Meno - Shape
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"Shape is that which alone of existing things always follows color."
"A shape is that which limits a solid; in a word, a shape is the limit of a solid."
In the play Meno, written by Plato, there is a point in which Meno asks that Socrates give a definition of shape. In the end of it, Socrates is forced to give two separate definitions, for Meno considers the first to be foolish. As the two definitions are read and compared, one is forced to wonder which, if either of the two, is true, and if neither of them are true, which one has the most logic. When comparing the first definition of shape: "that which alone of existing things always follows color," to the second definition: "the limit of a solid", it can be seen that the difference in meaning between the two is great. Not only in the sense that the first is stated simply and can be defended easily, while the later is more difficult to comprehend and back up; but also in the sense that the second would have to involve the defiance of mathematical theories and/or proofs in order to stand true, while the first does not. It should also be noted that in the first definition, the word "a" is never mentioned. Socrates is not making a statement about "a shape" or "a color", but about shape and color themselves. In the definition given to please Meno, Socrates' words are "a shape" and "a solid". It can be taken from earlier discussions in the play that the second definition is simply a definition of a shape, rather than a definition of shape in and of itself.
In the simple sentence that Socrates originally gives to Meno, he has not given then definition of a shape, rather he has given the definition of the term shape. For example, if a person was asked what a triangle is, the response would most likely be that it is a shape, but shape would never be defined as shape itself. It is simply an object that falls under the category of shape. Therefore, in one sentence, Socrates has put a definition to shape, for without color there can be no shape, there could not even be a shape to fall under the category that would have once been known as "shape". None of the examples that Socrates and Meno discussed could prove the definition false.
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Meno Shape Discussions Limit Category Always Sentence Definitions Wonder
If something is round, for instance, then it is a shape, and a shape cannot exist without color. Therefore, shape must be formed by color, proving that color must precede shape and that shape must proceed color. The same proves true of a square, trapezoid, cube, or any other shape that exists. For, a solid must have a specific area and volume, and the naked eye can tell that the solid is there and has color, because if it had no color it would not be visible, therefore it would not be known to exist. In order for a shape that is not a solid, such as a line, to be seen, it must be drawn or made visible in some other way. As soon as that occurs, color is what has formed it.
However, Socrates' statement is also disputable. Take the matter of the geometric plane. It is not visible. It can be represented for any purpose by drawing it, but as soon as it is drawn, it is no longer a plane for restrictions have been put upon it. A plane continues infinitely in all directions. Although geometric planes cannot be seen, it is a mathematical fact that they exist, although it is not known for certain if they occupy a certain amount of space. Because it has these properties, it is indeed a shape, but it is a shape that cannot be seen, an infinite shape, and one that requires no color to be called so. But the mystery of the geometric plane in relationship to this definition has not been solved, for an object such as a circle cannot exist without a geometric plane, but a geometric plane can exist with an object. So, since it has been stated by Socrates that shape cannot exist without color, what should be said when a circle - existing solely because of color - is on a geometric plane? The geometric plane must exist, as the circle is on it and as the circle cannot exist without it, but is the plane considered a shape since it's area is infinite? There is certainly the possibility that there are those who do not think of it as a shape because it has no restrictions put on it, but if this was so, why did Socrates not include this in his definition? It could have possibly been because by shape he meant objects with definite form.
There is the possibility that, in the mind of Socrates, his definition is unflawed, for it may have been that he did not view a geometric plane as a shape, but only as something that has an area which extends infinitely. If this was the case, then his statement is indisputable. However, if that was not the case, he may have stated it for the purpose of discovering how far he could stretch Meno's logic. However, there is also the slight possibility that Socrates did not consider all of the options and examples that were filed under the category of shape, and therefore he could very well be wrong. In this situation it is difficult to tell how truthful this definition is, for what was going on in Socrates' mind at that time cannot be known to us. It is for each to draw a conclusion from.
Then the question arises as to the truth and logic involved in Socrates' second definition, which is given purely to please Meno. The problem that occurs when this statement is made is that it is mathematically impossible to have a finite number of shapes; therefore, there are an infinite amount of solids, meaning that a solid cannot be limited. A shape can look like anything; it can have any form, but the instant that even the smallest part of that shape is moved or shifted, it becomes a different shape altogether. Several examples exist that can prove this statement untrue. Take the word "round", which Socrates used as an aid in an example that was given to Meno in a previous part of the text. A ball, for instance, is a round solid (round being any shape that has a circumference), so the conclusion can be reached that the ball is a solid and round is its shape, therefore the shape is limited by only the solidity of the ball. Thus, this does not support Socrates' definition, for it shows that the shape is limited by the solid, not that the solid is limited by the shape. In addition to this, there is another dispute against this definition of shape using the word round. A circle is round, and yet it is not a solid. Therefore, this statement does not define the term shape; rather it defines on a certain type of shape, a solid shape.
The logic that Socrates had in stating his second answer in those particular terms could have been several. It would have followed the theme that is seen throughout the play of the Meno and Socrates mocking each other. Socrates knew that the answer that would please Meno the most would be the one that sounded the smartest but made the least amount of sense. However, Meno does not seem to realize this, and accepts Socrates' answer. This should have made it especially interesting for Socrates, for he had agreed to give Meno this second definition in the form of Gorgias. Meno is always agreeing with him, and incorporates his points into many of the conversations that he tends to hold. Not only is Socrates secretly mocking Meno, he is also mocking Gorgias.
At first appearance, both definitions seem to hold some weight. However, upon further investigation, the second can be ruled out as truth altogether. The first holds much weight, and definitely contains a higher percentage of truth within it than the second. However, the debate about whether all shapes can fall under his original definition is still debatable; having many strong points, but one weak point. Nonetheless, the conclusion that, if one of the two had to be chosen as the truth, the first definition of Socrates would most certainly emerge victorious.
Plato's Euthyphro and Meno
Reading and Essays Questions
Exeter College, Oxford University, HT13
This is a syllabus for eight weeks work for the first-year course on Plato’s Meno and Euthyphro. Please email your assignments to me 24h before the tutorials. I am afraid that I will not be able to write comments on essays that are handed in later than this (unless – for exceptional reasons, e.g. illness – I have agreed to this beforehand).
You are required to do at least five essays in the course of the term, plus one set of gobbets. You should each write an essay for the first tutorial. In week 7, you will write gobbets (comments on passages) instead of an essay. In any week when you do not do an essay/gobbets, you should do the reading and think about the question in advance of the tutorial, so that you are ready to discuss the essay question in the tutorial.
We shall focus each week on one of the essays in the tutorial, alternating between you and the other student who will be attending the tutorials with you. If we are focusing on your essay, I’ll ask you to summarize it at the start of the tutorial. If we are focusing on someone else’s essay, you should have read her/his essay before the tutorial, and have spent some time thinking about whether you agree with it and how it might be improved.
You will do a collection on this paper at the beginning of MT.
Please do bring copies of the relevant text (Euthyphro and/or Meno) to the tutorials.
Some notes on how to approach the readings (from Ursula Coope)
It is essential to read, and think carefully about, the two dialogues: Meno and Euthyphro. I have also suggested some ‘optional secondary reading’. Doing some of these readings will be helpful. I have starred the things I particularly recommend. In general Dominic Scott’s book Plato’s Meno is a very good, recent, book on the Meno. In philosophy, however, it is always important to spend quite a bit of time thinking carefully about the questions. So don’t get too bogged down in the reading. If it starts to be the case that you are spending more time trying to understand what one of the secondary authors says than trying to understand Plato, then you should put the secondary author aside and just try to think for yourself about what Plato says.
(There’s a longer reading list, available on the web from the philosophy faculty web site – go to ‘undergraduates’ then ‘reading lists’ in Weblearn.)
Some notes on writing philosophy essays (from Ursula Coope)
In commenting on philosophy essays, tutors often find themselves saying that the student needs to write more clearly. It can be hard to know what this means when you are just beginning. The point is that, although in philosophy we often deal with big and difficult questions, in order to make progress with them we need to try to answer them in as simple and down-to-earth a way as possible. (This is what professional philosophers are trying – perhaps not always very successfully – to do, not simply what you are being asked to do.)
One way to do this, sometimes, is to try to give concrete examples when you are making a general point. So, for example, suppose I claim that it is possible to understand a word without being able to define it. I might then give an example: ‘for example, I can’t define the word red, but I know what ‘red’ means, in the sense that I can pick out red objects from objects of other colours’. Notice how giving this example forced me to think a bit more about the general claim I was making: in what sense do I understand what ‘red’ means? (In giving the example I spelt this out by saying that I could pick out red objects. But is the fact that I can do this really enough to show that I know what ‘red’ means?)
Another thing that is different about philosophy essays, is that you are typically asked not only to explain Plato’s views, but also to assess them in some way. In the question for the first week, for instance, you are asked whether a certain claim can be defended against Socrates’s objections. To answer this, you need first to understand what Socrates’ objections are (this itself is not an easy task), but you are also asked how one might reply to Socrates’ objections. That requires you to think for yourself about whether Socrates’ arguments are good ones, how you might answer them (and perhaps also even, how he might reply to your answer). In the second week, I have asked you to write an essay which answers three questions. The first question is about what Socrates says in the Meno and the Euthyphro, but the other two questions require you to think critically about the assumptions that lie behind what he says.
Good philosophy essays need not be long. About 1000-1500 words is usually enough.
On the web, there is some very good advice about writing philosophy from a distinguished philosopher in the US: http://www.jimpryor.net/teaching/guidelines/writing.html
I recommend that you read this, but bear in mind that not everything he says is relevant to you: he is writing for US students who are producing finished term papers for continuous assessment. You are producing less finished weekly tutorial papers for us to discuss (so you don’t need to write multiple drafts etc).
Requirements for the different versions of mods
Euthyphro: Greek text in OCT, ed. E.A. Duke et al. (Oxford 1995). The set translation is in The Last Days of Socrates, tr. Tredennick & Tarrant (Penguin revised 1993).
Meno: Greek text in OCT, ed. J. Burnet (Oxford 1903). Set translation: Meno in R.W. Sharples Plato: Meno (Aris & Phillips 1985): introduction, text, translation, and commentary.
If you are doing Course IA or IC you are expected to have read Meno in Greek and Euthyphro in English. If you are doing IIA, you are expected to read both works in translation. If you are taking IB or IIB, you are expected to have read Meno 70a-86d2 in Greek and the rest of Meno and Euthyphro in English.
Some notes on how to write Gobbets (from the Lit. Hum. handbook)
A gobbet is a short commentary on a passage.
For philosophy gobbets, the first requirement is to identify the argumentative context of the passage, e.g. `This passage occurs in Socrates' response to Thrasymachus' claim that the ruler properly so-called is expert in promoting his own advantage; in reply Socrates urges that all expertise aims to promote the advantage of that on which the expertise is exercised, hence the expert ruler must aim to promote, not his own advantage, but that of the subject'.
You should then set out the specific contribution of the passage to the argumentative context, e.g. a sub-argument (in which case the steps of the argument should be set out), or a distinction (in which case you should clearly state what is being distinguished from what), or the introduction of some key concept, which should be clearly elucidated. Where appropriate, elucidation should be followed by criticism; thus if the passage contains a fallacious or unsound argument, or a faulty distinction, the flaw should be briefly identified. If the significance of the passage goes beyond the immediate argumentative context (e.g. in introducing a concept which is important for a wider range of contexts) that wider significance should be indicated. Wider significance may be internal to the work as a whole, or may extend beyond it, for instance by relating to some theme central to the thought of the author (such as Plato's Theory of Forms or Aristotle's categories) or to some important topic in modern philosophy.
Your primary focus in philosophy gobbets should be on argumentative and conceptual content. Details of sentence construction, vocabulary etc should be discussed only in so far as they affect the content thus conceived. The same goes for the identification of persons etc named in the passage; note that where the passage is taken from a Platonic dialogue it will usually be relevant to identify the speaker(s).
It is vitally important to observe the time constraints imposed by the number of passages to be translated and commented on. Brevity, relevance and lucidity are crucial. It is especially important not to be carried away in expounding the wider significance of the passage (see above); a gobbet should not expand into an essay on the Theory of Forms or the problem of universals. Use your own judgement on how much you can afford to put in.
Topics and Readings
Week 1. Socrates’ Arguments against Euthyphro’s Definitions of Piety
This week we look at what Socrates is trying to do in the Euthyphro. What is Socrates’s method? Why does he seek definitions of ethical concepts? What kind of definitions is he looking for?
As you read Plato's text, I would recommend keeping track of each of Euthyphro's definitions of piety. For each definition, try and think about whether it fails to satisfy Socrates, and why. What would Socrates consider a successful definition of piety? Why does he think it is important to find such definition? More generally, what is the so-called Socratic 'elenchus'?
Could the definition of ‘the holy’ as ‘what is approved of by all the gods’ be defended against Socrates’ objections?
(1) Read the Euthyphro carefully.
Optional secondary readings
(2) Benson, H. 'Socratic Method', in D. Morrison (ed.), The Cambridge Companion to Socrates (CUP: Cambridge, 2011), pp. 179-200.
(3) *Geach, P. ‘Plato’s Euthyphro: An Analysis and Commentary’, Monist 50 (1966), 369-82
(4) Cohen, S. M. ‘Socrates on the Definition of Piety: Euthyphro 10A-11B’,Journal of the History of Philosophy 9 (1971), 1-13; reprinted in Vlastos (ed.), Socrates
(5) *Patzig, G. ‘Logic in the “Euthyphro”’, in S.M. Stern, A. Hourani, and V. Brown (eds),Islamic Philosophy and the Classical Tradition (Cassirer 1972).
Optional background reading
(6) Woodruff, P. 'Plato's Shorter Ethical Works', in Stanford Encyclopedia of Philosophy.
Week 2. Socratic definition
This week we take a closer look at one putative problem with Socrates’s demand for definitions. Socrates claims that Euthyphro cannot know whether his action is piuous until he knows what piety is. Similarly, he claims that he and Meno cannot know whether virtue is teachable until they know what virtue is. Try and spell out what grounds these claims, for Socrates. Do they depend on some specific view of knowledge? Is this a good view? How does this connect with Socrates's demand for definitions?
What requirements does Socrates impose on definition in the Euthyphro and the Meno? Is it true that, if a word has meaning, it must be definable in this way? Are there any definitions that satisfy these requirements?
(1) * Euthyphro.
(2) * Meno 70a-80e, 86d-e.
(2) Crombie, I. M, pp. 90-3 of ‘Socratic Definition’, Paideia 1976 (Special Plato Issue); reprinted as pp. 187-92 of Day, Plato’s Meno in Focus.
(3) * Vlastos, G. ‘What Did Socrates Understand by his “What is F?” Question?’, in Vlastos, Platonic Studies (Princeton 1981).
(4) * Nehamas, A. Part I of ‘Meno’s Paradox and Socrates as a Teacher’, Oxford Studies in Ancient Philosophy 3 (1985), 1-30; reprinted in Benson (ed.), Essays on the Philosophy of Socrates, and in J. Day, Plato’s Meno in Focus.
(5) Irwin, T. Plato's Ethics (OUP: Oxford, 1995), Sections 12-18, and 88-91.
(6) Brickhouse, T. and Smith, N. The Philosophy of Socrates (Westview Press: Oxford, 2000), Chapter 3.
(7) Wolfsdorf, D. 'The Socratic Fallacy and the Epistemological Priority of Definitional Knowledge', in Apeiron 31 (2011), pp. 35-68). [This is a very thorough examination of the Socratic Fallacy, with good summaries of the various positions commentators have taken.]
Week 3. Desire and the good
In a number of Platos' dialogues, Socrates makes some extremely interesting, and controversial, psychological claims. This week we will be examining what the Meno tells us about this psychological theory and how it relates to Socrates's broader philosophical beliefs.
Explain Socrates’ argument that no one desires what is bad. If you were in Meno’s position, how might you answer it? Could Socrates defend his argument against your reply?
(1) Meno 77b-78c.
(2) * Plato's Protagoras, 352a-358e.
(3) * Plato's Gorgias, 467c-468e. [How is this argument similar to Meno 77c-78b? How is it different? Compare, in particular, 77d7-e4].
(4) Bobonich, C. 'Socrates and Eudaimonia', in The Cambridge Companion to Socrates, pp 293- 332. [An excellent introduction to Socratic psychology – longish, but also easy to read.]
(3) Santas, G. X. ‘The Socratic Paradoxes’, Philosophical Review 73 (1964), 147-64; reprinted with revisions as Chapter 6 of his Socrates.
(4) Walsh, J. J. Aristotle’s Conception of Moral Weakness (Columbia 1964), ch. 1; reprinted as ‘The Socratic Denial of Akrasia’, in Vlastos (ed.), The Philosophy of Socrates.
(5) Irwin, T. Plato’s Moral Theory (Oxford 1977), pp. 78-82.
(6) * Scott, D. Plato’s Meno, ch4.
Week 4. Meno’s Paradox
This week we look at Meno's Paradox, which is supposed to show that inquiry is impossible. Carefully consider and compare Meno's (80d6-8) and Socrates's (80e1-5) formulations of the paradox. Do they differ significantly? Does any of them count as a paradox? Why? In your essay, make clear what definition of 'paradox' you are working with.
‘Which of the things that you don’t know will you suppose that it is, when you are searching for it? And even if you do come across it, how are you going to know that this is the thing you didn’t know?’ (Meno, 80d6-8). Is either of these a good reason for thinking that enquiry is impossible?
(1) Meno 79e-86c.
(2) * Fine, G. ‘Inquiry in the Meno’, in R. Kraut (ed.) The Cambridge Companion to Plato.
(3) * Nehemas, A. ‘Meno’s paradox and Socrates as a teacher’ Oxford Studies in Ancient Philosophy, 3, 1985. Reprinted in Jane Day (ed.), Plato’s Meno in Focus.
(4) * Scott, D. Plato’s Meno, Part 2, Chapters 6 and 7.
Week 5. The Theory of Recollection and the Immortality of the Soul
This week we consider Plato's theory of recollection. What's the theory? How does it relate to Meno's paradox? Does it imply that the soul is immortal? Or does it presuppose that the soul is immortal? Why?
‘The experiment with the slave proves that we have the capacity for knowledge, but not that the soul is immortal.’ Discuss.
(1) Meno 81a-86c.
(2) Plato's Phaedo 723-84b and Phaedrus 245c-249d [Two statements of the theory of recollection; compare them with the Meno's.]
(3) Readings for last week.
(4) * Scott, D. Plato’s Meno, Part 2, Chapters 8-10.
Week 6. Knowledge (Episteme) and Opinion (Doxa)
A common, although controversial, modern definition of knowledge is “justified, true belief”. A true belief falls short of knowledge, then, if it lacks adequate justification. At first glance, Socrates' view that the belief becomes knowledge only when it is tied down by an “aitias logismos” (98a) seems quite close to this modern account. This week we will consider whether or not, on closer inspection, this is indeed the case.
What is the role, in the Meno, of the distinction between knowledge and true belief? Does the Meno provide an adequate account of this distinction?
(1) Meno 85b-86c, 96d-end.
(2) Burnyeat, M. ‘Socrates and the jury: paradoxes in Plato’s distinction between knowledge and true belief’ Proceedings of the Aristotelian Society Suppl, v. 54 (1980), pp. 173-91. [Burnyeat argues that Plato's distinction is between true belief and understanding, where the latter requires more than justification (e.g. I have a justified, true belief that Einstein's theory of relativity is true, but I don't understand it).]
(3) *Scott, D. Plato’s Meno, Chapter 14.
(4) Fine, G. 'Knowledge and True Belief in the Meno', in Oxford Studies in Ancient Philosophy 27 (Winter 2004), pp. 41-81. [Fine argues that knowledge in the Meno is closer to justified true belief than is often assumed.]
Week 7. Virtue (Arete) and Knowledge (Episteme)
Assignment for this week
Two gobbets (to be distributed nearer the time).
Question to think about
Does the Meno provide any good arguments for or against the view that virtue is knowledge?
(1) Meno 86c-96d.
(2) Plato's Laches 194c-201c, Gorgias 466a-479d, and Protagoras 352a-362a.
(3) Devereux, D. T. ‘Nature and Teaching in Plato’s Meno’, in Phronesis 23 (1978), pp. 118-26. (4) * Wilkes, K. V. ‘Conclusions in the Meno’, Archiv für Geschichte der Philosophie 61 (1979), pp. 143-53; reprinted in Day, Plato’s Meno in Focus.
(4) T. Irwin, Plato’s Ethics, sections 96-103.
Week 8. Hypotheses and Philosophical Method in the Meno
This week we will consider what philosophical method is in play in the Meno, if any.
What should we conclude from the Meno about the teachability of virtue?
How seriously should we take the suggestion at the end of the Meno that civic excellence is a matter of 'divine dispensation'?
(1) Meno 86c-96d.
(2) * Wilkes, K. V. ‘Conclusions in the Meno’, listed under “Week 7” above.
(3) * D. Scott, Plato’s Meno, chapters 12-13.