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Information about 1101e4short

Published on April 30, 2008

Author: Marietta1

Source: authorstream.com

Slide1:  Now, how do we get from virtue to geometry? From something that is perceived as not requiring technical knowledge (perhaps) to something that is really very technical? Slide2:  The thematic link goes like this: Meno is not so much concerned with virtue - which he thinks he understands well enough. He is wondering about the nature of the mind, and the nature of knowledge, more or less. Slide3:  Meno’s little puzzle: For anything, F, either one knows F or one does not know F. If one knows F, then one cannot inquire about F. If one does not know F, then one cannot inquire about F. Therefore, for all F, one cannot inquire about F. http://plato.stanford.edu/entries/plato-metaphysics/#10 Slide4:  Definitions: Is it reasonable to ask for them? Well, yes. Is it reasonable to insist on them? Slide5:  A famous passage from Wittgenstein’s book, Philosophical Investigations §65: Here we come up against the great question that lies behind all these considerations. - For someone might object against me: “You take the easy way out! You talk about all sorts of language-games, but have nowhere said what the essence of a language-game, and hence of language, is: what is common to all these activities, and what makes them into language or parts of language. So you let yourself off the very part of the investigation that once game you yourself most headache, the part about the general form of propositions and of language.” Slide6:  . . .And this is true. - Instead of producing something common to all that we call language, I am saying that these phenomena have no one thing in common which makes us use the same word for all, - but that they are related to one another in many different ways. And it is because of this relationship, or these relationships, that we call them all “language”. I will try to explain this. Slide7:  §66 Consider for example the proceedings that we call “games”. I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? - Don’t say: “There must be something common, or they would not be called ‘games’” - but look and see whether there is anything common to all. - For if you look at them you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. To repeat: don’t think, but look! - Look for example at board-games, with their multifarious relationships. Now pass to card-games; here you find many correspondences with the first group, but many common features drop out, and others appear. Slide8:  Are they all ‘amusing’? Compare chess with noughts and crosses. Or is there always winning and losing, or competition between players? Think of patience. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared. Look at the parts played by skill and luck; and at the difference between skill in chess and skill in tennis. Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear. Slide9:  And the result of this examination: is we see a complicated network of similarities, overlapping and criss-crossing; sometimes overall similarities, sometimes similarities of detail. §67. I can think of no better expression to characterize these similarities than “family resemblances”; for thevarious resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and crisscross in the same way. - And I shall say: ‘games’ form a family. Slide10:  And for instance the kinds of number form a family in the same way. Why do we call something a “number”? Well, perhaps because it has a - direct - relationship with several things that have hitherto been called number; and this can be said to give it an indirect relationship to other things we call the same name. Slide11:  Plato thinks of the world we live in as having the same scientific interest that a picture in a geometry book has for a geometer. Namely, not much interest at all. Turning this point around. Plato thinks scientists who are empiricists - who look - are like Obtuse Ollie (a character from the geometry book I learned from, who always got everything wrong.) “It is clear from looking at the picture.” - Obtuse Ollie “It is clear from observing the world.” - Empiricist scientist Slide12:  “I cannot imagine a unified and reasonable theory which explicitly contains a number which the whim of the Creator might just as well have chosen differently, whereby a qualitatively different lawfulness of the world would have resulted. . . A theory which in its fundamental equations explicitly contains a constant would have to be somehow constructed from bits and pieces which are logically independent of each other; but I am confident that this world is not such that so ugly a construction is needed for its theoretical comprehension.” - A. Einstein Slide13:  And: “How can it be that mathematics, being after all a product of human thought independent of existence, is so admirably adapted to the objects of reality?” - A. Einstein It seems like Albert is hinting that the answer might be: there is a weird (at least intimate) link between human mathematical thought and the fundamental nature of reality. [To be fair: Einstein wasn’t actually a Platonist, let alone a Pythagorean. But he took the questions they asked seriously.] Slide14:  “Do you think it is possible to understand the nature of the soul, rationally, without understanding the nature of the whole Universe? - No.” - Plato, Phaedrus You can draw a pessimistic conclusion: so we aren’t going to understand the nature of the soul any time soon. Or an optimistic one: if only we could understand the soul, it would be the key to everything else. Slide15:  Confused? Good. Let me pose a problem to illustrate the Platonic intuition behind Einstein’s outlook:* Imagine that you are standing on the bank of a river containing two islands and five bridges connecting both banks and both islands . . . Confused again? As Obtuse Ollie would say, it’s clear from looking at the picture . . . * I got this puzzle from Bas Van Frassen, Laws and Symmetry Slide16:  Bank Bank Islands Slide17:  There has been a flood, as a result of which there is a 50% chance that each bridge is washed out. (That is, for each individual bridge, there is an independent 50% chance it is washed out.) The question: What are the odds that enough bridges remain standing, in suitable configurations, for a pedestrian on either bank to cross the river without getting her shoes wet? Slide18:  Bank Bank Islands Slide19:  Working out the probabilities is a bit tedious. (And I promised: no maths.) The neat thing about the problem is that, if you look at it the right way, you can instantly see the solution. You have to recognize a certain symmetry. Namely, that the pedestrian’s problem is equivalent to another one. Slide20:  The Pedestrian’s Problem (top to bottom) Entry Entry Connector Exit Exit The Boatman’s Problem (left to right) Entry Exit Connector Entry Exit Slide21:  P: Either the pedestrian can cross or the boatman can cross (not both and not neither). C: But the pedestrian problem and the boatman problem are the same problem. They are symmetrical and equivalent. Therefore, there is a 50/50 chance that the pedestrian can avoid getting her shoes wet. (Get it?) Slide22:  You can think it through later on your own time. For now, what is important is that we have migrated from mathematics to dialectic. The proof I offered, to get the answer, is dialectical. Plato would say: even deeper than mathematics - underlying all the math you would have to do to solve the probability problem in the standard way - there is dialectic. Or, rather, a need for dialectic. There are necessary relations between concepts, governed by logic. Slide23:  Consider the so-called Principle of Sufficient Reason: Everything happens for a reason. Nothing happens for no reason whatsoever. Slide24:  Which identical haystack will he choose? Slide25:  GUT* x GUT y WWZD? Let’s let Zeus stand in as our Einsteinian creator. (He sort of looks like Albert.) But, mind you, ‘z’ is just a variable. * Grand Unified Theory Slide26:  WWZD? And, come to think of it, this was Euthyphro’s problem as well, trying to have Zeus pick ethical theories. . . Slide27:  Descending from these heady, abstract heights, a few final words about ethics in the “Meno”: Meno & Anytus are not so different from one another, in Socrates’ eyes. They both sort of think they know it all; even while they sort of think nothing can be known. Slide28:  And the dialogue ends on a very ambivalent note. The question of whether virtue can be taught is left hanging by a question mark. It seems it ought to be teachable, since it is a form of knowledge. But if it is teachable, there ought to be teachers, which does not seem to be the case. Slide29:  The explanation of how good men are possible: “S: So true opinion is in no way an inferior guide to action than knowledge. This is what we overlooked in our investigation of the nature of virtue, when we said only knowledge can culminate in proper action; for true opinion can do just as well.” (p. 102) Slide30:  Plato, of course, is having none of it. Luck - like those statues of Daedalus he is always going on about - can run away. And then where will you be? You want to acquire virtue? That is, you want to succeed? Study mathematics. And dialectic. And be prepared for some surprising conclusions. “Yes, Yes, I know that, Sidney. . .everybody knows that!. . . But look: Four wrongs squared, minus two wrongs to the fourth power, divided by this formula, do make a right.” - Gary Larson, The Far Side

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