prove it from the Peano postulates, but the proof offers little towards an answer. In set theory Cartesian products match 1-1, and n.m dots when turned on its side has m.n dots, which explains it. | |
| From: Penelope Maddy (Sets and Numbers [1981], II) | |
| A reaction: 'Turning on its side' sounds more fundamental than formal set theory. I'm a fan of explanation as taking you to the heart of the problem. I suspect the world, rather than set theory, explains the commutativity. |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| Full Idea: The standard account of the relationship between numbers and sets is that numbers simply are certain sets. This has the advantage of ontological economy, and allows numbers to be brought within the epistemology of sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Maddy votes for numbers being properties of sets, rather than the sets themselves. See Yourgrau's critique. |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| Full Idea: I propose that ...numbers are properties of sets, analogous, for example, to lengths, which are properties of physical objects. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: Are lengths properties of physical objects? A hole in the ground can have a length. A gap can have a length. Pure space seems to contain lengths. A set seems much more abstract than its members. |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| Full Idea: A set of things is located where the aggregate of those things is located, ...but a number is simultaneously located at many different places (10 in my hand, and a baseball team) ...so numbers seem more like universals than particulars. | |
| From: Penelope Maddy (Sets and Numbers [1981], III) | |
| A reaction: My gut feeling is that Maddy's master idea (of naturalising sets by building them from ur-elements of natural objects) won't work. Sets can work fine in total abstraction from nature. |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| Full Idea: I am not suggesting a reduction of number theory to set theory ...There are only sets with number properties; number theory is part of the theory of finite sets. | |
| From: Penelope Maddy (Sets and Numbers [1981], V) |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| Full Idea: On the structuralist interpretation, theorems of analysis concerning the real numbers R are about all complete ordered fields. So R, which appears to be the name of a specific structure, is taken to be a variable ranging over structures. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: Since I am beginning to think that nearly all linguistic expressions should be understood as variables, I find this very appealing, even if Burgess hates it. Terms slide and drift, and are vague, between variable and determinate reference. |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| Full Idea: One might meet the 'Van Inwagen Problem' by saying that the intrinsic properties of the object playing the role of 2 will differ from one model to another, so that no statement about the intrinsic properties of 'the' real numbers will make sense. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: There seems to be a potential confusion among opponents of structuralism between relations at the level of actual mathematical operations, and generalisations about relations, which are captured in the word 'patterns'. Call them 'meta-relations'? |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| Full Idea: It is to set theory that one turns for the very definition of 'structure', ...and this creates a problem of circularity if we try to impose a structuralist interpretation on set theory. | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: This seems like a nice difficulty, especially if, like Shapiro, you wade in and try to give a formal account of structures and patterns. Resnik is more circumspect and vague. |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| Full Idea: Abstract algebra, such as group theory, is not concerned with the features common to all models of the axioms, but rather with the relationships among different models of those axioms (especially homomorphic relation functions). | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §1) | |
| A reaction: It doesn't seem to follow that structuralism can't be about the relations (or patterns) found when abstracting away and overviewing all the models. One can study family relations, or one can study kinship in general. |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| Full Idea: The 'Van Inwagen Problem' for structuralism is of explaining how a mathematical relation (such as set membership, or the ratios of an ellipse) can fit into one of the three scholastics types of relations: are they internal, external, or intrinsic? | |
| From: John P. Burgess (Review of Chihara 'Struct. Accnt of Maths' [2005], §5) | |
| A reaction: The difficulty is that mathematical objects seem to need intrinsic properties to get any of these three versions off the ground (which was Russell's complaint against structures). |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| Full Idea: The popular challenges to platonism in philosophy of mathematics are epistemological (how are we able to interact with these objects in appropriate ways) and ontological (if numbers are sets, which sets are they). | |
| From: Penelope Maddy (Sets and Numbers [1981], I) | |
| A reaction: These objections refer to Benacerraf's two famous papers - 1965 for the ontology, and 1973 for the epistemology. Though he relied too much on causal accounts of knowledge in 1973, I'm with him all the way. |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| Full Idea: Number words are not like normal adjectives. For example, number words don't occur in 'is (are)...' contexts except artificially, and they must appear before all other adjectives, and so on. | |
| From: Penelope Maddy (Sets and Numbers [1981], IV) | |
| A reaction: [She is citing Benacerraf's arguments] |
| 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] |
| 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 |
| 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? |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |