Plato's Parmenides, on the One and the Many

In Plato's Parmenides, the narrator is Cephalus of Clazomenae, who arrives in Athens and is greeted in the market place by Adimantus and his brother Glaucon. They go to meet Antiphon, the half-brother of Adimantus and Glaucon, in order to hear him recount a legendary conversation that Socrates once had with Zeno and Parmenides. Parmenides was about sixty-five years old at the time, Zeno was about forty, and Socrates was about twenty.
      The conversation began with Zeno arguing that if there is a plurality of things, then they must be both like and unlike one another. Socrates responded, however, that if unlike things cannot be like and like things unlike, then there must not be a plurality of things. Since Zeno agreed with this conclusion, Socrates remarked that Zeno shared with Parmenides the view that all things are one, and not many. (128b)
      Socrates proceeded to distinguish between being one thing and having many aspects, explaining that in this sense a given thing can be both one and many. (129d)
      Parmenides responded by asking Socrates whether the abstract form of something (such as largeness or smallness or beauty or justice) as a whole can be shared by a plurality of things, and whether, if this were the case, it would mean that the form as a whole would be in a number of separate things and would therefore be separate from itself. (131b)
      Socrates responded no, this would not mean that a form shared by many separate things would be separate from itself. The form itself would still be one and the same thing. (131b)
      Parmenides then responded that a form shared by many separate things must therefore be divisible into parts, and that each thing that shares in that form will therefore only be able to share a part of it. (131c) But if equality, for example, were a form that things could share, then they would only be able to share a part of it, and would share in something less than equality itself, so they must actually not be able to share in equality either in part or as a whole.
      Socrates admitted this would be a problem, if the abstract forms of things were taken to be divisible into parts. However, he explained that if a form covers all cases of a single thing, then it can still be one and the same in all cases of that thing.
      Parmenides then told Socrates that if he wanted his theory of forms to be thoroughly exercised, he must examine the consequences both for a plurality of things (with reference to one another) and for a single thing (with reference to itself) of there being, or not being, a plurality of things. (136a) The One cannot have a plurality of parts and still be the One. (136c) Moreover, it cannot have a beginning, middle, or ending, because such stages would be parts of it, and it would no longer be the One. (136d) Nor can it be at rest, because then it would remain in the same place, and would be encompassed by something other than itself. Nor can it be in motion, because then it would be undergoing alteration, and would not be the One. 
      Furthermore, the One cannot be different from itself or the same as another. Nor can it be the same as itself or different from another, because it is simply the One. (139b) For the same reason, it cannot be equal or unequal to itself or to another. (140b) It cannot be older or younger than anything, or the same age as anything. It has nothing to do with time, and thus has never become, was never becoming, and never was, and will not become, be becoming, or be in the future. (141e)
      Parmenides concluded there is no way in which the One can have being. How can this be the case with the One? In order to answer this question, Parmenides described the consequences of the contradictory proposition that the One can and does indeed have being. If the One has being, then number also has being. If number has being, then the One is both one and many, whole and parts, limited as well as indefinitely numerous. (145a) It is both at rest and in motion. It is both the same as, and different from, itself, and the same as, and different from, others. (146b) It is equal both to itself and to others, and it is both greater and smaller than others.
      The One is also becoming older than something becoming younger, and in this sense it is becoming both younger and older than itself. (152b) But since in being and becoming it must take the same time as itself, it also becomes neither younger nor older than itself. (152e)
      The One both is and is becoming older and younger than itself, and than others, and also neither is nor is becoming older or younger than itself, or than others. (155c)
      Parmenides then described the consequences of the proposition contradictory to the proposition that the One is, the proposition that the One is not. If there is no One, but only things other than the One, then those things cannot be One or many. There cannot be many without a One. Parmenides concluded that without the One, there is in fact nothing at all.
      The One, as defined by Parmenides, has an elusive and paradoxical nature, but this seems to be more a matter of definition than of cosmic or logical necessity. The dialogue between Socrates and Parmenides is perhaps more interesting for the philosophical and logical questions it raises than for the convoluted and often problematic arguments made by Socrates about the theory of forms and by Parmenides about the nature of unity and plurality.
      Parmenides' method of inquiry is dialectical. He considers the consequences of a given proposition, and then considers the consequences of a contradictory proposition in order to get at the truth of the matter. In this way, he is able to reveal unrecognized inconsistencies and overlooked implications of previous assumptions made by his interlocutors.
      Many of the logical arguments in the Parmenides fail to be persuasive or convincing. Nevertheless, they stimulate further examination of, and critical reflection upon, their meaning. For example, Socrates asks Zeno, "What does this statement mean, Zeno? 'If things are many,' you say, 'they must be both like and unlike. But that is impossible; unlike things cannot be like, nor like things unlike.'" (127e) Why exactly is it impossible that if there are many things, some may be like and others unlike one another? it is indeed possible. This fact wouldn't entail that the same things that are alike in some respect are simultaneously unlike in the same respect. That would indeed be contradictory. But Socrates does assume that this is what is entailed by Zeno's statement, and he then turns the statement around by saying, 'if things can't be both like and unlike, then there can't be a plurality of things.' His argument is formally valid (it takes the form of modus tollens or denying the consequent), but he commits the informal fallacy of equivocation by changing the implied meaning of Zeno's statement from 'among a plurality of things, some must be like and others unlike one another,' to 'in order for there to be a plurality of things, the same things that are alike in some respect must also be unlike in the same respect.'
      Similarly, the assumption that Parmenides initially seems to make in describing the One is that there is nothing other than the One. The many are actually nothing other than the One, and the One is all there is. Thus the One has no beginning or ending, no size or shape, no location in time or space, no boundaries or limits, and no relation of likeness or unlikeness to anything else. But then Parmenides makes the contradictory assumption that there are indeed things other than the One, and that they are a plurality. Thus, the One may consist of a plurality of things, and it may be both One and many. (145a) It may be a whole consisting of many parts, have a beginning and ending, be at rest as well as in motion, and be like or unlike other things. Neither of these assumptions seems any more plausible or justifiable than the other.
      

REFERENCES

"Parmenides," translated by F.M. Cornford, in The Collected Dialogues of Plato, edited by Edith Hamilton and Huntington Cairns (New York: Random House, 1961).


      

Perfectionist Fallacies

In logic, the perfectionist fallacy may be represented by the argument that if some solution to a problem doesn't solve the problem perfectly, then that solution is unacceptable. Any imperfect solution to a problem is unacceptable, even if a perfect solution is unnecessary or unavailable.
      In our thinking about ourselves, we may sometimes be misled by the perfectionist fallacy, which may take a variety of forms. These potentially harmful and deleterious forms of perfectionism are to be avoided if we want to be at peace with ourselves and in harmony with others.
      The first perfectionist fallacy may be committed when you say to yourself, "My thoughts are only worth expressing if they're totally original, groundbreaking, and revolutionary."
      The second perfectionist fallacy may be: "Anything I do or any activity I engage in is only meaningful if I'm 'making an impact' or 'making a difference' with regard to intellectual, philosophical, scientific, political, moral, or social problems."
      The third perfectionist fallacy may be: "My life will only mean something if I'm remembered by future generations for what I did, said, wrote, discovered, or accomplished."
      The fourth perfectionist fallacy may be: "I can only be happy if I don't feel guilty about anything. Happiness means freedom from guilt."
      The fifth perfectionist fallacy may be: "I can only be happy if I've truly fulfilled my potential for human, technical, professional, or social achievement."
      The sixth perfectionist fallacy may be: "If I'm an underachiever, then my life isn't (or wasn't) really worth living, or it isn't (or wasn't) really as worth living as it could have been."
      The seventh perfectionist fallacy may be: "In order to be the best I can be, I must constantly strive for perfection."
      The eighth perfectionist fallacy may be: "When I try to get better at something, and I reach a plateau, I've probably reached my limit, and I'm probably not going to get any better at doing it, even if I change my approach or redefine what it means to get 'better.'"
      The ninth perfectionist fallacy may be: "There is someone other than God who is perfect. Perfection is possible for me, just as surely as imperfection."
      The tenth perfectionist fallacy may be: "If I can't be perfect at something, then I can't be truly happy."
      In our thinking about others, we may similarly be misled by various forms of the perfectionist fallacy, involving false assumptions about the reliability or perfectness of our knowledge of others. These false assumptions may include:
      (1) "I can determine everything I need to know about a person just by looking at them."
      (2) "I can always (or almost always) determine a person's race, ethnicity, sexual orientation, or nationality just by looking at them or listening to them speak."
      (3) "If someone doesn't agree with me, it's because they're prejudiced, ignorant, uninformed, irrational, or haven't been listening to what I've been saying."
      (4) "If people don't understand what I'm saying, it's because they're ignorant, unenlightened, or haven't been paying attention, rather than because I haven't expressed myself clearly."
      (5) "If someone is homeless, then it's because of choices they've made. They're the ones who're responsible for the fact they're homeless."
      (6) "If someone is unemployed and on welfare, then it's because they lack a work ethic and don't want to work."
      (7) "If someone lacks job skills, then it's because they don't have the aptitude for a job and never applied themselves in school and never valued getting an education."
      (8) "The difference between wealthy and poor people is that poor people don't take advantage of educational, professional, and employment opportunities."
      (9) "If someone fails at something, then it means they're a loser."
      (10) "The difference between successful and unsuccessful people is the difference between winners and losers."
      All of these false assumptions may hinder or impair our capacity for compassion and understanding, as well as diminish our sense of our own well-being and our ability to promote the well-being of others.
     

The Metaphysics of Gender: A Glossary

androcentric vs. gynocentric metaphysics – as described by Sally Haslanger (2000), 1. the distinction between a theory that takes males or masculinity as the norm and females or femininity as the exception and a theory that takes females or femininity as the norm and males or masculinity as the exception. Also, 2. the distinction between a theory that emphasizes or is dominated by male perspectives, to the extent that female perspectives are marginalized or excluded, and a theory that emphasizes or is dominated by female perspectives, to the extent that male perspectives are marginalized or excluded.¹ 

anti-essentialism – 1. the theory that there is no essential characteristic that defines what it means to be a woman. 2. the theory that women don't share any essential characteristics without which they would not be women. 

anti-naturalism – 1. the theory that women don’t have certain natural qualities that aren’t possessed by men, and that men don’t have certain natural qualities that aren’t possessed by women. 2. the theory that women don't naturally have certain qualities that distinguish them from men, and that men don't naturally have certain qualities that distinguish them from women. 

anti-realism – 1. the theory that gender has no reality that is independent of its being experienced, perceived, or socially constructed. 2. the theory that there is nothing other than social construction, norms, or convention that determines a person’s gender.

biological determinism – 1. the theory that gender is biologically determined, rather than socially constructed (through socialization, assigned social roles, learned behaviors, etc.).

biological reductionism – 1. the theory that gender differences can be reduced to biological differences.

biologism – 1. the theory that gender differences are biological in nature. 2. the theory that women, by their biological natures, tend to possess certain psychological or social traits to a greater extent than men, and that men, by their biological natures, tend to possess certain psychological or social traits to a greater extent than women.

essentialism – 1. the theory that there is at least one characteristic shared by all women, possession of which is necessary for someone to be considered a woman. 2. the theory that there is at least one essential characteristic that makes someone a woman. 3. the theory that the gender of an individual is determined by at least one characteristic that is shared by all individuals of that gender. 4. the theory that gender is essential to a person’s identity, and that a given person would not be the same person if she were of a different gender. 

      Charlotte Witt (2000) distinguishes between individual essentialism (the theory that there are properties essential to an individual’s identity) and kind essentialism (the theory that there are properties essential to belonging to particular kinds or classes of individuals).² 

      Gender essentialism may take the form of biologism or naturalism.³ 

gender performativity – as described by Judith Butler, 1. the theory that gender attributes are performative, rather than expressive in nature, and that they themselves constitute the identity they are said to express or reveal.⁴ “Gender ought not to be construed as a stable identity or locus of agency from which various acts follow,” says Butler. ”Rather, gender is an identity...constituted...in an exterior space through a stylized repetition of acts.”⁵ 
      This theory has been attacked by Martha Nussbaum (1999), who accuses Butler of being pessimistic and politically disengaged regarding the self’s powers of agency prior to cultural construction, and thus also of being pessimistic and politically disengaged regarding the self’s capacity to effect cultural change.⁶   
      Butler's conception of gender performativity has also been criticized by Seyla Benhabib (1995), who says 
      

      “Butler also maintains that to think beyond the univocity and dualisms of gender categories, we must bid farewell to the “doer beyond the deed,” to the self as the subject of a life-narrative…If this view of the self is adopted, is there any possibility of changing those “expressions” which constitute us? If we are no more than the sum total of the gendered expressions we perform, is there ever any chance to stop the performance for a while, to pull the curtain down, and let it rise only if one can have a say in the production of the play itself? Isn’t this what the struggle over gender is all about? Surely we can criticize the supremacy of presuppositions of identity politics and challenge the supremacy of heterosexist and dualist positions in the women’s movement. Yet is such a challenge only thinkable via a complete debunking of any concepts of selfhood, agency, and autonomy? What follows from this Nietzschean position is a vision of the self as a masquerading performer, except of course we are now asked to believe that there is no self behind the mask.”⁷

      Butler (1995) responds to Benhabib's critique (as well as to Nussbaum's subsequent polemic) by saying

      “To claim that politics requires a stable subject is to claim that there can be no political opposition to that claim. Indeed, that claim implies that a critique of the subject cannot be a politically informed critique but, rather an act which puts into jeopardy politics as such…
      The critique of the subject is not a negation or repudiation of the subject, but, rather, a way of interrogating its construction as a pregiven or foundationalist premise…
      We may be tempted to think that to assume the subject in advance is necessary in order to safeguard the agency of the subject. But to claim that the subject is constituted is not to claim that it is determined; on the contrary, the constituted character of the subject is the very precondition of its agency. For what is it that enables a purposed and significant reconfiguration of cultural and political relations, if not a relation that can be turned against itself, reworked, resisted? Do we need to assume theoretically from the start a subject with agency before we can articulate the terms of a significant social and political task of transformation, resistance, radical democratization?...We need instead to ask: what possibilities of mobilization are produced on the basis of existing reconfigurations of discourse and power? Where are the possibilities of reworking that very matrix of power by which we are constituted, of reconstituting the legacy of that constitution, and working against each other those processes of regulation that can destabilize existing power regimes? For if the subject is constituted by power, that power does not cease at the moment the subject is constituted, for that subject is never fully constituted, but is subjected and produced time and again.”⁸ 

      Butler also explains, in a 2002 interview with art historian and writer Liz Kotz, 

      "What's not enough read in my work is the emphasis on power and the intense normativity that governs gender. I was trying to interrogate the painful ironies of being implicated in the very forms of power that one explicitly opposes, and trying to understand what kinds of agency might be derived from that situation. I think that it's inevitable that there's no position outside power, and in that way I'm linked with Foucault; but I don't think that means one is determined by power relations."⁹

      

naturalism – 1. the theory that women naturally possess certain characteristics that distinguish them from men. 2. the theory that women act according to their natures, and that they don’t act in ways that are contrary to their natures.

nominalism – 1. the theory that there is no universal property that belongs to all women. 2. the theory that women do not share any universal characteristics, and that they may merely resemble one another in various ways (resemblance nominalism).

realism – 1. the theory that gender is a real property that exists independently of any social construction. 2. the theory that there is something other than social construction that determines a person’s gender.

sex/gender distinction – 1. roughly, the distinction between the biological components of a person’s sexual identity and the psychological, social, and cultural components of their gender identity. 2. the distinction between biological sex (as defined by chromosomes, anatomy, hormones, secondary sex characteristics, and so on) and gender (as defined by experiences, perceptions, attitudes, and behaviors).
      This distinction is controversial. It has been criticized for being misleadingly dualistic, insofar as there may be cultural aspects of sex difference (impacting how individuals are assigned to different sexes) and biological aspects of gender difference (impacting how individuals experience their gender identity). It has also been criticized for implying that both sex and gender may be unequivocally described as male or female. It has also been criticized for implying that gender is fixed and stable, and that it can’t be fluid and variable.
      Judith Butler (1999) says that 

      “Taken to its logical limit, the sex/gender distinction suggests a radical discontinuity between sexed bodies and culturally constructed genders…Further, even if the sexes appear to be unproblematically binary in their morphology and constitution (which will become a question), there is no reason to assume that genders ought also to remain as two, The presumption of a binary gender system implicitly retains the belief in a mimetic relation of gender to sex whereby gender mirrors sex is or is otherwise restricted by it.”¹⁰

We have no reason to believe that gender is strictly binary in nature, says Butler. And if the sex of a person is itself something culturally constructed (at least to some extent), perhaps there is no real distinction to be made between sex and gender at all.¹¹    

social constructionism (or constructivism) – 1. the theory that gender is socially constructed, rather than biologically determined.
      Weak constructionism may not see gender (or the gendered self) as totally a matter of social construction, and may be realist in holding that gender (or the self) has some reality prior to, or apart from, its social construction. On the other hand, strong constructionism may see gender (or the gendered self) as totally a matter of social construction, and may be antirealist in denying that gender (or the self) has any reality prior to, or apart from, its social construction. 


FOOTNOTES

¹Sally Haslanger, “Feminism in Metaphysics: Negotiating the Natural,” in The Cambridge Companion to Feminism in Philosophy, edited by Miranda Fricker and Jennifer Hornsby (Cambridge: Cambridge University Press, 2000), p. 109.
²Charlotte Witt, The Metaphysics of Gender (Oxford: Oxford University Press, 2011), pp. 5-13.
³Elizabeth Grosz, “A Note on Essentialism and Difference,” in Feminist Knowledge: Critique and Construct, edited by Sneja Gunew (London: Routledge, 1990), p.334.
⁴Judith Butler, Gender Trouble: Feminism and the Subversion of Identity (New York: Routledge, 1999), p. 180.
⁵Ibid., p. 179.
⁶Martha Nussbaum, “The Professor of Parody,” in The New Republic, Feb 22, 1999, online at https://faculty.georgetown.edu/irvinem/theory/Nussbaum-Butler-Critique-NR-2-99.pdf.
⁷Seyla Benhabib, "Feminism and Postmodernism," in Feminist Contentions: A Philosophical Exchange, by Seyla Benhabib, Judith Butler, Drucilla Cornell, and Nancy Fraser (New York: Routledge, 1995), pp. 1-16.
⁸Judith Butler, "Contingent Foundations," in Feminist Contentions: A Philosophical Exchange, pp. 4-13.
⁹Judith Butler, "The Body You Want: An Interview with Judith Butler," ArtForum, November 1992, online at https://www.artforum.com/print/previews/199209/the-body-you-want-an-inteview-with-judith-butler-33505.
¹⁰Butler, Gender Trouble, p. 10.
¹¹Ibid., p. 11.