“If the One is not” (Prm. 160b-164b)
My focus in this paper is the third antinomy in the second part of the Parmenides (160b-164b).[1] I ask, How does this collection of arguments help the young Socrates grasp the truth with authority (136b6-c5; cf. 135d3-6), and thereby save the theory of Forms (135b5-c4)? It is my view that the principal lesson of the Parmenides is that the Forms must be “predicationally many”[2] — both in the sense that they are many things and in the sense that they are not many things. The groundwork for the latter, I claim, is laid in the third antinomy of the Parmenides, and brought to completion in the Sophist (256c-259b).
I assume the following with respect to the second part of the Parmenides: (1) Parmenides sincerely recommends the method of training to the young Socrates; (2) Parmenides’s demonstration of the method of training contains genuine antinomies[3]; it is not possible to accept all of the conclusions established in the dialogue’s second part[4]; and (3) all of the antinomies concern the same subject, namely, the One (to hen).[5]
The argument for my claim about the third antinomy proceeds in two stages. The first stage examines the relationship between the third antimony’s two deductions, what I will call its “positive deduction” and its “negative deduction.” The positive deduction establishes a number of conclusions about the One-that-is-not (hereafter, OTIN), some of which are certainly true. For instance, that OTIN is knowable (160c5-d2; 160d3-e2), is different from the others (160c5-d2; 160d3-e2), and partakes (meteinai) of not-being (162b5-6). But almost all of the positive deduction’s conclusions about OTIN are overturned in the negative deduction.[6] Why? My examination shows that the negative deduction overturns the conclusions of the positive deduction because of the meaning or signification (sêmeion) of the phrase mê estin, “is not”; in the negative deduction, mê estin signifies “nothing other than the complete absence of being from that which is said not to be” (163c2-4; cf. 163c4-d1). Since this is the case, nothing that is can belong to OTIN; for if something that is did belong to OTIN, then, “by partaking (metechon) of that, [OTIN] would partake (metechoi) of Being” (163e7-164a1).[7] Recognition of this point permits an interim conclusion: the positive deduction was able to establish a number of its conclusions about OTIN because there mê estin had a different signification.
The second stage of the argument determines what the different signification is. Here I restrict my focus to a difficult passage in the positive deduction that establishes that OTIN must partake somehow (metechein pê) of Being (161e3-162b8). This passage is naturally divisible into two parts. The first part (161e3-162a4) contains two short arguments that, collectively, establish why OTIN must partake of Being: to speak truly is to speak of onta, “things that are.” Since Parmenides and Aristoteles claim to speak truly about OTIN, therefore OTIN is (estin ara […] to hen ouk on; 161e4-162a2); in addition, if OTIN were not a not-being — that is, if it were to give up (anêsei) its being with respect to being a not-being — it would straightaway be a being (162a2-4).
The second part (162a4-162b8) establishes how OTIN partakes of Being. This is accomplished through a discussion of Being and Not-being themselves, which is then applied to OTIN: Being, if it is to be completely, must partake of Being with respect to being a being, and must partake of Not-being with respect to not-being a not-being (162a6-b1).[8] It is my view that this means that Being must have the attribute of being, since it is, and not have the attribute of not-being, since it is what being is, the nature of being. Similarly, Not-being, if it is to not be completely, must partake of Not-being with respect to not-being a not-being, and of Being with respect to being a not-being (162b1-3). I interpret this as asserting that Not-being has the attribute of not-being, since it is not identical with Being, but it also has the attribute of being, because it is not-being. Finally, since OTIN is a not-being, “it must have being a not-being as a bond to its not-being” (162a4-5). It is my view that this means that OTIN has the attribute of not-being, in the same way as Not-being itself, since neither is identical with Being itself (or with any other form). However, OTIN still has the attribute of being, because it is a not-being. Therefore, OTIN, since it is not, has a share of being with respect to its not-being (162b4-7). This passage, I conclude, distinguishes two ways of being: (1) being the nature of Being, what being is; (2) having the attribute of being.
If this is the case, What is the signification of mê estin and the phrase to mê on, “what-is-not” or “not-being,” in this passage? I maintain that what “is not” or what is said “not to be” is said only to be not identical with the what-it-is-to-be, with Being itself. Just as Not-being must partake of Not-being, so that it is not identical with Being itself (as well as all of the other not-beings), it must also partake of Being, so that it is not-being. Similarly, OTIN must partake of Not-being, so that it is not identical with Being itself, but also partake of Being, since it too is not-being. I suggest that this is the beginning of the account of “is not” and “not-being” developed in the Sophist.
Bibliography
Allen, R. E. 1997. Plato’s Parmenides. Translated with comment. New Haven: Yale Universit Press. (Revised edn. of Allen, 1983.)
Burnet, J. 1900–7. Platonis Opera (5 vols.). Oxford Classical Texts. Oxford: Clarendon Press.
Curd, P. K. 1989. “Some Problems of Unity in the First Hypothesis of the Parmenides.” The Southern Journal of Philosophy 27: 347–59.
Duke, E. A., W. F. Hicken, W. S. M. Nicoll, D. B. Robinson, J. C. C. Strachan. 1995. Platonis Opera. Vol. 1. Oxford Classical Texts. Oxford: Clarendon Press.
Friedländer, P. 1969. Plato (3 vols.), Vol. 1: An Introduction. Vol. 3: The Dialogues: Second and Third Period. Princeton: Princeton University Press.
Gill, M. L. 1996. “Introduction.” In M. L. Gill and P. Ryan, Plato: Parmenides. Indianapolis: Hackett. 1–123.
Gill, M. L. 2002. “Plato on Being a Not-Being: The Text of Parmenides 162A–B.” In B. Amden, P. Flemsted-Jensen, T. H. Nielsen, A. Schwartz, C. G. Tortzen (eds.), Noctes Atticae: Articles on Greco-Roman Antiquity and its Nachleben [Festschrift for Jorgen Mejer]. Copenhagen: Museum Tusculanum Press, University of Copenhagen. 121–9.
Gill, M. L. 2014. “The Design of the Exercise in Plato’s Parmenides.” Dialogue 53: 495-520.
Gill, M. L. and P. Ryan. 1996. Plato: Parmenides. Indianapolis: Hackett.
Meinwald, C. 1991. Plato’s Parmenides. Oxford: Clarendon Press.
Meinwald, C. 2014. “How Does Plato’s Exercise Work?” Dialogue 53: 465-494.
Miller, M. 1986. Plato’s Parmenides: The Conversion of the Soul. University Park: Pennsylvania State University Press.
Owen, G. E. L. 1970. “Notes on Ryle’s Plato.” In O. P. Wood and G. Pitcher (eds.) Ryle. 341-72. Anchor Books: Doubleday.
Peterson, S. 1996. “Plato’s Parmenides: A Principle of Interpretation and Seven Arguments.” Journal of the History of Philosophy 34: 167–92.
Peterson, S. 2000. “The Language Game in Plato’s Parmenides.” Ancient Philosophy 20: 19–51.
Peterson, S. 2003. “New Rounds of the Exercise of Plato’s Parmenides.” Modern Schoolman 80: 245–78. Special Issue, Scott Berman (ed.), The Metaphysics of Plato and Aristotle.
Rickless, S. C. 2007. Plato’s Forms in Transition. A Reading of the Parmenides. Cambridge: Cambridge University Press.
Russell, B. 1937. The Principles of Mathematics. 2nd edn. London: Allen & Unwin.
Ryle, G. 1939. “Plato’s Parmenides.” Mind N. S. 48: 97-147.
Sayre, K. M. 1978. “Plato’s Parmenides: Why the Eight Deductions are not Contradictory.” Phronesis 23: 133–50.
Sayre, K. M. 1983. Plato’s Late Ontology: A Riddle Resolved. Princeton: Princeton University Press. Repr. by Parmenides Publishing, 2006.
Sayre, K. M. 1996. Parmenides’ Lesson. Trans. and Explication of Plato’s Parmenides. Notre Dame: University of Notre Dame Press.
Schofield, M. 1977. “The Antinomies of Plato’s Parmenides.” Classical Quarterly N.S. 27: 139–58.
el Uno no es” (Prm. 160b-164b)
Esta comunicación se concentra en la tercera antinomia de la segunda parte del Parménides (160b-164b).[9] Mi pregunta es cómo es que esta colección de argumentos ayuda al joven Sócrates a asir la verdad con autoridad (136b6-c5; cf. 135d3-6) y, de esta manera, a salvar la teoría de las Formas (135b5-c4). Considero que la principal Enseñanza que nos deja el Parménides es que las Formas deben ser “muchas predicacionalmente hablando”[10] — tanto en el sentido de que hay muchas cosas, como en el de que no hay muchas cosas. El trabajo preparatorio para lo segundo, sostengo, se encuentra en la tercera antinomia del Parménides, pero es completada en el Sofista (256c-259b).
Con respecto a la segunda parte del Parménides estoy trabajando bajo la siguiente hipótesis: (1) Parménides recomienda sinceramente el método de entrenamiento al joven Sócrates; (2) la demostración del método de entrenamiento que hace Parménides contiene antinomias genuinas[11]; no es posible aceptar todas las conclusiones establecidas en la segunda parte del diálogo[12]; y (3) todas las antinomias conciernen al mismo tema, a saber, lo Uno (to hen).[13]
El argumento para defender mi posición sobre la tercera antinomia procede en dos tiempos. En el primero examino la relación entre las dos deducciones que componen la tercera antinomia, a las que llamaré su “deducción positiva” y su “deducción negativa”. La deducción positiva establece un cierto número de conclusiones acerca del “Uno que no es” (desde ahora, UNE), algunas de las cuales son en efecto verdaderas. Por ejemplo, que el UNE es cognoscible (160c5-d2; 160d3-e2), que es deferente de los otros (160c5-d2; 160d3-e2), y que participa (meteinai) del no-ser (162b5-6). Pero casi todas las conclusiones de la deducción positiva acerca de UNE son invertidas en la deducción negativa.[14] ¿Por qué? Mi examen muestra que la deducción negativa invierte las conclusiones de la deducción positiva por el sentido o significación (sêmeion) de la frase mê estin, “no es”; en la deducción negativa mê estin significa “nada distinto a la completa ausencia de ser en eso que se dice que no es” (163c2-4; cf. 163c4-d1). Dado que este es el caso, nada que es puede pertenecer a UNE, pues si algo que es perteneciera a UNE, entonces “por participación (metechon) de ello, [UNE] participaría (metechoi) del Ser” (163e7-164a1).[15] El reconocimiento de este punto permite llegar a una conclusión intermedia: la deducción positiva pudo establecer un cierto número de sus conclusiones sobre UNE porque allí mê estin tenía una significación diferente.
La segunda parte del argumento determina cuál es esa significación diferente. Aquí voy a restringir mi atención a un pasaje difícil en la deducción positiva que establece que UNE debe participar de alguna manera (metechein pê) del Ser (161e3-162b8). Este pasaje, por su propia naturaleza, es divisible en dos partes. La primera (161e3-162a4) contiene dos argumentos cortos que, en su conjunto, establecen por qué UNE debe participar del Ser: hablar verdaderamente es decir de los onta, “las cosas que son.” Dado que Parménides y Aristóteles declaran estar hablando verdaderamente sobre UNE, entonces OTIN es (estin ara […] to hen ouk on; 161e4-162a2). Adicionalmente, si UNE no fuera un no-ser –esto es, si renunciara (anêsei) a ser un no-ser — sería directamente un ser (162a2-4).
La segunda parte (162a4-162b8) establece cómo UNE participa del Ser. Esto es logrado por medio de una discusión sobre el Ser y el No-ser, que es luego aplicada a UNE: el Ser, para que sea completo, debe participar del Ser en lo relativo a ser un ser, y debe participar del No-Ser en lo relativo a no-ser un no-ser (162a6-b1).[16] Considero que esto significa que el Ser debe tener el atributo de ser, puesto que es, y no debe tener el atributo no-ser, puesto que esto es lo que ser es, la naturaleza de ser. De manera similar, No-ser, para que no sea completamente, debe participar del No-ser en lo relativo a no-ser un no-ser, y del Ser en lo relativo a ser un no-ser (162b1-3). Aquí interpreto esto como que el No-ser tiene el atributo de no-ser, puesto que no es idéntico con el Ser, pero también tiene el atributo de ser, porque es no-ser. Finalmente, dado que UNE es un no-ser, “debe tener el ser un no-ser como un vínculo a su no-ser” (162a4-5). Considero que esto significa que UNE tiene el atributo de no-ser, de la misma manera en que lo tiene el No-ser porque ninguno de los dos son idénticos con el Ser mismo. Sin embargo, UNE aún guarda el atributo de ser, porque es un no-ser. Por consiguiente, dado que UNE no es, tiene en parte el ser en lo relativo a su no-ser (162b4-7). Este pasaje, concluyo, distingue dos formas de ser: (1) ser la naturaleza del Ser, lo que ser es; (2) tener el atributo de ser.
Si este es el caso, ¿cuál es la significación de mê estin y de la frase to mê on, “lo que-no-es” o “no-ser” en este pasaje? Sostengo que lo que “no es” o lo que es dicho que “no es” es dicho solo que no es idéntico con lo que-es-ser, junto con el Ser mismo. Así como el No-ser deber participar del No-ser, para que no sea idéntico con el Ser mismo (así como todos los demás no-seres), también debe participar del SER, de manera que es no-ser. De manera semejante, UNE debe participar del No-ser, para que no sea idéntico con el Ser mismo, pero también debe participar del Ser, puesto que también es no-ser. Propongo que este es el comienzo de la explicación sobre “no es” y “no-ser” desarrollada en el Sofista.
Bibliografía
Allen, R. E. 1997. Plato’s Parmenides. Translated with comment. New Haven: Yale University Press. (Revised edn. of Allen, 1983.)
Burnet, J. 1900–7. Platonis Opera (5 vols.). Oxford Classical Texts. Oxford: Clarendon Press.
Curd, P. K. 1989. “Some Problems of Unity in the First Hypothesis of the Parmenides.” The Southern Journal of Philosophy 27: 347–59.
Duke, E. A., W. F. Hicken, W. S. M. Nicoll, D. B. Robinson, J. C. C. Strachan. 1995. Platonis Opera. Vol. 1. Oxford Classical Texts. Oxford: Clarendon Press.
Friedländer, P. 1969. Plato (3 vols.), Vol. 1: An Introduction. Vol. 3: The Dialogues: Second and Third Period. Princeton: Princeton University Press.
Gill, M. L. 1996. “Introduction.” In M. L. Gill and P. Ryan, Plato: Parmenides. Indianapolis: Hackett. 1–123.
Gill, M. L. 2002. “Plato on Being a Not-Being: The Text of Parmenides 162A–B.” In B. Amden, P. Flemsted-Jensen, T. H. Nielsen, A. Schwartz, C. G. Tortzen (eds.), Noctes Atticae: Articles on Greco-Roman Antiquity and its Nachleben [Festschrift for Jorgen Mejer]. Copenhagen: Museum Tusculanum Press, University of Copenhagen. 121–9.
Gill, M. L. 2014. “The Design of the Exercise in Plato’s Parmenides.” Dialogue 53: 495-520.
Gill, M. L. and P. Ryan. 1996. Plato: Parmenides. Indianapolis: Hackett.
Meinwald, C. 1991. Plato’s Parmenides. Oxford: Clarendon Press.
Meinwald, C. 2014. “How Does Plato’s Exercise Work?” Dialogue 53: 465-494.
Miller, M. 1986. Plato’s Parmenides: The Conversion of the Soul. University Park: Pennsylvania State University Press.
Owen, G. E. L. 1970. “Notes on Ryle’s Plato.” In O. P. Wood and G. Pitcher (eds.) Ryle. 341-72. Anchor Books: Doubleday.
Peterson, S. 1996. “Plato’s Parmenides: A Principle of Interpretation and Seven Arguments.” Journal of the History of Philosophy 34: 167–92.
Peterson, S. 2000. “The Language Game in Plato’s Parmenides.” Ancient Philosophy 20: 19–51.
Peterson, S. 2003. “New Rounds of the Exercise of Plato’s Parmenides.” Modern Schoolman 80: 245–78. Special Issue, Scott Berman (ed.), The Metaphysics of Plato and Aristotle.
Rickless, S. C. 2007. Plato’s Forms in Transition. A Reading of the Parmenides. Cambridge: Cambridge University Press.
Russell, B. 1937. The Principles of Mathematics. 2nd edn. London: Allen & Unwin.
Ryle, G. 1939. “Plato’s Parmenides.” Mind N. S. 48: 97-147.
Sayre, K. M. 1978. “Plato’s Parmenides: Why the Eight Deductions are not Contradictory.” Phronesis 23: 133–50.
Sayre, K. M. 1983. Plato’s Late Ontology: A Riddle Resolved. Princeton: Princeton University Press. Repr. by Parmenides Publishing, 2006.
Sayre, K. M. 1996. Parmenides’ Lesson. Trans. and Explication of Plato’s Parmenides. Notre Dame: University of Notre Dame Press.
Schofield, M. 1977. “The Antinomies of Plato’s Parmenides.” Classical Quarterly N.S. 27: 139–58.
[1] All references are to the Parmenides, unless I indicate otherwise.
[2] I borrow this phrase from Curd (1989).
[3] This interpretation is advocated by, among others, Russell (1937), Ryle (1939), Friedländer (1969), Owen (1970), Schofield (1977), Allen (1997), and Gill (1996), (2012) 45-72, and (2014).
[4] Meinwald (1991) and (2014) argues that there is a way to accept all of the conclusion established in the dialogue’s second part. See also Peterson (1996), (2000), and (2003). For criticisms of this interpretation see, among others, Rickless (2007) 102-6, Gill (2012) 52 with n. 17, and Gill (2014) 504-5.
[5] I disagree, therefore, with the Neoplatonist’s interpretation of the dialogue’s second part. This interpretation is defended by Miller (1986) and Sayre (1978), (1983), and (1996), among others.
[6] The sole exception is the conclusion that the One that is not neither ceases to be nor comes to be (163a7-b6; 163d7-8).
[7] I follow the translation of Gill and Ryan (1996), unless I indicate otherwise.
[8] I accept Shorey’s emendations at 162a8 and 162b2. See Gill (1996) 94-9 and Gill (2002) for a case against Shorey’s emendations. Gill translates the lines as what-is, “if it is to completely be, partak[es] of being in regard to being a being and of not-being in regard to being a not-being.”
[9] Todas las referencias son al Parménides, salvo indicación contraria.
[10] Tomo prestada esta frase de Curd (1989).
[11] Esta interpretación es defendida, entre otros, por Russell (1937), Ryle (1939), Friedländer (1969), Owen (1970), Schofield (1977), Allen (1997), y Gill (1996), (2012) 45-72, y (2014).
[12] Meinwald (1991) y (2014) sostiene que hay una forma de aceptar todas las conclusiones alcanzadas en la segunda parte del diálogo. Véase también Peterson (1996), (2000), y (2003). Para críticas a esta interpretación véase, entre otros, Rickless (2007) 102-6, Gill (2012) 52 y n. 17, y Gill (2014) 504-5.
[13] Estoy en desacuerdo, por consiguiente con la interpretación neoplatónica de la segunda parte del diálogo. Esta interpretación es defendida por Miller (1986) y Sayre (1978), (1983), y (1996), entre otros.
[14] La única excepción es la conclusión de que lo Uno que no es ni cesa de ser ni llega a ser (163a7-b6; 163d7-8).
[15] Sigo la traducción de Gill y Ryan (1996), a menos que indique lo contrario.
[16] Acepto las enmiendas de Shorey en 162a8 y en 162b2. Véase Gill (1996) 94-9 y Gill (2002) para una posición en contra a las enmiendas de Shorey. Gill traduce las líneas como lo que es, “si debe ser completamente, participa del ser en lo relativo a ser un ser y del no ser en lo relativo a ser un no-ser.”