Schmid and Linford provide the following definition of the Trinity:
Orthodoxy, conciliar Trinitarianism (henceforth “Trinitarianism”) is
committed to the following theses: (i) there is one God existing as three
divine persons; (ii) the three divine persons are not numerically identical to
one another; (iii) the divine persons are consubstantial or homoousios;
and (iv) the divine persons are distinguished and related by eternal
processions—the Father begets the Son, and the father and Son (or else the
Father alone) spirate the Spirit . . .
(Joseph C. Schmid and Daniel J. Linford, Existential Inertia and
Classical Theistic Proofs [Cham, Switzerland: Springer, 2023], 312-13)
They argue that the “Neo-Platonic proof inimical to
Trinitarianism on two fronts” (ibid., 313). The first one is:
Uniqueness
The first problem derives from Feser’s inference to the uniqueness of
the absolutely simple being. Feser writes:
For suppose there were two or more noncomposite or utterly simple causes
of things. Then there would have to be some feature the possession of
which distinguishes one of them from the other. Noncompositie or simple cause A
would differ from noncomposite or simple cause B insofar as A has feature F,
which B lacks, and B has feature G, which A lacks. But in that case neither A
nor B would really be simple or noncomposite after all. A would be a simple or
noncomposite cause plus F, and B would be a simple or noncomposite cause
plus G. F and G would be different parts, one of which each of
these causes has and the other of which it lacks. ([Five Proofs for the
Existence of God] 2017, pp. 74-75)
The central premise employed here seems to be that for there to be two
or more x’s, there would have to be some feature in virtue of which they are
individuated. And since the possession of such a feature entails composition,
there would not in principle be two or more absolutely simple beings.
There are at least three problems wit this argument. First, Feser
mistakenly assumes that a differentiating feature between absolutely simple
causes A and B must be in terms of some feature that A (or B) has in
addition to its simple nature. But this is simply untrue. Cause A need not
be a simple cause plus F, and cause B need not be a simple cause plus
G. Instead, A could be identical with its F-ness while B is identical
with its G-ness. In this case, we have a differentiating feature between A
and B—A is F, whereas B isn’t F; and B is G, whereas A isn’t G. Nevertheless, A
and B are both absolutely simple—A just is its F-ness, pure and simple,
and B just is its G-ness, pure and simple. Hence, composition doesn’t
follow from the possession of a differentiating feature. Feser’s argument
therefore fails.
Second, Feser (and other trinitarian classical theists) must grant that being
trinitarian is compatible with being absolutely simple. But then so is being
unitarian, being binitarian, and so on, since there’s no non-arbitrary
reason to think that the latter entail composition while the former doesn’t.
But then there are, in principle, candidate differentiating features
between absolutely simple things—one might be unitarian, another might be
binitarian, a third might be trinitarian, and so on. (This is just a toy
example of candidate differentiating features consistent with being absolutely
simple. Other candidates abound. For instance, perhaps simple being A is
identical to its own impassibility (F-ness), whereas simple being B is
ndentical to its diff-impassibilty (G-ness), where a being is diff-impassible
just in case its conscious state slightly differs in qualitative character from
an impassible being’s conscious state (which, as traditionally understood, is
pure, infinite bliss/joy/happiness/delight). We all know that different types
of tokens of joy, happiness, and delight have slightly different
phenomenological feels, so there’s nothing in principle absurd here.
Third, the argument seems incompatible with Trinitarianism. For the
exact same reasoning equally applies to there being two or more divine
persons; the motivation for thinking that some individuating feature is
needed to distinguish two or more x’s is a perfectly general one, applying to any
x’s. The main reason favoring such a demand seems to e explicability:
if there were no feature that one of x1 or x2 possesses
that the other doesn’t, then (so the reasoning goes) the fact that x1
and x2 are distinct is inexplicable. In other words, if x1
and x2 share all and only the same features, then the non-identity
between x1 and x2 would be inexplicable. But this
motivation seems entirely general, applying to any numerically distinct
realities.
And it that’s true, then it equally applies to divine persons. In order
for there to be more than one divine person, there would have to be some
feature that one had that the others lacked. But in that case—per Feser’s own
reasoning—the divine person would not be absolutely simple (and hence wouldn’t
even be divine after all).
Philosopher W. Matthews Grant describes a Thomistic argument for
uniqueness similar to Feser’s. Grant writes that for Aquinas, “for any
perfection P, it is not possible for there to be more than one subject that is
essentially or subsistent P [i.e., identical to P as such]. For if
subjects x and y were both identical to P,” Grant continues, “then there would
be nothing to constitute the one subject as distinct from the other. Thus,
there could be only one subsistent P and, likewise, only one subsistent existence”
([Free will and God’s universal causality: The dual sources account] 2019,p.
33). But applying this to divine persons, we can see that if both the father
and Son were identical to subsistent existence (P), then there would be nothing
to constitute one of them as distinct from the other; there would, in other
words, be nothing that one had which the other lacked. There would be nothing
in virtue of which they are distant or individuated. For if there were such
an individuating principle, they would no longer be identical to subsistent
existence but would instead be subsistent existence plus this
difference. Thus, at least one of them isn’t subsistent existence. But under
classical theism, to be divine is to be subsistent existence—there is no
distinction between God’s essence and existence, for them God would be an
essence-existence composite. Thus, since (i) at least one of the trinitarian
persons isn’t subsistent existence, but (ii) to be divine is to be subsistent
existence, it follows that (iii) one of the trinitarian persons isn’t divine.
And this contradicts conciliar Trinitarianism.
Feser’s inference to uniqueness plays an essential role in his argument.
Without uniqueness, the argument faces a quantifier shift problem: merely from
the fact that each chain of causes-of-unity has a first non-composite member,
it doesn’t follow that there is a single first member for all such
chains. And without uniqueness in place, the inferences to various other divine
attributes are undercut. For instance, Feser’s inference to omnipotence
presupposes that every (possible) composite entity must derive that entity’s
being from the causal activity of the single absolutely simple being,
for only in that case is there a being from which all causal power derives. (Ibid.,
313-, emphasis in original)
The classical theist cannot avoid this objection by holding that each
divine person isn’t simple. For if each divine person isn’t simple, then
they’re composite. But under classical theism (and the Neo-Platonic Proof),
anything composite is created, efficiently caused thing. But nothing divine
could be a created, efficiently caused thing. Moreover, if the divine persons
are composite, then there would be composite things in God. But then God
couldn’t be simple, since then there would be things in God that are not
God. (For God is simple, and yet such things in God are not simple.) (Ibid.,
313 n. 16)