Plato's point is made with a line, not with a pair of numerical ratios. But this is what we should expect given the predominantly geometrical (i.e. non-arithmetized) nature of the mathematics of Plato's (and Euclid's) day. If Euclid had wanted to express the fact that 2 : 4 :: 4 : 8, he would have drawn two unequally divided line segments, thus:
This 5 page paper compares the presentation of Socrates by Plato with the Socrates of Aristophanes and asserts that by simply denying that he has corrupted the youth, asserting that he has a personal oracle to which he gives allegiance and invalidating his belief in the Gods of Athens by believing that he can prove the oracle of Delphi wrong if he can find a person who is wiser than he.
Critical and plato compares a number of things in this essay Historical Essays plato compares a number of things in this essay Leopold von Rankeâs History of the Popes Thomas Babington Macaulay.
Platoâs argument for rule by philosopher kings is neither persuasive nor realistic in theory, but traces of the plato compares a number of things in this essay characteristics of his ideal form of rule do appear.
Socrates lived during the time of the transition from the height of the Athenian hegemony to its decline with the plato compares a number of things in this essay defeat by Sparta and its allies college application example essays in the â¦.
These features of the dialogues show Plato's awareness that hecannot entirely start from scratch in every work that he writes. Hewill introduce new ideas and raise fresh difficulties, but he will alsoexpect his readers to have already familiarized themselves with theconversations held by the interlocutors of other dialogues—evenwhen there is some alteration among those interlocutors. (Meno does notre-appear in Phaedo; Timaeus was not among the interlocutorsof Republic.) Why does Plato have his dominant characters(Socrates, the Eleatic visitor) reaffirm some of the same points fromone dialogue to another, and build on ideas that were made in earlierworks? If the dialogues were merely meant as provocations to thought—mere exercises for the mind—there would be no need forPlato to identify his leading characters with a consistent andever-developing doctrine. For example, Socrates continues to maintain,over a large number of dialogues, that there are such things asforms—and there is no better explanation for this continuitythan to suppose that Plato is recommending that doctrine to hisreaders. Furthermore, when Socrates is replaced as the principalinvestigator by the visitor from Elea (in Sophist andStatesman), the existence of forms continues to be taken forgranted, and the visitor criticizes any conception of reality thatexcludes such incorporeal objects as souls and forms. The Eleaticvisitor, in other words, upholds a metaphysics that is, in manyrespects, like the one that Socrates is made to defend. Again, the bestexplanation for this continuity is that Plato is using both characters—Socrates and the Eleatic visitor—as devices for thepresentation and defense of a doctrine that he embraces and wants hisreaders to embrace as well.
What I have been concerned to argue in this essay is that these two points are distinct, that the divided line analogy does not imply that for each of the four psychic conditions Plato distinguishes and relates in the epistemological proportion there corresponds a separate category of object. If there is a progression in the divided line (a) it is within each of the sections of the line, and (b) it is an epistemic progression without some of the ontological implications it is commonly taken to have.
It is noteworthy, to begin with, that Plato is, among other things,a political philosopher. For he gives expression, in severalof his writings (particular Phaedo), to a yearning to escapefrom the tawdriness of ordinary human relations. (Similarly, he evincesa sense of the ugliness of the sensible world, whose beauty pales incomparison with that of the forms.) Because of this, it would have beenall too easy for Plato to turn his back entirely on practical reality,and to confine his speculations to theoretical questions. Some of hisworks—Parmenides is a stellar example—doconfine themselves to exploring questions that seem to have no bearingwhatsoever on practical life. But it is remarkable how few of his worksfall into this category. Even the highly abstract questions raised inSophist about the nature of being and not-being are, afterall, embedded in a search for the definition of sophistry; and thusthey call to mind the question whether Socrates should be classified asa sophist—whether, in other words, sophists are to be despisedand avoided. In any case, despite the great sympathy Plato expressesfor the desire to shed one's body and live in an incorporeal world, hedevotes an enormous amount of energy to the task of understanding theworld we live in, appreciating its limited beauty, and improvingit.
How ? If we draw a circle with a compass and pencil and then place a ruler beside it, how do we decide whether the circle and ruler have more than one point in common? The scale of our ruler can be divided indefinitely by 2 (as in 1-inch, 1/2 inch, 1/4, 1/8, etc.), and so by this means there are a logically possible unlimited number of points at which the ruler may touch the circle. And therefore what are we calling a 'point' here? Is it not ambiguous? If by 'point' we mean something with extension (i.e. length), then a tangent may intersect a circle at an infinite number of points. But according to the geometers "a point is that which is without extension"; in Euclid's geometry a circle and a line can have either one (as in the case of a tangent) or two points (as e.g. in the case of the diameter of a circle) in common. At how many points, according to Protagoras, does a tangent touch a circle? Is he not imagining the word 'point' to be the name of an object (An object must, by definition -- i.e. this belongs to the grammar of object-words -- be of some size or other)?
The translation I shall use throughout this essay is that of Robin Waterfield, Plato Republic (Oxford, 1993). However, rather than following Waterfield in using "type" to translate Plato's eidos I shall keep the traditional "form"; and I render expressions such as to agathon as "the good" rather than as "goodness." 
We are of course familiar with the dialogue form through ouracquaintance with the literary genre of drama. But Plato's dialogues donot try to create a fictional world for the purposes of telling astory, as many literary dramas do; nor do they invoke an earliermythical realm, like the creations of the great Greek tragediansAeschylus, Sophocles, and Euripides. Nor are they all presented in theform of a drama: in many of them, a single speaker narrates events inwhich he participated. They are philosophical discussions—“debates” would, in some cases, also be an appropriate word—among a small number of interlocutors, many of whom can beidentified as real historical figures; and often they begin with adepiction of the setting of the discussion—a visit to a prison,a wealthy man's house, a celebration over drinks, a religious festival,a visit to the gymnasium, a stroll outside the city's wall, a long walkon a hot day. As a group, they form vivid portraits of a social world,and are not purely intellectual exchanges between characterless andsocially unmarked speakers. (At any rate, that is true of a largenumber of Plato's interlocutors. However, it must be added that in someof his works the speakers display little or no character. See, forexample, Sophist and Statesman—dialogues inwhich a visitor from the town of Elea in Southern Italy leads thediscussion; and Laws, a discussion between an unnamed Athenianand two named fictional characters, one from Crete and the other fromSparta.) In many of his dialogues (though not all), Plato isnot only attempting to draw his readers into a discussion, but is alsocommenting on the social milieu that he is depicting, and criticizingthe character and ways of life of his interlocutors. Some of thedialogues that most evidently fall into this category areProtagoras, Gorgias, Hippias Major,Euthydemus, and Symposium.