The Platonic Form as Self-Generating Triunity

The Resolution of the Third Man Argument

Abstract: Self-predication defines the Form. Unity is constituted (not invalidated) by the Third Man regress. Participation is envisaged as a cognitive process. The harmful consequences of anti-Platonic philosophy in the modern era is discussed.

Keywords: Platonism, Participation, religious faith, Bradley’s regress, Plato, Aristotle, Wilfred Cantwell Smith, Arbogast Schmitt, Richard Gaskin.

Although Plato never arrives at a final definition of the Forms it is evident that they must be understood as otherworldly particulars, i.e., perfect and eternal ‘things’ that serve as models for all earthly things. This is the theory of Forms as explicated in the Republic. To the modern mind, it comes across as naïve, as we today reason in terms of abstract universals and concrete particulars. But Francis A. Grabowski III (2008) has established without a doubt that this is how we must understand the theory of Forms. Bertrand Russell comes to the same conclusion, although he is less sympathetic:

Plato makes a mistake analogous to saying ‘human is human’. He thinks that beauty is beautiful; he thinks that the universal ‘man’ is the name of a pattern man created by God, of whom actual men are imperfect and somewhat unreal copies. He fails altogether to realize how great is the gap between universals and particulars; his ‘ideas’ are really just other particulars, ethically and aesthetically superior to the ordinary kind. (2009, p. 112)

As I understand it, Plato does not say ‘human is human’. He says that the human Form is human, something which could be formulated, in terms of set theory, as a set containing itself. Russell understands the theory of Forms to be a premature attempt to cope with the problem of universals. He argues that much of Plato’s thought belongs to the “infantile diseases of philosophy”. However, it is important to remember that Forms are not to be understood as abstract universals dressed up in poetic language. On the contrary, the Form is the real thing, belonging to an ontological realm superior to sublunar existence. The latter is ontologically inferior and contains particulars that are less real, because they are mere imitations of their ultimate exemplars. Even to this day, philosophers continue to wrestle with this arcane theory. Evidently, Russell gravely underestimates its value, considering that people remain enamoured by it. It has a hold on the human psyche. Plato says through Socrates:

If anything else is beautiful besides Beauty itself, it is beautiful for no other reason than because it participates in that Beauty, and this applies to everything. (Phaedo, 100c)

But can it be logically defended? If we grant that the Form of Beauty is itself beautiful (Symposium 210e, Phaedo 100c), then it leads to a regress called the Third Man argument (Parmenides 132a-e): the Form must itself participate in Beauty, which must itself participate in Beauty, etc. Both Plato and Aristotle believed that the theory of Forms was vulnerable to the Third Man argument. I shall argue that they were wrong and that the regress infinitism is really what constitutes the Form. The Third Man argument does not invalidate the theory of Forms — it does just the opposite! Self-predication belongs to the very definition of the Form and self-participation is what generates the unity of the Form. Instead of saying that the Form of Beauty has beauty or is beautiful, we could also say:

(1) The Form of Beauty participates in Beauty

A Form is really a triunity. The copula conjoins subject and object, and that’s why it constitutes a triunity. For the very reason that the Form of Beauty is Beautiful and the Form of White has Whiteness it is evident that Platonic Form must be defined this way — as a oneness of three, a triunity.

What was thought to be the refutation is really the solution, i.e., to acknowledge that the Form of Beauty is generated by participation. The presence of the logical copula is essential. I rely on Richard Gaskin’s (2008) argument that the unity of the proposition is, contrary to expectation, constituted (not invalidated) by Bradley’s regress (a variant of the Third Man). It arises from the fact that relations cannot connect their relata if they are not themselves connected to their relata. This gives rise to a never-ending series of relations connecting relata. Gaskin argues that it is a harmless and constituting regress, the solution to the unity problem (cf. Winther, 2021). The regress occurs due to the fact that the relation between Form and Beauty is conceived as an independent third element. Unity is continually inherited from the previous proposition in the series:

  1. Form and Beauty are One by Participation

  2. Form, Beauty and Participation are One by Participation1

  3. Form, Beauty, Participation and Participation1 are One by Participation2 , and so on ad infinitum

Unlike what F. H. Bradley himself thought, the regress does not involve the interminable practical task of connecting links. Gaskin says:

Bradley’s regress, like the structure of the rational or real line, is infinitistic in a metaphysical, not a practical, sense, and for that reason is not vicious: it imposes a specific infinitistic condition on the structure of propositions — and so ultimately […] on the structure of the world itself — and not an infinitistic, and so unperformable, task for the understander. (Gaskin, 2008, p. 351)

Cantorian set theory allows us to define multiplicity as a unit, and thus the Form of Beauty may be formulated as a set. Sets are denoted by any number of members embraced by curly brackets. We may represent participation in Beauty as a set that contains itself as a member, where f = form, p = participation, and b = beauty.

P = { f, {p}, b }

Because the set contains itself it leads to an eternal regress. It represents a unifying process from eternity that is always generating the Form of Beauty. Participation is one with the Form and identical to the unified Form itself. As proven by Georg Cantor, this is an ‘actual infinity’, that is, something completed and definite (cf. Wiki, ‘Actual infinity’). Hence an infinity can be regarded as a unity, that is, as a unique Form. This was not known to Plato who, along with Aristotle, thought that it simply denoted a limit that could never be reached. Augustine explains that if something acquires unity it acquires being:

For order reduces to a certain uniformity that which it arranges; and existence is nothing else than being one. Thus, so far as anything acquires unity, so far it exists. (De morib., 6.8)

In perpetual self-participation the Form is forever becoming real and its unity reconstituted. In the dialogues a Form is said to be one (hen or monoeides) (even though some passages suggest that a Form cannot be simple in the strict sense). This criterion is also satisfied, in the sense that perpetual participation manifests the Form as One. The composite generates the simple in the way that the Form of White generates perfect whiteness. Note that we could just as well talk about the procession of the Form, because it doesn’t matter if we climb up or down the ladder, so to speak. A Form is an instance of itself. It is more of a self-generative dynamism than a static thing.

Does this make sense? Arguably, this is Platonic logics pertaining to the otherworldly realm, and we needn’t worry so much about its scientific applicability. Plato’s dictum ‘one over many’ is important to religion, especially Christian religion:

For just as through the disobedience of the one man the many were made sinners, so also through the obedience of the one man the many will be made righteous. (Romans 5:19)

This is Platonic in the sense that the universal exemplar encompasses individual plurality. Inasmuch as Adam is the representative of mankind, all his descendants are thought to be personally involved in his sin. In a corresponding way we partake of Christ’s work of atonement. We fell in Adam but are exalted again in Christ: “For as in Adam all die, so in Christ all will be made alive” (1 Cor. 15:22). Religion makes use of Platonic Ideas and would lose its validity without them. It can’t be helped that it seems contrary to science — without the doctrine of original sin we could not understand ourselves. Blaise Pascal (1623-1662) says:

Original sin is folly in the eyes of men, but it is given as such. You must not, therefore, reproach me for the lack of reason in this doctrine, since I give it as being without reason. But this folly is wiser than all the wisdom of men, is wiser than men. For without it, what will we say man is? His whole state depends on this imperceptible point. And how could he perceive it through his reason, since it is something contrary to his reason, and his reason, far from discovering it by its own ways, draws away when presented with it? (Pascal, Pensées)

Platonic and religious statements are not statements about the world as disjunct from man. They are human statements about the world and man in interrelation. For this we have recourse to symbols, archetypes and Forms, as well as the principle of ‘one over many’. Rationalists such as Russell may be right that it is folly, but in that case folly is indispensable in human life. That’s why Paul says:

For since, in God’s wisdom, the world did not know God through wisdom, God was pleased to save those who believe through the foolishness of the message preached. (1 Cor. 1:21)

“We are fools for Christ’s sake”, he says. As Prof. Wilfred Cantwell Smith (scholar of religious studies, 1916-2000) explains, modern rationalists hold the view that a system of thought must satisfactorily explain reality. This seems adequate, aside from the fact that by “reality” they mean the non-human world only. It is unduly limited in that we have not only to interpret reality but also to live with it and with each other (cf. Smith, 1977, p. 28). Smith says:

Any system of thought, ostensibly “scientific” or whatever, that finds Christian (or Islamic, or Buddhist) discourse either meaningless or simply false, is announcing that it can understand and interpret the world of physical nature but not the world of man. (Smith, 1977, p. 33)

We know today that transcendental concepts are necessary to come to grips with human reality. But we do not know why it is so. We aren’t sure why Platonic thinking is effective; nor can we be certain that the Forms really exist “out there”. It’s as if they abide forever in the hyperuranion or in God’s mind, and we only know them when they take shape in the soul. However, we can be certain that transcendental Forms affect the human condition and that human beings in turn have a great impact in the world.

Smith explains that people in history have never defined religious faith in terms of its object. Faith was always regarded a quality of the person, but never as an externalized viewing. The meaning of faith is to pledge heart and soul to the divine. In the modern understanding, however, religious “belief” is directed towards an object. As a consequence, religious life has taken a wrong turn: “a great modern heresy of the Church is the heresy of believing” (p. v). Instead we ought to commit ourselves to transcendental Truth and live in loyalty with God.

Faith means to have God in one’s heart; it does not mean to “believe” that God invisibly exists “out there”. In his important work, Modernity and Plato: two paradigms of rationality (2012), Arbogast Schmitt explains what caused this change of view. It stems primarily from the rejection of the epistemology of Plato and Aristotle, which took its beginning in the late 14th century with the writings of Duns Scotus and William of Occam. Earlier it was thought that the senses receive the perceptible forms sans the matter, as explicated in Aristotle’s De Anima (ii-iii). The thing perceived is received in the soul, like an imprint in wax, and it is the intellect which brings about this unity. Minds, in a non-literal way, become isomorphic with their objects (cf. Shields, 2020). Thus, we must always perform an intellectual work of discrimination and understanding. For example, a pair of scissors is only truly perceived when one understands its function. A cognitive process, together with values of feeling, has to rely on abstract concepts to model a corresponding form in the soul. According to Plato and Aristotle, perception requires an intellectual act of discrimination between what is essential and what is not; experience must originate from the memory records of repeated perceptions.

In modernity, however, unity is found immediately in “intuition”, insomuch as the individual object is a given, already intellectually determined in itself. According to Duns Scotus, the senses can forthwith receive the multiplicity of sense impressions as a uniform whole (simul totum). Consequently, the intellect is construed as secondary whereas the outside object, as such, is endowed with a primary and foundational role for perception. Such a “philosophy of representation” is characterized by a “metaphysical overload of the individual object” (p. 28). It is really an “epistemologically naïve copy-realism that lies in the conviction that in thinking one can begin with individual objects and derive one’s concepts ‘from experience.’ ” (p. 36). Says Schmitt:

The central impulse in this turn [of thinking] onto itself is the acceptance of empirical reality and one’s own existence in the here and now as the sole yardstick of insight and action: only that which is presently there and can be sensually experienced and verifiably exists is recognized as being real and as something thought can draw on in forming its concepts. This conviction was originally and is even today anti-Platonic in intent: it rejects the Platonic doctrine of a reality to ideas, that is, of a “thing itself” that is recognizable in a purely rational way, and, instead, insists on the immediate evidence of sensually experienceable individual objects. Historically, this development, through which this anti-Platonism became accepted as the virtually unanimous conviction, had several phases. However, even after these speculative theories were allegedly overcome, Plato remained and remains the antipode in relation to whom the individual “critical turn” is executed each time. (p. xxiii)

Only a Form can manifest as an instance of itself, in the manner of a transcendent individual. To the extent that a particular participates in the one Individual, it receives a measure of the divine. But in the modern era, the individual has become sufficient unto himself. The intellect has turned onto itself. The ruinous consequences of anti-Platonism and nominalism have become evident in the growing egotism among people. An individual is understood as an instance of himself. Accordingly, any person is everybody’s equal, even if he has a criminal background. One is no longer expected to participate in the Form of the Individual. On the contrary, being curved into oneself fulfills the value of the individual (incurvatus in se; Augustine). Schmitt says:

The early modern period was well aware of the theological implications of making the individual absolute. Declaring the individual to be an instance of itself means nothing other than declaring the world to be the direct and immediate embodiment of God, that is, of an absolute rationality (“God does not play at dice”). When one recalls that Hegel’s projection of the Christian doctrine of trinity onto the history of the development of the world itself emerged from this concept and that the idea of the embodiment of the absolute spirit in the individual peoples and thus the modern religious idealization of the nation-state in turn emerged from his projection, one has an eminent example of the tremendous significance of this metaphysical turn to experience. (pp. 29-30)

We can now better understand Paul’s model of faith as participation in Christ and why Augustine saw the Eucharistic meal as the eating of the “inner bread”. Inner representation depends on a Platonic-Aristotelian epistemology of participation, through which a corresponding form is moulded in the soul. To have faith means that Christ takes form in the soul (“[I]t is no longer I who live, but Christ lives in me”; Gal. 2:20). The horrors of the modern era have their explanation in the decline of the Christian-Platonic worldview and epistemology. The modern bias, that truth exists nowhere but outside us and is ready to be appropriated, continues to undermine society and overall mental health. It is not the question of submitting to the belief that Forms exist external to us. Rather, we are supposed to participate in the Forms in order for them to incarnate. The rationalist views it as folly; but according to Paul, the participation in the Logos is the only way of redemption. In this article I have augmented the Platonic principle of participation by proposing that it is part and parcel of the Form.


© Mats Winther, 2022.


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