Why Epistemology is not Ancient: From Device and Drama into Philosophy

Why Epistemology Is Not Ancient: From Device and Drama into Philosophy JEAN DE GROOT Catholic University of America

Abstract: This paper traces the significance of first principles (archai) in Greek philosophy to cognitive developments in colonial Greek Italy in the late fifth century BC. Conviction concerning principles comes from the power to make something true by action. Pairing and opposition, the forerunners of metonymy, are shown to structure disparate cultural phenomena—the making of figured numbers, the sundial, and the production, with the aid of device, of fear or panic in the spectators of Greek tragedy. From these starting points, the function of the gnômôn in knowledge is explored.

I

n the late fifth to early fourth centuries BC, the Greek colonies of southern Italy and Sicily were home to a burgeoning intellectual culture. The cities of Tarentum, Metapontum, Syracuse and many others were hungry for the plays of the great dramatists. There were both local productions of the plays and traveling troupes from the Peloponnesian cities. Aeschylus himself oversaw productions in Sicily. It has been argued that these plays were enjoyed by the indigenous population and not only by Greek colonists. Certainly, scenes from Greek tragedy became common on funeral vases of local design.1 At roughly the same time in southern Italy, mathematicians, most prominently Philolaus of Croton and Archytas of Tarentum, were bringing mathematical practice into interpretation of nature in ways that did not distinguish number or geometry from natural things. Archytas is famous for his solution of the duplication of the cube problem by using mathematical figures that move—something that mathematical objects, according to Plato and Aristotle, do not do.2 Archytas likely had in hand the most important generalization of mechanics before Archimedes, the principle of the moving radius: points along a line rotating about one fixed endpoint are all moving at different speeds (Figure 1).

© 2015. Epoché, Volume 19, Issue 2 (Spring 2015). ISSN 1085-1968. DOI: 10.5840/epoche2014123132

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Figure 1: The mathematical principle of the lever: the moving radius Every point on a rotating radius is moving at a different speed. Points more interior to the circle cover a shorter distance in the same time than points on the circumference. (Plato, Laws 10, 893d1–5; Aristotle, De Caelo 2.8, 289b15–18; Aristotle, Mechanica 848a12–19)

This principle explained the action of the lever, wheel and axle, winch, and rudder. Archytas refers obliquely to the principle in addressing the question of why animal limbs, the thorax, and plant branches and stems grow in a circular shape.3 We have here two important cultural developments in the Greek colonies—the love of theatrical production and the mixing of mathematics and natural explanation at a high level of refined imagination. I wish to explore a relation between the two developments, because I believe it can tell us something about the frame of mind the Greeks brought to philosophy and science in the Aristotelian period, in particular the conviction accompanying first principles (archai). The key to the relation between these two cultural items is action, both naturally occurring action and action by human intention. Action has a greater power to convince someone of the truth of something than does the simple utterance of words that express thought. Action compels, threatens, delights, and can inform one of what is possible or is the case. An element common to theater and southern Italian mathematical science, I believe, is device or contrivance (mêchanê), the production of action that would otherwise not happen. Device is associated by the Greeks with wonder (thauma) at the overcoming of natural impediment by the use of simple machines. These machines were the lever, wheel and axle, wedge, pulley, and screw. Nautical practice, the moving of great weights in building, as well as the permanence of the finished building itself, were all activities penetrated throughout with device. In these activities, the natural and the contrived merged to produce a moving or static wonder—the fleetness and maneuverability of a sailing ship, the static grandeur of pillars instituting a monumental temple space. There is also the wonder of a fearful and terrible happening portrayed in drama. The outdoor theater used simple machines, like the pulley or crane (aiôrêma, mêchanê) to raise or lower an actor. There were simpler contrivances,

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such as rattling sheet metal for deafening noise, but the simplest and most elegant device of drama was the mask.4 I will connect the mask to scientific thinking by following two insights. The first is that device figures in theater as only a part of the overall impact of Greek drama, which is that the spectator so suspends belief as nearly to become what he sees. In this accomplishment, the boundary between himself and the action enacted by the actor is indistinct or porous. The second insight is this: at this period of time the artificial really could be taken for natural occurrence, if it simulated nature in relevant particulars. By device, the boundary between artifice and nature becomes indistinct. That theater and practical mechanics both involve action is key here. Both natural activity and contrived action take place or transpire. In the late fifth century, both theater and science rode to credibility on their ability to make something true in action.

Becoming What One Sees: The Tragic Mask In the fifth to fourth centuries BC, prosôpon, face or countenance, meant either face or mask.5 The mask portrayed the character as the agent of his action and its consequences. Expressing a person’s character as others experience it, the mask was very assertive. This is evident in the commentary given or amplification of emotion effected by the masked chorus. The masked actor seems foreign in our own time. Indeed, the Greek mask is rarely successful in contemporary theater, which depends on a psychological naturalism familiar to modern audiences. Studies on Greek masks of the fifth century, however, point to the distinctively Greek naturalism of the mask. David Wiles reports the experiences of modern actors in performing Greek drama outdoors with masks. The outdoor theater changes how the actors project their voices and the mask leads them to move their bodies more slowly. With the mask, the voices of the actors resonate differently to themselves, both because walls do not affect the acoustics and because they hear their own voices differently in the mask. Wiles’s view is that the mask “creates a link between human beings and the natural world. The boundary between an inanimate environment and the flesh of the human subject comes to be experienced as permeable.”6 Wiles is not the only student of Greek drama to make this point about the function and effect of the actor’s mask. Drawing upon neuroscience, Peter Meineck points out that the spectator himself merges the mask, character, and action in his reception of the spectacle. The interface between nature and the human actor is porous for both actor and spectator. Meineck writes, “our cognitive abilities to imitate, learn, speak, understand, and empathize are linked to embodiment—our minds and our bodies are connected in experiential cognition and we process the emotion of others through a system of ‘action representation.’”7 Meineck refers to the

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spectator processing the speech of the actor in mask. The mask makes the character alive. For the Greek viewer, the mask would not have seemed artificial or stilted. Let me make this point as specific as possible by reference to something Gregory Nagy says concerning the tragic mask. Addressing the experience of fear in Greek performance, he says that an audience “can experience . . . ekplêxis (being struck with fear or awe) vicariously by way of collectively reacting to primal fear experienced by one single person who is larger than life, the hero. That is what Aristotle has in mind in the Poetics (1455a17) when he speaks of the ekplêxis experienced by the audience in reacting to the primal fear experienced by Oedipus as acted by an actor in the tragedy of Sophocles that bears the hero’s name, Oedipus Tyrannus” (33).8 The mask plays a key role in making awe or panic subjective, something shared between masked actor and spectator, because the mask offers up in continuous direct vision the emotion the viewer is to share. Nagy sees a connection between theatrical experience and grammatical subjectivity. The subjective persons, “I” and “you,” precede the objectivity of the third person.“I” and “you” comprise a linked pair, the basis of dialogue (35). Nagy says, “Just as subjectivity can be analyzed in terms of the person in grammar, it can also be analyzed in terms of the persona in theater” (37).9 The grammatical subjectivity expresses “the mutuality of looking straight at another person who is looking straight back at you” (37). The mask is an “I-to-you” device of shared pathos. In the case of the theatês, the viewer in the theater, the duality of looking is not so much a duality of dialogue as of shared subjectivity. The panic of one becomes the panic of the other.

How One Thing Stands for Another: Explanation by the Gnômôn Nagy’s grammar of opposition in subjectivity makes plausible how the spectator can be emotionally assimilated into the action of the spectacle. I believe there is a parallel cognitive phenomenon in the fifth century in the type of empiricism attendant upon one of the earliest tools of Greek science, the gnômôn.

Stylus or gnômôn

Figure 2: Stylus or gnômôn

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Gnômôn means knower or what discerns.10 In its meaning of what discerns, gnômôn was the stylus, or perpendicular, casting a shadow on a sundial (Figure 2). Herodotus says that the Greeks learned the gnômôn and the twelve divisions of the day from the Babylonians.11 The gnômôn is taken into concrete mathematical speculation with the Pythagorean technique of figured numbers.12 Figured numbers were laid out by arrangement of pebbles (psophoi). By placing around a given configuration another number of pebbles, the same shape is maintained. The number of pebbles added in straight line configuration that accomplishes the larger same shape is the gnômôn, discerner, because this number of pebbles produces a new total sum that continues the numerical series in the appropriate way. In a particularly clear case, in a square configuration (Figure 3), repetition of each bar of two combined with the addition of one pebble in the empty corner produced the next square number.13 Continued addition in this manner yields the count of successive bars of pebbles to make up the series of odd numbers. The sum of the count of successive bars in the series up to any given odd number is always a square number, n2. So, 1+3+5+7=16, a square number.

Figure 3: The γνώμων in square numbers— the carpenter’s square

These connections, and others like it for differently shaped figured numbers, arise from an array of perceptible counters augmented in real time by action that someone takes in a sort of spatial calculation. For present purposes, we should take our point of departure in interpreting the gnômôn from Aristotle and Euclid, who both emphasize 1) the sameness of shape that a gnômôn maintains, and 2) the complementarity between successive members of a series that the gnomon makes possible.14 Euclid uses the word gnômôn for any complement to a figure created by drawing a line within an already existing closed plane figure. The parallelogram is especially suited to exploration of such complements because its divisions produce interior complement figures that are also parallelograms (Figure 4).

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Figure 4: Euclid’s parallelogram complements (παραπληρώματα) Παντὸς δὲ παραλληλογράμμου χωρίου τῶν περὶ τὴν διάμετρον αὐτοῦ παραλληλογράμμων ἓν ὁποιονοῦν σὺν τοῖς δυσὶ παραπληρώμασι γνώμων καλείσθω. “For any parallelogram area, let any one of the parallelograms about its diameter with its two complements be called the gnômôn.” Elements Bk 2, def. 2 E.g., KGCF is taken along with ABGH and HKFD.

In general, then, the gnômôn is an agent of discernment of significant pairings. It is reasonable to think that the complementarity of the gnomon is what the fifth century Pythogarean, Philolaus, had in mind when he said, “Number makes all things knowable and mutually agreeing (potagora allalois) in the way characteristic of the gnomon.”15 To analyze the duality of one thing agreeing with another because of the gnômôn, I will consider the simplest case of the gnômôn, a naturally occurring permanent feature of a landscape, a cliff or escarpment, casting a shadow that moves during the day. Someone who works outdoors all day may rely upon the shadow cast by a high cliff to tell him when to head home. The shadow reaching a particular length as judged in reference to some other natural outcropping signals the lateness of the day (Figure 5). A natural object simply as selected for use is thus the most primitive kind of device. The shadow expresses the time of day because of what obstructs the sun’s light, the promontory. The shadow itself, however, can signify it is time to go home. All

shadow just after sun’s zenith

shadow near sundown Figure 5: A natural feature instrumentalized as a γνώμων

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other things being equal, the shadow takes the place of the expended portion of the day for purposes of judgment and thought. This substitution is seldom noticed but nevertheless remarkable. The natural promontory, the moving sun, and the moving shadow exist alongside other natural occurrences—the height of the escarpment, its vegetation, the vertical erosion, the changes in location of the shadow through the seasons. Taking the moving shadow as a token of the time of day is to treat one part of this entire state of affairs instrumentally.Vegetation, even the height of the promontory, fade into the background. The shadow is a sumbolon, one of a pair and possessed of a particular narrow cogency or intelligibility. It is interesting that what discerns the pair, the promontory, itself fades into the background in favor of the shadow and the viewer’s special concern, how much of the day has now past. The gnômôn thus fades in and out of significance depending on the need of the timekeeper to go back to the origin of his judgment. Not a contrivance at all, the promontory also now is and then is not a device. As such, the promontory as sundial is a particularly striking example of our coming to look through, or look past, what is the source of discernment and to focus instead on an outcome of the discernment as simply being what we sought to know. The shadow might as well be the time of day. The tool, or gnômôn, accomplishes this pairing.Yet, the gnômôn is not the sign; the shadow is. This compression of signifier with the means of being signified extends to an entire made object, the sundial. Returning to Figure 2, the sundial as a whole, not just its stylus, is understood to tell the time of day. The gnômôn brings thought and thing closer together rather than separating them. This is paradoxical considering the gnomon is the discerner. In the process, though, the gnomon becomes itself harder to see. When this happens, the sharp contour of what device is also becomes more vague and harder to comprehend. It seems to me that there are many similarities to be found between such an analysis of the gnômôn and the effect of the theatrical mask. Pairing is a first level of cognitive function in the human being, so we should not be surprised to see it playing a large role in both theater and science at this period of time. The most important aspect of emotive and epistemic pairing is being able to take one member of a pair as simply being the other. This trope of thinking is called metonymy.16 The fear of the actor-in-mask within the story is the fear of the spectator immersed in the story. In the same way, when device (our contriving) enters into nature to rearrange nature for a new outcome, the device itself is lost to the new face-to-face encounter it makes possible. As we have seen, the gnômôn is that by means of which we see an important connection in nature. Succeeding this enlightenment, however, the knower focuses on the connection, thereby taking the device as transparent. To this extent, the gnômôn by discerning also produces a sort of cognitive impairment or confusion. It is no longer clear to us how the principle by which we explain something gave way to what now just stands for its explanandum. Knowledge itself becomes mysterious, once it is at-

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tained. Naming things is subject to this confusion (names seem to guarantee beings having the name), also the collecting of related phenomena for a common explanation (Aristotle’s method in giving functional definitions of the soul in De Anima 2). An interesting question is whether or not there is any similar loss or impairment in the identification that occurred in Greek theatrical performance. Certainly, the mask receded in sense and perception as the reality of fear, awe, or wonder struck the spectator through the actor and the surrounding spectacle. Yet, this seems in theater not the impairment or covering over that so readily obscures the sources of knowledge. I will conclude by returning to my original theme of the way of living/ thinking/acting in colonial culture in southern Italy. It seems to me that mechanical technique is typical of a young culture founded on commerce and asserting itself in new cultural combinations. The emphasis on action found in a colonial culture shows itself also in theater. Enculturation of drama was the most desirable route to participating in the high culture of the Peloponnese. On the scientific side, calculation by movement and action even precedes the universalizing of a concept. Number was welded into activity with and around things. From a philosophical standpoint, this means that in effect there is no epistemological problem in Greek science. That is, there is no question of the justification of knowledge. The discerner, the gnômôn, links word and object without a question of the source of knowledge ever really arising. The link in a gnomonic pair between an action or outcome, on the one hand, and the thing itself being sought, on the other, may shed light on features of the search for principles in Plato and Aristotle. Each philosopher seeks a primordial cause—to on, dunamis, or archê—in action or characteristic functions.17 It would be possible to show how there is metonymy at work in their discernment of principles. In just what way the structure of discernment by means of the gnômôn remains a part of their philosophical practice is something that remains to be investigated.

Notes 1.

On this topic, see Chris Deardon, “Plays for Export,” Phoenix 53:3–4 (1999): 222–48; Margot Schmidt, “Southern Italian and Sicilian Vases,” in The Western Greeks, ed. G. Pugliese Caratelli (London: Thames and Hudson, 1996), 443–56; Oliver Taplin, Pots and Plays: Interactions Between Tragedy and Greek Vase-painting of the Fourth Century B.C. (Los Angeles: Paul Getty Museum, 2007), 2–46. For the vases themselves that bear witness to the influence of Greek drama, see A. D. Trendall, The Red-Figured Vases of Lucania, Campania, and Sicily, 2 vols. (Oxford: Clarendon Press, 1967). A particularly interesting vase in the Harvard Art Museum (1960.367; #644 in Trendall) shows scenes related to the Oresteia on a nestoris of Lucanian design. It has the distinctive tall amphora arms of local origin but with disk figures reduced in size and presented, it seems to me, as wheels and axle.

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2. Diels-Kranz, Die Fragmente der Vorsokratiker 1 (Berlin: Weidmann, 1956), A14 from Eutocius, Commentary on Archimedes’ On the Sphere and Cylinder II. 3. [Pseudo]-Aristotle, Physical Problems 16.9. For the connection between Archytas and the lever principle, see Jean De Groot, Aristotle’s Empiricism: Experience and Mechanics in the Fourth Century BC (Las Vegas: Parmenides Publishing, 2014), chap. 7. 4. All the aspects of the non-linguistic features of theatrical re-creation and storytelling are covered by Aristotle’s term opsis in his classification of parts (merê) of tragedy in Poetics 6 (1450a10). Display includes scenery, simple machines for special effects, as well as displays of sound and light that might figure also in festivals. Although most of our information about automata as moving figures in a theater comes from Hero of Alexandria (AD first century), there is evidence that automata of some sort were involved in simulation of animate movement and the production of other marvelous effects much earlier. See, for example, Aristotle, Movement of Animals 7, 701b2–7. 5. L-S, πρόσωπον; David Wiles, Mask and Performance in Greek Tragedy (Cambridge: Cambridge University Press, 2007), 1. Aristotle uses prosôpon, not the later prosôpeion, in Poetics 5, 1449a36, to refer to a comic mask. Homer uses prosôpon only in the plural. 6. Wiles, Mask and Performance, 163. 7. Peter Meineck, “Neuroscience of the Tragic Mask,” Arion 19:1 (2011). An earlier version of the paper appeared in Athens Dialogues: Stories and Histories, 2010. 8. Gregory Nagy,“The Subjectivity of Fear as Reflected in Ancient Greek Wording,” Dialogues 5 (2010): 29–45. Note in Nagy’s formulation the very relevant reiteration of the countenance of fear in variations on the paradigmatic expression—the mask, Oedipus, the actor, the play, the hero’s name, the hero’s name as the name of the play. These reiterations are part and parcel of the accomplishment of mutualized subjectivity. 9. The word in each case is the same for grammatical person and theatrical mask, whether in Greek (prosôpon) or Latin (persona) (Nagy, “Subjectivity,” 37). 10. Heath says the literal meaning of gnômôn is “a thing enabling something to be known, observed or verified, a teller or marker, as we might say” (Euclid’s Elements 1, 370). Heath comments on Book 2, Def. 2. 11. Histories II, 109.11. 12. See Heath, History of Greek Mathematics 1, 76–86, and Burkert (Lore and Science in Ancient Pythagoreanism, trans. Edwin Minar, Jr. [Cambridge, Mass.: Harvard University Press, 1972], 427–8). 13. For a more detailed treatment of the gnômôn on this interpretation, see De Groot, Aristotle’s Empiricism, chap. 11, 347–8. 14. Euclid’s Elements Book 2, Def. 2; Aristotle, Physics III.4, 203a13–15 and Categories 14, 15a30. 15. See Diels–Kranz Fragmente 1, Philolaus B11 (411.14–412.3). The passage, from Stobaeus’s Extracts (Eclogai) (AD fifth century), is quoted in Heath, ed., Elements 1, 371. The term ποτάγορα comes from προσαγορεύειν. For more on the gnômôn, see Heath, Elements 1, 370–2, and Cohen and Drabkin (Sourcebook in Greek Science [Cambridge, Mass.: Harvard University Press, 1966], 9, and 9n1). Citing vocabulary in the passage, Huffman has argued that Fragment 11 is not by Philolaus. He cites the similarity of language in the passage to Republic 546b7. Huffmann does not

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discuss the word gnômôn in Fragment 11. He does, nevertheless, cite the reference to things limited and unlimited in the passage as belonging to Philolaus as well as the idea of things fitting together (harmosthen) (Huffman, Philolaus of Croton [Cambridge: Cambridge University Press, 1993], 61–2, 347–50). Since Philolaus is associated by Speusippus with figured numbers, it is reasonable that gnômôn, being a pre-Platonic word in natural philosophy, was used by Philolaus with the connotation of the complementarity of pairs. For him, that this complementarity continues successively in figured numbers is especially significant. See Heath for earlier scholarly interpretations (History 1, 78 and 78n4–5). 16. Ian Hacking argues for the centrality of metonymy for understanding an Aristotelian type of categories in “Aristotelian Categories and Cognitive Domains,” Synthese 126:3 (2001): 473–515, especially §4.5. 17. See Plato’s reconciliation of the Giants and friends of the Forms in Sophist 242d–249d, and Aristotle’s defining of soul in close association with the life functions that seem to call for a special principle in De Anima 1.2, 403b25–27, and 2.2, 413b10–13.

Bibliography Burkert, Walter. Lore and Science in Ancient Pythagoreanism., trans. Edwin L. Minar, Jr. (Cambridge, Mass.: Harvard University Press, 1972). Deardon, Chris. “Plays for Export,” Phoenix 53:3–4 (1999): 222–48. http://dx.doi.org/10.2307/1088985 Diels, Hermann, and Walther Kranz, eds. Die Fragmente der Vorsokratiker griechisch und deutsch, 3 vols. (Berlin: Weidmann, 1956). Hacking, Ian. “Aristotelian Categories and Cognitive Domains,” Synthese 126:3 (2001): 473–515. http://dx.doi.org/10.1023/A:1005221431872 Heath, Thomas L. History of Greek Mathematics, 2 vols. (New York: Dover, 1981). Heath, Thomas L. The Thirteen Books of Euclid’s Elements, with Introduction and Commentary, 2nd ed., rev. with additions, vol. 1 (New York: Dover, 1956). Huffman, Carl. Philolaus of Croton: Pythagorean and Presocratic (Cambridge: Cambridge University Press, 1993). Meineck, Peter. “Neuroscience of the Tragic Mask,” Arion 19:1 (2011). Nagy, Gregory.“The Subjectivity of Fear as Reflected in Ancient Greek Wording,” Dialogues 5 (2010): 29–45. Schmidt, Margot.“Southern Italian and Sicilian Vases,” in The Western Greeks, ed. G. Pugliese Caratelli, 443–56 (London: Thames and Hudson, 1996). Taplin, Oliver. Pots and Plays: Interactions Between Tragedy and Greek Vase-painting of the Fourth Century B.C. (Los Angeles: Paul Getty Museum, 2007). Trendall, A. D. The Red-Figured Vases of Lucania, Campania, and Sicily, 2 vols. (Oxford: Clarendon Press, 1967). Wiles, David. Mask and Performance in Greek Tragedy (Cambridge: Cambridge University Press, 2007).