Republic (Barnes & Noble Classics Series)

by Plato

  33 (6.510b) There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the inquiry can only be hypothetical ... ; in the higher of the two, the soul passes out of hypotheses ... proceeding only in and through the ideas themselves: Despite Socrates’ initial emphasis on the differences among the objects represented by the divided line, his concern—beginning with this sentence—shifts to distinguishing the cognitive processes and faculties whereby mathematical objects and the ideas are apprehended. Mathematicians, as Socrates and Glaucon agree at 7.531e-532a, are not required “to give and take a reason” for the objects they study; they hypothesize, for example, a circle, and study its properties, but never question whether the circle they study actually exists or not. They rely, moreover, on visible images (for example, circles that are physically drawn) for their investigations. In contrast, dialecticians—that is, those who study the ideas—depend on no such physical models and, most importantly, test their hypotheses; they do not take for granted the existence of the ideas they investigate. Mathematical “objects” per se, then, do not differ substantively from the ideas, and they are capable of being apprehended by the faculty of “reason” (noesis) as well as that of “understanding” (dianoia); see 6.511d. It is, rather, the exercise of noesis that differs radically from the exercise of dianoia. The distinction here between noesis and dianoia looks ahead to the description of the philosopher’s education at 7.521c-540a, in which training in mathematical subjects—that is, “number science” (arithmetikê), plane and solid geometry, astronomy, and harmonics—constitutes a mere “prelude” that prepares the future philosopher for his or her study of dialectic (7.531d).

  34 (6.511b) that other sort of knowledge which reason itself attains by the power of dialectic: Dialectic and its use are described in more detailed, albeit still tentative, terms at 7.531d-539d.

  35 (6.511d-e) let there be four faculties in the soul ... and let us suppose that the several faculties have clearness in the same degree that their objects have truth: The terms Socrates now uses for the four cognitive faculties, which are rendered differently by different translators, are noesis (“reason”), dianoia (“understanding”), pistis (“faith” or “conviction”), and eikasia (“perception of shadows” in Jowett, but often translated elsewhere as “imagination”). Noesis and dianoia fall under the rubric of epistemê (gnosis, gnome), the terms used in book 5 to describe the general cognitive faculty that enables one to apprehend objects in the “higher” intelligible realm, whereas pistis and eikasia are different species of doxa, the general faculty by which phenomenal objects are perceived. See note 33 on 6.510b and note 24 on 5.476d.

  Book 7

  1 (7.514a) Behold! human beings living in an underground den: Socrates’ allegory of the cave builds on the image of the divided line as well as the analogy established in the simile of the sun comparing the eye’s ability to apprehend the objects in the physical realm to the mind’s ability to apprehend intelligible objects. Likening the prisoners to “ourselves” (7.515a) and the world of daily experience to mere shadows and echoes, it vividly reinforces Socrates’ contention that most people are mistaken in their belief that the phenomenal world is real and knowable (see 7.517a-c). In contrast to the simile, the allegory accentuates the difficulties of apprehending the idea of the good, which is once again represented by the sun, and consequently of developing the cognitive faculty that enables this apprehension. It emphasizes the emotional as well as physical distress of the prisoner (that is, future philosopher) who, upon being released from his bonds, is disabused of his assumptions about “reality” as he makes the arduous upward journey out of the cave into the bright light of day (7.515c-d). The released prisoner, once accustomed to looking at the sunlit world and the sun itself, will also have difficulties when he is forced to reenter the dark and shadowy cave; the description of his tense dealings with his former fellow-prisoners at 7.517a-e harks back to Socrates’ explanation of the philosopher’s apparent uselessness in 6.488a-489a, and it resonates as well with what is suggested in Republic and other dialogues (for example, Phaedo, Gorgias) about the philosopher’s disdain for material goods and “prizes.”Not all the details in the allegory stand up to logical analysis. For example, the identity of the individuals responsible for the parade of shadow-casting objects and for the releasing of the prisoner (7.514c-515d) is not accounted for, nor is it clear how the released prisoner could be “compelled to fight in courts of law... about the images or the shadows of images of justice” once he returns to the cave (7.517d). Moreover, whereas the divided line’s differentiation of cognitive faculties is clearly important to the allegory’s distinctions among stages of cognitive development, it does not seem necessary to insist on precise correspondence between the stages of the released prisoner’s upward progress and the line’s four segments. The allegory’s purpose, however, is to be powerfully suggestive, and logic is not its primary concern. Its point is simply, as Socrates intimates in 7.516e-519a, that the situation of the prisoners in the cave represents the lot of most people. Just as the prisoners (except for the fortunate few who are released) are unable to conceive of a world outside the dim cave, so most people are incapable of apprehending anything other than the phenomenal world (the world of “becoming”—see 518c, and also note 24 on 5.476d). Moreover, just as only a few prisoners are released, only a few people are permitted (by a lucky and rare combination of circumstances) to develop the higher cognitive faculties of dianoia and noesis and thus the ability to apprehend the intellectual world (the world of “being”).

  2 (7.515e) And suppose once more, that he is reluctantly dragged up a steep and rugged ascent: Socrates’ description of the released prisoner’s upward journey evokes the mythological motif of anabasis—that is, an upward journey out of the underworld. Compare 7.521c.

  3 (7.517b) and you will not misapprehend me if you interpret the journey upward to be the ascent of the soul into the intellectual world, in my view, at least, which, at your desire, I have expressed—whether rightly or wrongly, God knows: Compare Socrates’ reluctance to describe the idea of the good at 6.504b and 6.509c.

  4 (7.518b) certain professors of education: Some sophists and professional teachers of rhetoric claimed to be able to instill knowledge (epistemê) in their students. According to Socrates’ argument, however, the faculty of epistemê is already in the soul; as the discussion of books 6 and 7 makes plain, cultivating this faculty is a challenging and difficult process that few are capable of undertaking since, as he states in the immediately following paragraph, it involves the reorientation of the whole soul away from “becoming” and toward “being.”

  5 (7.520c) Wherefore each of you, when his turn comes, must go down to the general underground abode, and get the habit of seeing in the dark: The verb “go down” (or “descend”) in Greek is katabainein. Katabasis (the opposite of anabasis; see note 2 on 7.515e) typically refers to a journey to the underworld undertaken by a heroic figure such as Heracles, Theseus, or Orpheus.

  6 (7.521c) as some are said to have ascended from the world below to the gods?: The reference may be to individuals like Asclepius, who was apothe osized after being killed by Zeus, and Semele, the Theban princess who was pregnant with Dionysus when she was killed by Zeus’ thunderbolt.

  7 (7.521c) the turning over of an oyster-shell: Ostrakon in Greek actually means “potsherd” (pottery fragment), not “oyster-shell.” For the purposes of the game to which Socrates alludes, a potsherd was painted black on one side and white on the other; when it was flipped in the air, the players called “night” or “day,” just as people today call “heads” and “tails” when coins are flipped. Socrates’ meaning is that education is a serious affair that cannot be left to chance.

  8 (7.521d) Usefulness in war: Arithmetic, plane and solid geometry, and astronomy, which constitute four of the five preparatory disciplines that future philosophers should study as they train their souls to move from “becoming to b
eing,” all had obvious military applications. Nonetheless, when discussing geometry and astronomy, Socrates insists that utility in war is not the most important determinant of these disciplines’ value to guardians in training (7.526a and 7.528d-529a). Rather, they are useful primarily because they “make more easy the vision of the idea of good” (7.526d-e).

  9 (7.522c) The little matter of distinguishing one, two, and three—in a word, number and calculation: do not all arts and sciences necessarily partake of them?: “Number” (arthmos) and “calculation” (logismos) lead “the soul toward being” (7.523a) because they help people make sense of confusing appearances and thus lead them to look beyond mere appearances (7.523b). All of the mathematical disciplines that Socrates goes on to describe, beginning with arithmetikê (the “science of number”), are essential to the philosopher’s training since it helps him (or her) “rise out of the sea of change and lay hold of true being” (7.525b).

  10 (7.523a) It appears to me to be a study of the kind which we are seeking, and which leads naturally to reflection, but never to have been rightly used; for the true use of it is simply to draw the soul toward being: Compare 7.527a-b and 7.529a-531c for critiques of the methods and emphases of those who currently study geometry, astronomy, and harmonics.

  11 (7.524d) And to which class do unity and number belong?: That is, do “unity and number” belong to the class of impressions that are not innately confusing and require no “calculation” or to the class that requires abstract reasoning to be properly understood? The phrase “unity and number” reflects the fact that Plato did not consider “one” a number.

  12 (7.524e) “What is absolute unity?”: Any single object in the phenomenal world (that is, a visible “one”) is actually both “one” and “many”; for example, one flower has many petals, one piece of fruit has many seeds. The realization that every visible “one” is in fact both “one” and “many” accordingly leads one to wonder about the “absolute unity” that is not also “many,” and to realize eventually that this “absolute unity” is not to be found in the phenomenal world.

  13 (7.525d-e) absolute unity: That is, the unit that is adopted for the purpose of a given calculation and which is, for the purpose of that calculation, indivisible. Such a unit is, strictly speaking, hypothetical.

  14 (7.527a-b) They have in view practice only, and are always speaking ... of squaring and extending and applying and the like—they confuse the necessities of geometry with those of daily life; whereas knowledge is the real object of the whole science: In the fifth century B.C.E., some geometers tried their hand at town planning; for example, Hippodamus of Miletus designed the grid-iron layouts of streets in Piraeus and the Athenian colony of Thurii (in Italy). Such undertakings seem to have struck many people as “ridiculous”; in Aristophanes’ Birds (produced in 414 B.C.E.), the geometer Meton is comically represented as a pompous would-be town planner.

  15 (7.527d) I am amused, I said, at your fear of the world, which makes you guard against the appearance of insisting upon useless studies: Socrates’ gentle admonition resonates with what has been established about the “un-philosophic” nature of the many and their current prejudice against philosophy; see, for example, 6.488e-489a and 6.494a.

  16 (7.528a) Then take a step backward, for we have gone wrong in the order of the sciences: Solid geometry, which Socrates proposes as the logical follow-up for the study of plane geometry, is less complex and abstract than astronomy, which is the study of “solid objects in revolution [that is, motion].” The subjects of the entire preparatory curriculum (that is, arithmetikê, plane geometry, solid geometry or stereometry, astronomy, harmonics) are increasingly complex and abstract, and they are organized so as to make future philosophers ready for the supremely difficult and wholly abstract operations of dialectic.

  17 (7.528b) but so little seems to be known as yet about these subjects: Problems of solid geometry had concerned several theoreticians (for example, Anaxagoras, Democritus, some in the Pythagorean school) in the fifth century. What Glaucon apparently means here is that solutions to complex stereometrical problems (that is, beyond simple problems such as the doubling of a cube) had not yet been discovered.

  18 (7.529b) whether a man gapes at the heavens or blinks on the ground, seeking to learn some particular of sense, I would deny that he can learn, for nothing of that sort is matter of science: As in the case of geometry (7.527a), Socrates argues that astronomy ought not be pursued for the sake of understanding physical phenomena (that is, the movements of heavenly bodies), but rather as abstract geometry in four dimensions that is concerned with “true motions of absolute slowness and absolute swiftness.” So too “harmonics,” which is concerned with the motion of sounds (7.530d), is to be studied for the sake of understanding abstract “harmonies” of number as opposed to those that can be physically heard (7.531c).Plato perhaps has Socrates specifically disavow interest in problems dealing with “some particular of sense” in order to distance him further from the figure of “Socrates” in Aristophanes’ Clouds, whose “Think-Factory” sponsors ridiculous research in “astronomy” and other fields. See note 22 on 2.378b and note 10 on 7.523a.

  19 (7.530d) There is a second, I said, which is the counterpart of the one already named: Astronomy, which has been “already named,” is the study of the motion of solid bodies in space; its “sister science” is harmonics, the study of the motion of sound. For the comparison of the functions of the ear and eye, see 6.507c-d.

  20 (7.530d) as the Pythagoreans say: The reference is to the followers of Pythagoras, the religious thinker and theorist who settled in Croton in southern Italy during the sixth century B.C.E. Pythagoreans were known in the classical period for their ascetic way of life, their belief in the reincarnation of the soul, and their mathematically based study of music and harmonics.

  21 (7.531a) The teachers of harmony compare the sounds and consonances which are heard only, and their labor, like that of the astronomers, is in vain: This is most likely a reference to the Pythagoreans.

  22 (7.531a) condensed notes, as they call them: Pyknomata in Greek is a technical term that apparently refers to combinations of two quarter-tone (or semi-tone) intervals.

  23 (7.531b) one set of them declaring that they distinguish an intermediate note and have found the least interval which should be the unit of measurement: For example, the quarter-tone. Other theorists (perhaps including Plato himself) posited the semi-tone as “the least interval,” with a view not only to simplifying the analysis of music, but also encouraging simplicity in musical composition.

  24 (7.531b) plectrum: The plectrum was the pick by which the strings of an instrument were plucked. The metaphor developed in the first sentence of this paragraph plainly alludes to the torturing and beating of slaves.

  25 (7.531d) the prelude, or what?: Prooimion in Greek refers broadly to the introductory section of a song (or poem or speech). The musical metaphor is continued in the following paragraphs, where Socrates refers to the nomos, or “song,” that dialectic performs.

  26 (7.531d-e) For you surely would not regard the skilled mathematician as a dialectician?: Compare 6.510b-511d. Unlike the mathematician who, for example, assumes the existence of “absolute unity” (7.525d-526a,) the dialectician’s study of “the idea of one” would not be complete until he had “ascended to first principles” (6.511a-b) and showed by argument that such a concept is essential to the rational understanding of both the intelligible and phenomenal worlds.

  27 (7.532d) This, however, is not a theme to be treated of in passing only.... And so, whether our conclusion be true or false, let us assume all this, and proceed at once from the prelude or preamble to the chief strain, and describe that in like manner: Socrates’ reticence in describing dialectic mirrors the reserve he displays when discussing the idea of the good, which is the ultimate object of dialectic. Compare 7.517b. The word translated here as “chief strain” is nomos, which also means “law” and/or “custom.”

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sp; 28 (7.533d) Custom terms them sciences: That is, epistemai (the plural of epistemê). Whereas the term epistemai is “customarily” used to refer to disciplines, or fields of study, Socrates has earlier used epistemê to designate the cognitive faculty by which objects in the intelligible world are apprehended.

  29 (7.534d) you would not allow the future rulers to be like posts, having no reason in them, and yet to be set in authority over the highest matters?: Jowett’s interpretation, that grammai in this context refers to the lines at the start of racecourses (hence his translation “posts”), is disputable. The reference is more likely to alogoi grammai—that is, “irrational quantities” such as the square root of negative one. If so, there would be a witty play on the adjective alogos (“irrational,” “having no reason”) since those who are unable to approach the idea of the good through dialectic are unable to give an account (logon dounai) of it. Compare 7.531e, where Socrates and Glaucon agree that mathematicians are incapable of reasoning (literally, unable to logon dounai).

  30 (7.536c) Certainly not, I said; and yet perhaps, in thus turning jest into earnest I am equally ridiculous.... I had forgotten ... that we were not serious, and spoke with too much excitement. For when I saw philosophy so undeseruedly trampled under foot of men. . . . : Socrates painted a vivid (and somewhat playful) picture of philosophy bereft of legitimate “suitors” and forced to “marry ... a bald little tinker” at 6.495c-496a. His statement that he and his interlocutors “are not serious” may come as a surprise, given the stress repeatedly laid on the importance of the issues raised in Republic; see note 14 on 1.344e. Nonetheless, it is in keeping with the many advertisements concerning the provisional nature of the conversation, and it perhaps should stand as a reminder that Plato did not hope to accomplish anything truly “serious” in this or any other dialogue. For the fundamentally “playful” nature of writing, see Phaedrus 274c-278e.