Beyond Classical Identity
Identity, Classical Metaphysics, and the Trinity
The question of identity is often approached today as if it were first and foremost a logical matter: under what conditions can we say that x is the same as y? By contrast, much of the classical tradition treats “being the same” as a surface expression of deeper realities: what a thing is, how it exists, and what underlies its properties and relations. In that older picture, identity is not primitive. It is an outcome of metaphysics. This becomes especially clear when we look at how the tradition thinks about God’s simplicity and the Trinity.
What follows traces that pattern. First, I sketch how Aristotle, Aquinas, Bonaventure, and Plato talk about substance, form, and participation. Then I turn to Avicenna and Maimonides on essence and existence, before contrasting Leibniz, Hume, and Descartes as early modern reconfigurations of identity. Finally, I show how patristic and medieval accounts of the Trinity presuppose this classical metaphysics, and how, on that basis, identity is best seen as downstream of act, essence, and origin.
Following this Initial essay, as outlined above, we’ll get into the technical logic of Identity as logic, if you need to see how it works technically. And beyond that we’ll survey the history in that syntax. Enjoy…
1. Substance, form, and what really underlies everything else
In Aristotle’s Categories, the discussion of substance immediately shifts the focus away from bare logical sameness to the question of what really underlies other things. Substance “in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject; for instance, the individual man or horse” (Aristotle 1941). That is a very dense sentence. In plain terms, Aristotle is saying: there are things which are not just “said of” another, and not just “in” another as a feature. Socrates is not in something else the way his pallor is; the horse is not in something else the way its color is. These “this-such” concrete beings are what most deserve the name substance.
On that basis he can say that “everything except primary substances is either predicated of a primary substance or present in a primary substance” (Aristotle 1941). “Animal” is said of this or that human being. Color is present in this or that body. “Thus everything except primary substances is either predicated of primary substances, or is present in them, and if these last did not exist, it would be impossible for anything else to exist” (Aristotle 1941). Substance is not just one more item in a flat inventory; it is what carries everything else.
Aquinas takes this on board and sharpens it. Because “being is not a genus,” he argues, “being cannot be of itself the essence of either substance or accident.” You cannot define substance as “a being of itself without a subject.” Instead, “it belongs to the quiddity or essence of substance ‘to have existence not in a subject’; while it belongs to the quiddity or essence of accident ‘to have existence in a subject’” (Thomas Aquinas 1948). An accident is a way something is; a substance is the something that has those ways of being. In a later scholastic formulation, properties and relations “are that whereby a suppositum is thus or such, id quo aliquid est” (Marshner The Debate About Universals).
Form completes the picture. In the Metaphysics, Aristotle remarks that “the bronze is potentially a sphere, and when it is made round it constitutes an actual one—a single sphere of bronze” (Aristotle 1984). Matter is a “can be”; form is the determinate “is.” This is why “the whole is not like a heap” (Aristotle 1984). A heap is just a pile of parts side by side. A true whole is one being whose parts exist and function through a shared form.
Aquinas applies this directly to the human soul. The soul is not just a driver of an inert machine. It is the substantial form of a living body. “Since the soul is united to the body as its form, it must necessarily be in the whole body, and in each part thereof. For it is not an accidental form, but the substantial form of the body. Now the substantial form perfects not only the whole, but each part of the whole” (Thomas Aquinas 1948). He goes further: “the soul communicates that existence in which it subsists to the corporeal matter; and thus from the soul and the matter there results unity of existence, so that the existence of the whole composite is also the existence of the soul” (Thomas Aquinas 1948). The human “I” is not a stack of separate existences, but a single act of being, given by the soul to the body.
Bonaventure develops the same insight in explicitly spiritual and teleological terms. “The soul, Bonaventure insisted, is something in itself” (Bonaventure, Commentary on the Sentences). It is a real principle, not a mere abstraction. “But he also argued that the soul is the active principle that brings existence to the human composite in its union with its body and enables it to function properly in the physical realm of being” (Bonaventure, Commentary on the Sentences). For that reason, “the soul is ordered to its body, not imprisoned within it. It realizes its perfection in union with its body, not in spite of it” (Bonaventure, Commentary on the Sentences).
In all of this, identity is not treated as an abstract relation superimposed on neutral items. It is rooted in the fact that there is one underlying subject (the primary substance), informed by one act of being (the substantial form), to which properties and relations belong. To say that “this is the same man” through change is to say that the same substantial subject and the same soul–body composite continue to underlie the shifting accidents.
Plato helps fill out another dimension: participation in forms. In the Phaedo, he takes as his “safest answer” that “all beautiful things are beautiful by the Beautiful” (Plato 1997). Likewise, “if there is anything beautiful besides the Beautiful itself, it is beautiful for no other reason than that it shares in that Beautiful” (Plato 1997). He generalizes: “all beautiful things are beautiful by the Beautiful,” and similarly for “absolute greatness, and health, and strength, and the essence or true nature of everything” (Plato 1997). These realities are not ultimately grasped by sense; “he attains to the knowledge of them in their highest purity who goes to each of them with the mind alone, not allowing when in the act of thought the intrusion or introduction of sight or any other sense in the company of reason” (Plato 1997). The world of sensible things is one of participation and image; the forms are the stable standards that give them what they are.
Again, the pressure is downward: from the changing and many to what really gives unity. A thing is what it is by something deeper: its form, its participation, its underlying act of existence. Identity talk trails behind this structure.
2. Essence and existence in creatures and in God
The medievals then formalize a distinction that was implicit in Aristotle and Plato: the difference between what a thing is and that it is. Avicenna states bluntly that “essence considered in itself is indifferent to existing or not existing” (Avicenna 2005). The quiddity “horseness,” taken just as such, “is neither one nor many, and exists neither in concrete things nor in the soul” (Avicenna 2005). Unity, plurality, existence in the world, and existence as an idea are all extra to the essence as such. They are “concomitants of existence” (Avicenna 2005). In created things, this means that essence and existence are really distinct: what they are does not entail that they are.
All of this changes when Avicenna turns to God. For the First, or Necessary Existent, “there is no quiddity other than His individual existence” (Avicenna 2005). Here, what God is and that God is coincide. There is no metaphysical composition of “nature plus existence.”
Maimonides presses this point from another angle, with an eye toward idolatry. “You must understand that God has no essential attribute in any form or in any sense whatever,” he writes, and concludes that “there cannot be belief in the unity of God except by admitting that He is one simple substance, without composition or plurality of elements” (Maimonides 1956). If you start distributing positive, distinct essential attributes in God the way we do in creatures, you have already fractured divine simplicity.
Bonaventure translates these lines into a luminous metaphysical–theological image. God is “an undivided light of pure act, in whom all distinct forms subsist in absolute simplicity” (Bonaventure, Commentary on the Sentences). Creatures are “shadows, echoes, pictures… of that Eternal Source and Art” (Bonaventure 1978). All multiplicity of forms is in God as in their simple source, without composition or partition; in creatures they are parceled out under conditions of finitude.
Taken together, Aristotle, Avicenna, Aquinas, Maimonides, and Bonaventure give us a very definite hierarchy. For creatures, essence and existence are distinct, substance underlies accidents, and forms configure matter into concrete beings. What a thing is and that it is must be combined. For God, there is no such combination. God is pure act, without a quiddity standing apart from existence, “one simple substance, without composition or plurality of elements” (Maimonides 1956). Identity, in God’s case, is the identity of this one simple act with itself. It is not the result of a genus narrowed by differentia, nor the overlap of many positive attributes.
3. Early modern reconfigurations: concepts, bundles, and the suspicion of forms
The early moderns both inherit and unsettle this classical picture. Leibniz still wants a rich inner core to things, but he relocates that core from metaphysical act into conceptual content. “The nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to include and to allow the deduction of all the predicates of the subject to which this notion is attributed” (Leibniz 1976). On this view, “the nature of an individual substance is to have a notion so complete that it suffices to contain all its predicates” (Leibniz 1976).
In his Correspondence with Arnauld, he famously claims that “the individual concept of each person includes once and for all everything that will ever happen to him” (Leibniz 1988). Thus “the concept of the individual Caesar includes everything that ever happened to him, such as that he was dictator, that he conquered Pompey, that he was assassinated in the Senate on the Ides of March, and all the other details of his life” (Leibniz 1988). Likewise, the individual notion of Alexander contains that “he vanquished Darius and Porus,” and God “even knows a priori (and not by experience) whether he died a natural death or whether he was poisoned” (Leibniz 1988). More radically, Leibniz says that “this complete concept… involves everything that happens to me” and that it is “by virtue of this concept that all my predicates are connected in a subject, me” (Leibniz 1988). He can then say that “every substance is like an entire world and like a mirror of God, or indeed of the whole world which it portrays, each one in its own fashion,” and that “every monad expresses the whole universe in its own way” (Leibniz, Monadology). “In nature there are never two beings which are perfectly alike and in which it is not possible to find an internal difference” (Leibniz, Monadology).
Identity here is no longer keyed primarily to underlying act and form. It is tied to a unique, complete concept that includes all predicates. God’s intellect grounds these concepts, but the emphasis has shifted from act-of-being to “notion so complete.”
Hume represents the opposite extreme. When he looks inward to the self, he does not find a substantial core but only a succession of mental states: “when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception” (Hume 1978). He concludes that we are “nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement” (Hume 1978). The mind “is a kind of theatre, where several perceptions successively make their appearance; pass, re-pass, glide away, and mingle in an infinite variety of postures and situations” (Hume 1978). If Leibniz internalizes the substantial core into a complete concept, Hume dissolves it into a stream of impressions and rejects a substantial self altogether.
Descartes, meanwhile, explicitly sidelines the older language of substantial forms. In a letter to Regius, he says he does not “entirely reject substantial forms,” but finds them “unnecessary in setting out my explanations” (Descartes 1988). He treats them as “a mere explanatory tool that may be replaced by a better one,” and suggests that “any material thing is only an aggregate of qualities and properties” (Descartes 1988). He even “argues… against the habit to apply ‘substantial form’ when defining the human being” (Descartes 1988). Here again, whatever unity a thing has is no longer grounded in a form giving existence to matter as one act. It is an arrangement of qualities, describable by physics.
These moves prepare the modern habit of treating identity as a thin equivalence relation on property-bundles or on sets of predicates, abstracted from the classical priority of act, substance, and form. That is precisely the habit the classical tradition resists.
4. Simplicity, Trinity, and identity in God
When the tradition turns to God, it brings all of this metaphysics with it. If God is the first principle of all, then, as Étienne Gilson puts it, “the principle of principles is that a philosopher should always put first in his mind what is actually first in reality” (Gilson 1952). What is first in reality about God is not an abstract identity relation, but the sheer fact of simple, uncaused act.
Avicenna’s claim that in God “there is no quiddity other than His individual existence” (Avicenna 2005) and Maimonides’s insistence that God is “one simple substance, without composition or plurality of elements” (Maimonides 1956) are two riffs on this theme. Bonaventure’s description of God as “an undivided light of pure act, in whom all distinct forms subsist in absolute simplicity” (Bonaventure, Commentary on the Sentences) captures the same point in an exemplarist idiom: God is not a being with properties; God is the simple act in which all perfections exist in a higher, non-composite way.
At the same time, Scripture and the councils insist that God is not an impersonal absolute but Father, Son, and Holy Spirit. The Cappadocians are explicit that this does not add three substances to the one God. Gregory of Nyssa points out that “the divine operation is always observed to be one,” and concludes that “the name [God] derived from operation cannot be divided among many where the result of their mutual operation is one… so neither are they called three Gods” (Gregory of Nyssa 1994). Gregory of Nazianzus speaks of “a Monarchy that is not limited to one Person, but one which is made of an equality of Nature and a Union of mind, and an identity of motion, and a convergence of its elements to unity—a thing impossible to created nature—so that though numerically distinct there is no severance of Essence” (Gregory of Nazianzus 1994). Gregory Palamas can therefore say that “God multiplies Himself without division,” and that “He is divided without being divided,” because “God is One in essence and energy: the Father, the Son and the Holy Spirit” (Palamas, Dialogue with a Barlaamite).
Here, numerical distinction belongs to the “who” side—the hypostases—and not to a plurality of essences. The one divine “what” is not a shared kind under which three instances fall. It is a simple essence that subsists in three ways, distinguished by relations of origin: the Father as unbegotten, the Son as begotten of the Father, the Spirit as proceeding from the Father and the Son. Chalcedon’s Christological formula—“one and the same Christ… in two natures, unconfusedly, immutably, indivisibly, inseparably” (Council of Chalcedon 1990)—shows the same pattern. Once you put the metaphysical structure in the right order (one person, two natures), identity and non-identity statements fall into place: one and the same Christ, not two; two natures, not one; no confusion, no separation.
In this framework, to say “the Father is God” and “the Son is God” is not to equate two items of the same type by an abstract identity sign. It is to say, more carefully, that the Father and the Son each subsist as the one simple essence. What each Person is is the divine essence; how each Person is distinct lies in the pattern of origin. The Cappadocians’ insistence on one operation, one name “God,” and three who’s is metaphysical before it is logical.
5. Identity as downstream of metaphysics
If we step back, a consistent pattern emerges. In the classical picture, identity is not the first explanatory idea. What is first is the structure of being: substances that underlie accidents, forms that give act to matter, essences that may or may not exist, and, in the case of God, an essence that simply is existence, “one simple substance, without composition or plurality of elements” (Maimonides 1956). Bonaventure’s “undivided light of pure act, in whom all distinct forms subsist in absolute simplicity” (Bonaventure, Commentary on the Sentences) is a compressed way of saying that every multiplicity we see in creatures is grounded in, and exceeded by, a simple source.
Within that frame, identity statements are reports about how this structure is arranged. To say that Socrates is the same man through change is to say that the same primary substance and the same soul–body composite underlie the shifting accidents. To say that two statues are not the same is to say that they do not share a substantial subject, even if they share matter or shape. To say that “all beautiful things are beautiful by the Beautiful” (Plato 1997) is to locate their sameness in their relation to a single form, not in a purely logical equivalence.
For God, the same pattern holds at a higher pitch. The most fundamental fact is that there is one simple act of being, not in a genus, not composed of essence and existence. Within that act, there are three subsisting relations of origin: Father, Son, and Spirit. Once that is granted, identity language falls into place. We can truthfully say that God is one, that the divine nature is numerically one, that the Father is not the Son, that the Son is not the Spirit, that each is truly and wholly God. None of these identity and non-identity claims “make” God what God is. They summarize what is already there at the level of essence, act, and relation.
By contrast, when Leibniz treats the “nature of an individual substance” as “to have a notion so complete that it is sufficient to include, and to allow the deduction of, all the predicates of the subject” (Leibniz 1976), or when he says that “the individual concept of each person includes once and for all everything that will ever happen to him” (Leibniz 1988), identity is pulled into the space of concepts. When Hume says “I never can catch myself at any time without a perception, and never can observe any thing but the perception,” and concludes that we are “nothing but a bundle or collection of different perceptions” (Hume 1978), identity is loosened from any underlying act or subject altogether. When Descartes deems substantial forms “unnecessary in setting out my explanations” (Descartes 1988), identity risks becoming a matter of descriptive convenience about aggregates of qualities.
The classical tradition, especially as it comes to a head in the doctrine of divine simplicity and the Trinity, quietly resists this flattening. Following Gilson’s maxim that “a philosopher should always put first in his mind what is actually first in reality” (Gilson 1952), it puts act, essence, and origin at the foundation. Identity and non-identity, whether of creatures or of the three Persons, then appear as the logical shadow of that deeper metaphysical arrangement. The self, the world, and God are not “made” by an identity relation. They are what they are first, and only then do we rightly say: this is the same, that is different, and God, in his simple being, is one.
Let’s now do the above in technical notation so you can see the moves clearly:
The Logic of the TrinityTrinitarian Set Up
Symbol key
DP, DE = types; f, s, sp, e = constants; N = nature function; R = “is from”; ∀ “for all”; ∃ “there exists”; ¬ “not”; ∧ “and”; = / ≠ identity / non-identity.
- DP
The type “Divine Persons.” This is the kind or domain in which f, s, and sp live. - DE
The type “Divine Essence.” This is the kind or domain in which e lives. - f
A constant of type DP. Stands for the Father. - s
A constant of type DP. Stands for the Son. - sp
A constant of type DP. Stands for the Holy Spirit. - e
A constant of type DE. Stands for the one divine essence (the single divine nature). - N
A function from DP to DE. N(x) means “the nature of x,” where x is one of the divine Persons. - R
A binary relation on DP, read “is from.” R(x, y) means “x is from y” (a relation of origin between Persons). - ∀
The universal quantifier, read “for all” or “for every.” - ∃
The existential quantifier, read “there exists” or “for some.” - ¬
The negation sign, read “not.” - ∧
The logical conjunction sign, read “and.” - =
The identity sign within a type, read “is identical to.” - ≠
The non-identity sign within a type, read “is not identical to.”
Let’s separate “person” and “essence” into different types, so we do not treat a hypostasis and the essence as the same kind of thing. “The Father is God” is written as N(f) = e, where N picks out the nature of a person. We also build in f ≠ s, f ≠ sp, s ≠ sp, and that there is one divine essence and three divine Persons.
Types (the kinds of things)
• DP = Divine Persons
The person type, with domain {f, s, sp}.
• DE = Divine Essence
The essence or nature type, with domain {e}, the one divine essence.
We only compare things of the same type with “=”.
Constants (named things)
• f : DP the Father
• s : DP the Son
• sp : DP the Holy Spirit
With f ≠ s, f ≠ sp, s ≠ sp.
• e : DE the one divine essence
Function (picking out a nature)
• N : DP → DE
N(f) = “the nature of the Father”
N(s) = “the nature of the Son”
N(sp) = “the nature of the Holy Spirit”
We require: ∀x ∈ DP, N(x) = e. So:
• N(f) = e
• N(s) = e
• N(sp) = e
Each Person has, or is of, the one divine essence. e is not a fourth person, but what the three Persons wholly are.
Relations of origin (real distinctions)
We add a relation R(x, y) on DP, read “x is from y”:
• ¬∃y R(f, y) the Father is from no one
• R(s, f) the Son is from the Father
• R(sp, f) ∧ R(sp, s) the Spirit is from the Father and the Son as one principle
Equality and inequality
• “=” is identity within a type (for example, N(f) = e).
• “≠” is non-identity within a type (for example, f ≠ s).
Expressions like f = e are ill formed, since they mix types. This “typed safety” forces us to say “has the divine essence” via N and keeps us from collapsing person and essence into a single undifferentiated logical item.
How simplicity shows up here
Simplicity means there is one divine what, not built out of parts, and all perfections are one act of being. In the system:
• DE has only one element, {e}. There are no multiple divine natures.
• N is constant on DP: for all x in DP, N(x) = e. There are not three essences or three instances of divinity, only one essence fully belonging to each Person.
You are not picturing “essence plus three things.” You have one essence type with one item e, and a function N that always picks out that same e. At the level of what God is, this is simple and strictly one.
How Trinity shows up here
The Trinity requires three really distinct Persons, distinct by origin, not by three essences. In the system:
• DP = {f, s, sp} with f ≠ s, f ≠ sp, s ≠ sp. There are exactly three Persons.
• R encodes origin: the Father is from no one, the Son is from the Father, the Spirit from Father and Son as one principle.
The Persons differ, not by different natures, but by the pattern of R.
How Trinity and simplicity are one reality
• Simplicity: one essence e, with N(f) = N(s) = N(sp) = e.
• Trinity: three distinct Persons f, s, sp related by R.
So:
• There is one what, e.
• There are three who, f, s, sp.
• What each Person is in nature is identical, the one divine essence e.
• How they are distinct is given by origin, R.
Nothing in DE is split or added to. The plurality lies on the DP side, in how the one simple essence subsists as three relations of origin. There is not really “simplicity and Trinity” as two items, but one simple divine being seen under the aspect of what (DE) and under the aspect of who (DP with R).
Why the post-Leibnizian era “classical” logic objection does not apply
The objection runs: f = God, s = God, so f = s by transitivity. In this framework we never write f = e or s = e at all. Those are not just false, they are not well formed, since f and e have different types. Instead we write N(f) = e and N(s) = e. Identity applies only within a type, so the transitivity move that collapses the Persons is blocked at the level of syntax.
At the same time, you are not introducing a hidden fourth thing behind the Persons. The one simple essence is e in DE, the three subsisting relations are f, s, sp in DP with R, and N connects them as “the same divine being, three origin-distinct Persons.” You can then say: one will, one power in e, and all external works are one undivided act of this single essence, from the Father, through the Son, in the Holy Spirit.
How classical metaphysics of identity shows up here
Seen through classical metaphysics, this whole setup is just a careful way of writing in symbols what the tradition already said in prose. In God, identity is not a bare logical relation. It is the fact that there is one simple act of being and one undivided essence. That is what DE and the single element e capture. The three Persons in DP are not three substances with three acts of being, but three subsisting relations of origin in that one simple act. That is what R encodes. The function N is the formal way of saying what the Fathers meant when they said “the Father is God” and “the Son is God”: each hypostasis is wholly the one essence, not a part of it and not a bearer of a shared genus. So the identity of God as the one simple “what” lies at the level of e, while the real distinctions of “who” are carried by f, s, sp and their origin structure. Classical identity talk about God as “one simple substance without composition” appears here as the fact that the only real identity claim at the level of nature is N(f) = N(s) = N(sp) = e, and that everything else, the non-identity of the Persons and their relations of origin, is how that same indivisible being subsists in three distinct ways.
How identity is downstream of the older classical metaphysics here
In this setting, the identity symbol “=” is not doing the deepest work. The real work is done by the metaphysical structures we have already built in: the one essence e in DE, the three hypostases f, s, sp in DP, the origin pattern R that distinguishes the Persons, and the nature map N that sends each Person to that one essence. Once those are fixed, the true identity and non-identity statements are just the logical shadows of that deeper structure. For example, N(f) = e is not a mysterious logical fact about two featureless items. It is a compact way of saying that the Father is subsistent in, and nothing other than, the simple divine act of being that e names. Likewise, f ≠ s is not a brute logical stipulation, but a short way of recording that the relations of origin encoded by R for f and s are really distinct. In Gilson’s terms, what is first in reality are act, essence, and origin. The identity and non-identity signs simply report, at the level of notation, how that underlying classical metaphysics is already arranged.
Identity as Accomplishment Theory: Identity as Down Stream of Being
Symbol key
C, T, KND, M = types; x, y, z, w = continuant variables; t = time variable; k = kind variable; m = exemplar variable; Exists, O, S, KSame, ConstitutedBy, PartOf, ParticipatesIn, ExemplarOfKind, I, E = predicates/relations; ∀ “for all”; ∃ “there exists”; ¬ “not”; ∧ “and”; ∨ “or”; → “implies”; ↔ “iff”; = / ≠ identity / non-identity.
• C
The type “Continuants.” Domain of enduring things like persons, ships, statues, animals. Variables: x, y, z, w range over C.
• T
The type “Times.” Domain of moments or instants. Variable: t ranges over T.
• KND
The type “Kinds.” Domain of sortal kinds such as Human, Ship, OakTree. Variable: k ranges over KND.
• M
The type “Exemplars” or “Forms.” Domain of ideal patterns or forms that concrete things participate in. Variable: m ranges over M.
• x, y, z, w
Variables of type C. Stand for particular continuants.
• t
Variable of type T. Stands for a particular time.
• k
Variable of type KND. Stands for a particular kind.
• m
Variable of type M. Stands for a particular exemplar or form.
• Exists(x, t)
Binary predicate C × T. Read: “x exists at time t.”
• O(x, y)
Binary predicate C × C. Read: “x and y have the same origin” or “x shares origin with y.”
• S(x, y)
Binary predicate C × C. Read: “x and y share one unforked story” or “x shares a single continuous history with y.”
• KSame(x, y)
Binary predicate C × C. Read: “x and y are the same kind realized properly” (same kind with integrity under act).
• ConstitutedBy(x, y, t)
Ternary predicate C × C × T. Read: “at time t, x is constituted by y” (y is the constituting stuff or basis of x at t).
• PartOf(z, x, t)
Ternary predicate C × C × T. Read: “at time t, z is part of x.”
• ParticipatesIn(x, m)
Binary predicate C × M. Read: “x participates in exemplar m” (x takes part in the form m).
• ExemplarOfKind(m, k)
Binary predicate M × KND. Read: “m is an exemplar of kind k.”
• I(x, y)
Binary predicate C × C, defined abbreviation:
I(x, y) := O(x, y) ∧ S(x, y) ∧ KSame(x, y).
Read: “x and y have accomplished identity” or “x and y are the same continuant in the strong, triadic sense.”
• E(x, y)
Binary predicate C × C (introduced in the representation section). Read: “x and y are seriously identical” as a primitive equivalence relation to be represented by some triad O, S, KSame.
• ∀
Universal quantifier. Read: “for all” or “for every.”
• ∃
Existential quantifier. Read: “there exists” or “for some.”
• ¬
Negation sign. Read: “not.”
• ∧
Conjunction sign. Read: “and.”
• ∨
Disjunction sign. Read: “or.”
• →
Conditional sign. Read: “implies” or “if … then …”
• ↔
Biconditional sign. Read: “if and only if” or “iff.”
• =
Identity sign within a type. Read: “is identical to” or “is the very same.”
• ≠
Non-identity sign within a type. Read: “is not identical to.”
Start with a many sorted first order language.
There are four kinds of things:
- Continuants C (enduring things like persons, ships, animals).
- Times T.
- Kinds KND (human, ship, oak tree).
- Exemplars M (forms or patterns things participate in).
We add basic relations:
• Exists(x, t): x exists at time t.
• O(x, y): x and y have the same origin.
• S(x, y): x and y share one unforked story.
• KSame(x, y): x and y are the same kind realized properly.
• ConstitutedBy(x, y, t): at time t, x is constituted by y.
• ParticipatesIn(x, m): x participates in exemplar m.
• ExemplarOfKind(m, k): m is an exemplar of kind k.
Ordinary equality “=” is kept in its usual first order form on each sort.
Define accomplished identity:
I(x, y) holds if and only if O(x, y), S(x, y), and KSame(x, y) all hold.
That already encodes the classical intuition that “same thing” is downstream from origin, story, and kind.
Axioms T_A then say, among other things:
• Time is linearly ordered, existence is persistent.
• O, S, KSame are equivalence relations.
• S(x, y) forces x and y to exist at exactly the same times.
• Constitution and participation respect I (if x and y are I related, they cannot differ in what constitutes them at a given time, or in what forms they participate in).
• If I(x, y) then x = y (I never links two numerically distinct continuants).
Now define “admissible formulas”: properties of a continuant that are built only from Exists, O, S, KSame, ConstitutedBy, ParticipatesIn, ExemplarOfKind, the logical connectives, quantifiers, and equality. This is the language of origin, story, kind, constitution, and participation.
Accomplishment Lemma. In any model of T_A, for continuants x and y:
I(x, y) holds
if and only if
x and y satisfy exactly the same admissible formulas.
Sketch:
• If I(x, y) holds, the axioms ensure they match on every atomic admissible predicate (existence profile, origin class, story class, kind class, constitution facts, participation facts). Induction on formulas then shows they match on all admissible properties.
• Conversely, if x and y match on all admissible properties, then in particular they match on “O(z, y),” “S(z, y),” and “KSame(z, y)” viewed as properties of z with parameter y. Since O(y, y), S(y, y), and KSame(y, y) are always true, the matching forces O(x, y), S(x, y), and KSame(x, y). Hence I(x, y).
So Leibniz style “same properties” is not the definition of identity. It becomes a theorem about I in the right language.
Next step: Representation. Suppose we add an abstract equivalence relation E(x, y) on continuants that respects existence, constitution, and participation the way any serious identity should. Then in any model you can reconstruct O, S, and KSame so that:
E(x, y) holds iff O(x, y) and S(x, y) and KSame(x, y).
So any respectable identity like relation factors through the triad.
Conservativity: If you add all this structure on top of any base theory T₀, you do not change what is provable in the old language. You can always expand any model of T₀ to a model of T₀ + T_A, so no new old language theorems appear. Logic and equality are untouched.
Finally, a typed Trinitarian language with separate sorts for essence and persons plus a nature map N shows “the Father is God” is N(f) = e, not f = e. Cross sort equations like “f = e” are ill formed, and person person equalities like “f = s” are explicitly false. So the classical Trinity is consistent with ordinary identity; the old paradox is just bad typing.
That is to say, in brief, identity is down stream of more fundamental realities where there are more fundamental realities.
Bibliography (Chicago author–date)
Aristotle. 1941. The Basic Works of Aristotle. Edited by Richard McKeon. New York: Random House.
Aristotle. 1984. The Complete Works of Aristotle, vol. 2. Edited by Jonathan Barnes. Translated by W. D. Ross. Princeton: Princeton University Press.
Avicenna (Ibn Sīnā). 2005. The Metaphysics of The Healing (al-Shifāʾ: al-Ilāhiyyāt). Translated by Michael E. Marmura. Provo, UT: Brigham Young University Press.
Bonaventure, Saint. 1978. The Soul’s Journey into God (Itinerarium Mentis in Deum). Translated by Ewert Cousins. New York: Paulist Press.
Bonaventure, Saint. 2005. Breviloquium. Translated by Dominic Monti. St. Bonaventure, NY: Franciscan Institute.
Bonaventure, Saint. 13th c. Commentary on the Sentences of Peter Lombard (Commentaria in Quatuor Libros Sententiarum).
Council of Chalcedon. 1990. “Definition of Faith (451).” In Decrees of the Ecumenical Councils, edited by Norman Tanner. London: Sheed & Ward.
Descartes, René. 1988. Selected Philosophical Writings. Translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press.
Gilson, Étienne. 1952. Being and Some Philosophers. 2nd ed. Toronto: Pontifical Institute of Mediaeval Studies.
Gregory of Nazianzus. 1994. Orations. In Nicene and Post-Nicene Fathers, Second Series, vol. 7. Peabody, MA: Hendrickson.
Gregory of Nyssa. 1994. “To Ablabius: On ‘Not Three Gods’.” In Nicene and Post-Nicene Fathers, Second Series, vol. 5. Peabody, MA: Hendrickson.
Gregory Palamas. 14th c. Dialogue with a Barlaamite. Ed. Christos Christou.
Hume, David. 1978. A Treatise of Human Nature (1739–40). Edited by L. A. Selby-Bigge, revised by P. H. Nidditch. Oxford: Clarendon Press.
Leibniz, Gottfried Wilhelm. 1976. “Discourse on Metaphysics” (1686). In Leibniz: Philosophical Papers and Letters, edited by Leroy Loemker. Dordrecht: Reidel.
Leibniz, Gottfried Wilhelm. 1988. “Correspondence with Arnauld” (1686–87). In Leibniz: Discourse on Metaphysics and Related Writings, translated by R. Martin and Stuart Brown. Manchester: Manchester University Press.
Leibniz, Gottfried Wilhelm. 1714. Monadology. Translated by Robert Latta.
Maimonides, Moses. 1956. The Guide of the Perplexed. Translated by M. Friedländer. 2nd ed. Reprint. New York: Dover.
Marshner, William H. n.d. “The Debate About Universals.” Unpublished manuscript.
Plato. 1997. “Phaedo.” Translated by G. M. Grube. In Plato: Complete Works, edited by John M. Cooper. Indianapolis: Hackett.
Thomas Aquinas. 1948. Summa Theologiae. 5 vols. Translated by the Fathers of the English Dominican Province. New York: Benziger Bros.
Substance, Soul & IdentitySubstance, Soul, and Identity: Classical Metaphysics, Divine Simplicity, and the Fate of the Self
INTRODUCTION: PUTTING FIRST THINGS FIRST
Étienne Gilson’s methodological axiom sets the tone for what follows. He writes:
“The principle of principles is that a philosopher should always put first in his mind what is actually first in reality.”
If we take that seriously, then questions about identity and the self cannot begin with psychological appearances or with merely logical schemas. They must begin with what classical thinkers regard as ontologically basic: substance, form, act, and the Creator whose simple act of being grounds everything else.
This essay therefore starts from a metaphysical order and only then descends to questions about the self. It proceeds from what is first in reality to what can be said about identity. The core claim is simple, though its consequences are far reaching:
Identity is primordially the being of a thing as that thing, grounded in its essence and existence. In creatures, identity is the accomplished unity of a substance’s form and act of being. In God, identity is less fundamental and therefore downstream from what makes being to be, let alone being itself. All properties and traits are expressions and consequences of that underlying reality.
What follows is an attempt to retrieve a classical line that runs from Aristotle, Plato, Avicenna, Maimonides, Aquinas, and Bonaventure to the Cappadocian Fathers and Palamas, and then to set that line alongside Leibniz, Hume, and Descartes. The thread that runs through all of this is a question: what makes something to be this one, rather than a mere heap of features or a passing bundle of impressions?
We will see that for the classical tradition, the deepest answer is never “a set of predicates” or “a complete concept” in abstraction from act. The deepest answer is always a unified act of being, specified by form, received by matter or by a created essence, and at the summit identical with the one simple act of God. When those deeper conditions are met, we are licensed to give an identity verdict. In that sense, identity is an accomplishment, not the primitive starting point.
PART I: CLASSICAL SUBSTANCE – WHAT UNDERLIES EVERYTHING ELSE
Aristotle’s starting point is famously spare and ontologically thick. He writes in the Categories:
“Substance, in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject; for instance, the individual man or horse.” (Aristotle, Categories, in The Basic Works of Aristotle, ed. Richard McKeon, 1941)
Substance is the sort of thing that underlies predication and inherence rather than being either. This is why he can say a few lines later:
“Everything except primary substances is either predicated of a primary substance or present in a primary substance. This becomes evident by reference to particular instances which occur. ‘Animal’ is predicated of the species ‘man’, therefore of the individual man, for if there were no individual man of whom it could be predicated, it could not be predicated of the species ‘man’ at all. Again, colour is present in body, therefore in individual bodies, for if there were no individual body in which it was present, it could not be present in body at all. Thus everything except primary substances is either predicated of primary substances, or is present in them, and if these last did not exist, it would be impossible for anything else to exist.” (Aristotle, Categories)
Later in the same work he restates the point in a compact way:
“Moreover, primary substances are most properly called substances in virtue of the fact that they are the entities which underlie everything else, and that everything else is either predicated of them or present in them.” (Aristotle, Categories)
Substances are not logical constructs built out of properties. They are what bear properties and serve as the ultimate subjects of predication. This is the root of what later authors will call supposita or hypostases. If identity is to track what is most fundamentally “this one,” it must ultimately track substances rather than floating sets of features.
Aristotle’s Metaphysics and De Anima deepen this picture by introducing act and potency and the form–matter composite. In a famous example, he writes:
“the bronze is potentially a sphere, and when it is made round it constitutes an actual one–a single sphere of bronze.” (Aristotle, Metaphysics, trans. W. D. Ross, in The Complete Works of Aristotle, ed. Jonathan Barnes, vol. 2, 1984)
Matter is a principle of potentiality, form is a principle of actualization, and the concrete thing is one, not a heap. Hence his terse remark:
“The whole is not like a heap,” (Aristotle, Metaphysics)
A heap is just a many accidentally together. A substantial whole is a many under one form and one act of being. Identity in the strong sense belongs to the whole that is one by form and act, not to a pile of elements that could just as well be arranged otherwise.
Later metaphysics will make heavy use of an example that arises from this hylomorphic framework. Aristotle writes:
“And when the whole has been generated, such and such a form in this flesh and these bones, this is Callias or Socrates; and they are different on account of their matter (for it is different), but one in form (for their form is indivisible).” (Aristotle, Metaphysics, as cited through Avicenna and Aquinas discussions)
The “this flesh and these bones” are individuating matter under one form. Callias and Socrates are numerically distinct supposita sharing one specific form. Identity at the level of kind is by form; haecceity at the level of this one is by matter as informed.
The Thomistic tradition refines Aristotle’s insight by making a clear distinction between substance and accident that still respects the priority of the underlying subject. Thomas insists that “being” itself cannot be the definition of either substance or accident:
“Since being is not a genus, then being cannot be of itself the essence of either substance or accident. Consequently, the definition of substance is not–’a being of itself without a subject,’ nor is the definition of accident–’a being in a subject’; but it belongs to the quiddity or essence of substance ‘to have existence not in a subject’; while it belongs to the quiddity or essence of accident ‘to have existence in a subject.’ But in this sacrament it is not in virtue of their essence that accidents are not in a subject, but through the Divine power sustaining them; and consequently they do not cease to be accidents, because neither is the definition of accident withdrawn from them, nor does the definition of substance apply to them.” (Thomas Aquinas, Summa Theologiae, trans. Fathers of the English Dominican Province, 1948)
William Marshner captures the same logic in his discussion of supposit and properties:
“Properties and relations belong to supposita but [unless identical with an immaterial referent] are not things which exist in their own right; they are that whereby a suppositum is thus or such, id quo aliquid est.” (William H. Marshner, “The Debate About Universals”)
Accidents and relations do not compete with the supposit for full-fledged existence. They are that by which a subject is thus or such. Identity at the deepest level belongs to the underlying suppositum, not to the shifting array of acquired predicates.
Seen through Gilson’s axiom, this means that in the order of reality, being as the act of a substance is prior. In the order of our reflection, if we want to respect that order, identity must be read off from the way act and form make a subject one, rather than defined first as a bare logical relation that we then try to fit back onto substances.
PART II: ESSENCE, EXISTENCE, AND THE NECESSARY ONE
The classical line becomes sharper and more architectonic in Avicenna. He radicalizes the distinction between what a thing is and that it is. On the one hand, he can say:
“Essence considered in itself is indifferent to existing or not existing,” (Avicenna, The Metaphysics of The Healing, trans. Michael E. Marmura, 2005)
On the other, he offers a sharp characterisation of quiddity as such:
“According to Avicenna, the quiddity (or essence) considered strictly in itself excludes not only the idea of existence, whether external or mental, but also the concomitants of existence, such as unity and plurality. Thus, in his typical example of “horseness” as a quiddity considered in itself, he states that “it is neither one nor many, and exists neither in concrete things nor in the soul.” Moreover, he maintains, the quiddity considered in itself excludes the ideas of universality and particularity. In short, the quiddity as such excludes the ideas of existence, unity, plurality, particularity, and universality.” (Avicenna, Liber de Philosophia Prima / Metaphysics of The Healing, trans. Marmura)
Essence in itself is, so to speak, neutral with respect to being, unity, and mode. That opens conceptual space for a being whose essence is not neutral in this way. Hence Avicenna’s doctrine of the Necessary Existent, of whom he can say:
“there is no quiddity other than His individual existence.” (Avicenna, The Metaphysics of The Healing)
God’s “what” is not something that may or may not exist. His very quiddity just is His this one existence.
Maimonides presses this into a strict doctrine of simplicity:
“You must understand that God has no essential attribute in any form or in any sense whatever… There cannot be belief in the unity of God except by admitting that He is one simple substance, without composition or plurality of elements.” (Moses Maimonides, The Guide of the Perplexed, trans. M. Friedländer)
The classical trajectory is clear. Created substances receive existence; they have essences that are indifferent to being and can be many. At the summit there is One whose essence is His existence, without added attributes, parts, or internal composition. Identity here is not a thin logical relation between two terms already in place. It is the sheer indivisible actuality of the first principle.
Gilson’s maxim now bites more deeply. If “what is first in reality” at the summit is pure act in which essence and existence are identical, then identity, as a way of saying “this is that,” is conceptually and explanatorily downstream. God’s being is not grounded in identity. Rather, our identity statements about God are late, analogical attempts to track the singular reality that grounds all identity in creatures.
PART III: SOUL AND BODY – THE FORM THAT PERFECTS THE WHOLE AND EACH PART
Hylomorphism becomes most vivid when applied to the living body. Aristotle in De Anima defines the soul as:
“the cause or source of the living body” (Aristotle, De Anima, trans. J. A. Smith, in The Basic Works of Aristotle)
and elaborates:
“the soul is the cause of the body ‘alike in all three senses which we explicitly recognize. It is (a) the source or origin of movement, (b) the end, (c) the essence of the whole living body.'” (Aristotle, De Anima)
Soul is at once efficient source, final cause, and formal cause of the living composite. It is not a ghost inside a machine, but the act by which a certain kind of body is alive at all. The body is not a neutral container that then houses a separate self. The self is the living composite that the soul animates.
Aquinas draws out the consequences for the presence of soul in the body:
“As we have said, if the soul were united to the body merely as its motor, we might say that it is not in each part of the body, but only in one part through which it would move the others. But since the soul is united to the body as its form, it must necessarily be in the whole body, and in each part thereof. For it is not an accidental form, but the substantial form of the body. Now the substantial form perfects not only the whole, but each part of the whole. For since a whole consists of parts, a form of the whole which does not give existence to each of the parts of the body, is a form consisting in composition and order, such as the form of a house; and such a form is accidental. But the soul is a substantial form; and therefore it must be the form and the act, not only of the whole, but also of each part.” (Thomas Aquinas, Summa Theologiae, I, q. 76, a. 8, Benziger edition)
The living body is one by a substantial form that is present as act in each part. The unity here is not like the unity of a heap, but of a living organism whose parts exist as parts only by the one act of soul. Identity as a living self is grounded in that unified act.
In the same register, Aquinas can say of the soul’s relation to matter:
“the soul communicates that existence in which it subsists to the corporeal matter; and thus from the soul and the matter there results unity of existence, so that the existence of the whole composite is also the existence of the soul.” (Thomas Aquinas, Summa Theologiae, Benziger edition)
Existence is not double counted. There is not the existence of the soul and the existence of the body as two parallel acts. Rather, the soul’s act of existing is communicated to the body so that the composite has one existence. The being of the living person is one, and that unity of being is the deepest ground of personal identity.
Bonaventure, while remaining within a broadly hylomorphic framework, places greater stress on the soul’s interiority and destiny. He insists that:
“The soul, Bonaventure insisted, is something in itself (Bonaventure, 2 Sent. d. 17, a. 1, q. 2). The human spirit is a fully functioning organism with or without its corporeal body. But he also argued that the soul is the active principle that brings existence to the human composite in its union with its body and enables it to function properly in the physical realm of being (Bonaventure, 4 Sent. d. 43, a.1, q.1 fund. 5). Thus, the soul possesses an innate tendency to unite with its body (unibilitas). The soul is ordered to its body, not imprisoned within it. It realizes its perfection in union with its body, not in spite of it; and with its body, it engages in the cognitive reductio that leads to its proper end in the knowledge of God and ecstatic union with God.” (Saint Bonaventure, Commentary on the Sentences of Peter Lombard)
Or in the shorter formulation:
“But he also argued that the soul is the active principle that brings existence to the human composite in its union with its body and enables it to function properly in the physical realm of being. Thus, the soul possesses an innate tendency to unite with its body (unibilitas). The soul is ordered to its body, not imprisoned within it.” (Bonaventure, Commentary on the Sentences)
and likewise:
“The soul is ordered to its body, not imprisoned within it. It realizes its perfection in union with its body, not in spite of it; and with its body, it engages in the cognitive reductio that leads to its proper end in the knowledge of God and ecstatic union with God. Its relationship with its body is so intimate that it no longer functions properly at the moment of its body’s death.” (Bonaventure, Commentary on the Sentences)
On this view, the soul is both subsisting principle and form-giving act. It “is something in itself” and yet “realizes its perfection in union with its body, not in spite of it.” Identity of the human person is neither reducible to mere bodily continuity nor detachable from the ordered unity of soul and body. The self is a living substance whose form communicates one existence to the whole, from within.
Here the central thesis about identity comes into focus from below. To ask “Who am I?” in a classical hylomorphic frame is to ask about the very act of being by which this soul and this body are one living person. Psychological traits, memories, and relations are real, but they are secondary. They are expressions of the deeper unity of substance, form, and act.
PART IV: PARTICIPATION, EXEMPLARISM, AND THE SIMPLE TRIUNE GOD
Plato’s Phaedo offers a different but complementary angle on what grounds identity and predication. The focus is not on underlying substances but on Forms and participation. Socrates asks:
“And did you ever reach them with any other bodily sense? (and I speak not of these alone, but of absolute greatness, and health, and strength, and of the essence or true nature of everything). Has the reality of them ever been perceived by you through the bodily organs? or rather, is not the nearest approach to the knowledge of their several natures made by him who so orders his intellectual vision as to have the most exact conception of the essence of that which he considers? Certainly. And he attains to the knowledge of them in their highest purity who goes to each of them with the mind alone, not allowing when in the act of thought the intrusion or introduction of sight or any other sense in the company of reason, but with the very light of the mind in her clearness penetrates into the very light of truth in each; he has got rid, as far as he can, of eyes and ears and of the whole body, which he conceives of only as a disturbing element, hindering the soul from the acquisition of knowledge when in company with her-is not this the sort of man who, if ever man did, is likely to attain the knowledge of existence?” (Plato, Phaedo, trans. G. M. A. Grube, in Plato: Complete Works, ed. John M. Cooper, 1997)
Here, what is “most truly” is the intelligible form. Sensible things derive their identity from participation in such Forms. Socrates later articulates this in the language of the Beautiful itself:
“It seems to me that if there is anything beautiful besides the Beautiful itself, it is beautiful for no other reason than that it shares in that Beautiful, and I say so about all things… I will not insist on the precise nature of the relationship, but all beautiful things are beautiful by the Beautiful. That, I think, is the safest answer I can give myself or anyone else.” (Plato, Phaedo, trans. Grube)
On a Christian Platonist reading, creatures “are what they are by the Forms” in the sense that they receive their determinate natures from exemplars in the divine mind; all beautiful things are beautiful by participation in the divine Beauty. Bonaventure expresses this with characteristic poetry:
“All creatures are shadows, echoes, pictures… of that Eternal Source and Art” (Bonaventure, Itinerarium Mentis in Deum, trans. Ewert Cousins)
For him, these exemplars subsist in God as Word. He can describe God as:
“an undivided light of pure act, in whom all distinct forms subsist in absolute simplicity.” (Bonaventure, Commentary on the Sentences)
and as the One
“in whom [God] ordered all things,”
so that creatures are brought forth in a rational and ordered way and bear a “likeness” of that Word. (Bonaventure, Commentary on the Sentences)
The Fathers of the Church then articulate how this simple God is triune. Gregory of Nyssa, responding to the charge that belief in Father, Son, and Spirit compromises monotheism, writes:
“the divine operation is always observed to be one,”
and argues that:
“the name [God] derived from operation cannot be divided among many where the result of their mutual operation is one… so neither are they called three Gods.” (Gregory of Nyssa, To Ablabius: On “Not Three Gods,” in Nicene and Post-Nicene Fathers, Second Series, vol. 5)
Gregory of Nazianzus speaks of a monarchy that is not numerical solitude but unity of essence and operation:
“It is… a Monarchy that is not limited to one Person, … but one which is made of an equality of Nature and a Union of mind, and an identity of motion, and a convergence of its elements to unity–a thing impossible to created nature–so that though numerically distinct there is no severance of Essence.” (Gregory of Nazianzus, Third Theological Oration, Oration 29, in Nicene and Post-Nicene Fathers, Second Series, vol. 7)
Gregory Palamas, in the Byzantine tradition, presses the same paradoxical language of simplicity and multiplicity:
“God multiplies Himself without division”
and
“He is divided without being divided”
because
“For God is One in essence and energy: the Father, the Son and the Holy Spirit.” (Gregory Palamas, Dialogue with a Barlaamite, §37, ed. Christou; “The Simplicity of God according to Saint Gregory Palamas”)
The Council of Chalcedon applies a similar logic of unity and distinction to Christ:
“one and the same Christ… in two natures, unconfusedly, immutably, indivisibly, inseparably.” (Council of Chalcedon, Definition of Faith, 451, in Decrees of the Ecumenical Councils, ed. Norman Tanner)
God is one simple substance in Maimonides’ sense, yet the Fathers insist on real personal distinctions and on one undivided operation “from the Father, through the Son, in the Holy Spirit.” Christ is one person in two natures. The pattern here is not bundle theoretic or aggregate. It is unity of act and essence that can accommodate ordered distinctions without fragmentation.
For our purposes, the important point is that at the summit, what “makes God to be this one” is not a bare identity relation but a simple plenitude of act. Identity language in Trinitarian and Christological dogma serves to safeguard this act and to deny both division and confusion. Identity, even here, is downstream from the single, simple act of divine being.
PART V: LEIBNIZ – THE COMPLETE CONCEPT OF THE INDIVIDUAL
Leibniz rephrases much of the earlier metaphysical inheritance in a rationalist idiom. Starting from an Aristotelian idea that substance underlies predicates, he proposes that the essence of substance is to have a complete concept. He writes:
“The nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to include and to allow us to deduce from it all the predicates of the subject to which this notion is attributed. An accident, on the other hand, is a being whose notion does not include everything that can be attributed to the subject to which the notion is attributed. Thus, being a king, which is true of Alexander the Great, being an abstraction of his mind, does not determine the individual notion of this prince; whereas God, seeing the individual notion or haecceity of Alexander, sees in it at the same time the basis and reason for all the predicates which can be said truly of him, for example, that he vanquished Darius and Porus; he even knows a priori (and not by experience) whether he died a natural death or whether he was poisoned, something we can know only through history.” (G. W. Leibniz, Discourse on Metaphysics, in Philosophical Papers and Letters, ed. Leroy Loemker)
In another formulation he states:
“We have said that the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to include, and to allow the deduction of, all the predicates of the subject to which that notion is attributed.” (Leibniz, Discourse on Metaphysics)
and summarises it more briefly still:
“the nature of an individual substance is to have a notion so complete that it suffices to contain all its predicates” (Leibniz, Discourse on Metaphysics)
The complete concept of Alexander contains, in principle, every true predicate about him, including that
“he would conquer Darius and Porus… and die a certain death, and so on”
or that
“he vanquished Darius and Porus; he even knows a priori (and not by experience) whether he died a natural death or whether he was poisoned.” (Leibniz, Correspondence with Arnauld, in Discourse on Metaphysics and Related Writings, trans. R. Martin and Stuart Brown, 1988)
Likewise,
“The concept of the individual Caesar includes everything that ever happened to him, such as that he was dictator, that he conquered Pompey, that he was assassinated in the Senate on the Ides of March, and all the other details of his life.” (Leibniz, Correspondence with Arnauld)
This is what Leibniz means when he says:
“As the individual concept of each person includes once for all everything which can ever happen to him, in it can be seen a priori the evidences or the reasons for the reality of each event and why one happened sooner than the other. But these events, however certain, are nevertheless contingent being based on the free choice of God and of his creatures. It is true that their choices always have their reasons but they incline to the choices under no compulsion of necessity.” (Leibniz, “Correspondence with Arnauld”)
and again:
“The individual concept of each person involves, once for all, all that will ever happen to him. If this is so, God was free to create or not to create Adam, but supposing he decided to create him, all that has since happened to the human race or which will ever happen to it has occurred and will occur by a necessity more than fatal.” (Leibniz, “Correspondence with Arnauld”)
For Leibniz, the complete concept of an individual is paradigmatically “an idea in the mind of God.” He writes:
“Surely since God can form and does actually form this complete concept which involves whatever is sufficient to give a reason for all the phenomena that happen to him, the concept is therefore possible. And this is the true complete concept of that which I call the me. It is in virtue of this concept that all my predicates pertain to me as to their subject. We are, therefore, able to prove it without mentioning God, except in so far as it is necessary to indicate my dependence. This truth is expressed more forcefully in deriving the concept which is being examined from the divine cognizance as its source.” (Leibniz, “Correspondence with Arnauld”)
or, in another closely related wording:
“Surely, since God can form this complete concept which involves everything that happens to me, and since this concept is possible, this concept is the complete concept of me, by virtue of which all my predicates are connected in a subject, me.” (Leibniz, “Correspondence with Arnauld”)
From this perspective, Leibniz can say that a person’s individual concept
“involves whatever is sufficient to give a reason for all the phenomena that happen to him” (Leibniz, “Correspondence with Arnauld”)
Identity is thus bound up with a complete intelligible pattern, grounded in the divine intellect, that contains the reasons for every predicate and event.
The Monadology generalises this:
“Every monad expresses the entire universe, but more clearly in the things to which it is more related and whose affections it expresses more distinctly, principally expressing God or the universe in terms of its relation with all the rest of the world. The monad must not only exhibit properties, but contain within itself ‘virtually’ or ‘potentially’ all the properties it will exhibit in the future, as well as contain the ‘trace’ of all the properties it did exhibit in the past. In a word, every substance is like an entire world and like a mirror of God, or indeed of the whole world which it portrays, each one in its own fashion; almost as the same city is variously represented according to the various situations of him who is regarding it. Thus the universe is multiplied in as many ways as there are substances, and the glory of God is multiplied in the same way by as many wholly different representations of his works.” (Leibniz, “Metaphysics,” Internet Encyclopedia of Philosophy)
In such a world, no two substances can be perfectly alike. Hence Leibniz’s famous principle of the identity of indiscernibles:
“Indeed, each Monad must be different from every other. For in nature there are never two beings which are perfectly alike and in which it is not possible to find an internal difference, or at least a difference founded upon an intrinsic quality.” (Leibniz, Monadology, §9, trans. Robert Latta)
or in the briefer paraphrase:
“In nature there are never two beings exactly alike, without an internal difference.” (Leibniz, Monadology, §9)
Here identity is still an “accomplishment” of sorts. It flows from an internally differentiated complete concept that is, in its fullness, an idea in the mind of God. But it has also been translated into a quasi logical structure. The complete set of predicates for an individual, held together by a divine conception, is doing much of the work that classical thinkers assigned to form, act, and participation.
The danger, from a classical standpoint, is that identity becomes too closely identified with an ideal description. The being of a thing as that thing tends to be equated with the totality of true propositions about it. Gilson’s “first in reality” risks being replaced by “first in concept.”
PART VI: HUME AND DESCARTES – THE DECOMPOSITION OF SUBSTANCE
Hume’s Treatise famously denies that introspection reveals any unified self. He writes:
“For my part, when I enter most intimately into what I call myself, I always stumble on some particular perception or other, of heat or cold, light or shade, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never can observe any thing but the perception. When my perceptions are remov’d for any time, as by sound sleep; so long am I insensible of myself, and may truly be said not to exist. And were all my perceptions remov’d by death, and cou’d I neither think, nor feel, nor see, nor love, nor hate after the dissolution of my body, I shou’d be entirely annihilated, nor do I conceive what is farther requisite to make me a perfect non-entity.” (David Hume, A Treatise of Human Nature, ed. Selby-Bigge and Nidditch)
He goes on to generalise this to all persons:
“I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. Our eyes cannot turn in their sockets without varying our perceptions. Our thought is still more variable than our sight; and all our other senses and faculties contribute to this change; nor is there any single power of the soul, which remains unalterably the same, perhaps for one moment. The mind is a kind of theatre, where several perceptions successively make their appearance; pass, re-pass, glide away, and mingle in an infinite variety of postures and situations.” (Hume, Treatise of Human Nature)
This is sometimes summarised as the view that the self is “nothing but a bundle or collection of different perceptions.” But Hume’s fuller statement shows how radical the claim is. Where Aristotle and Aquinas had posited a substantial form that perfects the whole and each part, and Leibniz a complete concept that grounds the predicates, Hume finds only a “theatre” where appearances come and go with no underlying actor.
On the metaphysical side, Descartes plays a parallel role with respect to substantial forms. In a letter to Henricus Regius he says he does not so much deny as sideline the traditional doctrine:
“In a letter to Henricus Regius (1598-1679), Descartes states that he does not reject substantial forms but finds them “unnecessary in setting out my explanations”. He clearly sees them as a mere explanatory tool that may be replaced by a better one. Instead, Descartes suggests any material thing is only an aggregate of qualities and properties. He argues, in the same letter, against the habit to apply “substantial form” when defining the human being.” (René Descartes, Selected Philosophical Writings, trans. Cottingham, Stoothoff, and Murdoch, 1988)
Or in his own words, more sharply:
“I do not entirely reject substantial forms, but I hold that they are unnecessary in setting out my explanations.” (Descartes, Selected Philosophical Writings)
If substantial forms are “unnecessary,” then the unity they supported becomes suspect. Material things risk becoming aggregates of measurable features. Hume takes the next step by making the mental life itself an aggregate of perceptions. The underlying subject that Aristotle called a primary substance and that Aquinas called a suppositum threatens to vanish from the picture. Identity, on such a view, ceases to be grounded in a unified act of being. It begins to look like a convenient label for a flowing bundle.
In terms of Gilson’s axiom, Hume and Descartes invert the order. Rather than putting first in their mind what is first in reality, they let what is first in their experience of impressions and concepts set the terms, and then try to reconstruct or replace the deeper realities of substance and form. What is lost is precisely the sense in which identity is the being of a thing as that thing, grounded in its act and essence.
PART VII: IDENTITY AS ACCOMPLISHMENT ON CLASSICAL GROUNDS
Against this background, the classical and Christian tradition can be seen as treating identity neither as a primitive logical relation nor as a mere bundle of qualities, but as the visible face of deeper ontological realities.
Aristotle’s primary substances are “the entities which underlie everything else, and that everything else is either predicated of them or present in them.” They are what they are by form and act, not by being the mere intersection of predicates. The human soul is “the cause or source of the living body” and is the substantial form that “perfects not only the whole, but each part of the whole.” Aquinas can say that “the soul communicates that existence in which it subsists to the corporeal matter,” so that there is “unity of existence.” Bonaventure insists that “the soul is something in itself” and yet “realizes its perfection in union with its body.”
At the level of essence, Avicenna shows that essence in itself is indifferent to existence and even to unity, so that in the created order one must always distinguish what something is from that it is. Only in the Necessary Existent is there “no quiddity other than His individual existence,” and Maimonides concludes that God is “one simple substance, without composition or plurality of elements.” The Christian Platonist tradition sees all creatures as “shadows, echoes, pictures… of that Eternal Source and Art,” dependent on an “undivided light of pure act, in whom all distinct forms subsist in absolute simplicity.”
At the level of divine life, the Cappadocians and Palamas show that unity of essence and operation can coexist with real distinctions of origin. “The divine operation is always observed to be one,” so “the name [God] derived from operation cannot be divided among many where the result of their mutual operation is one… so neither are they called three Gods.” The divine monarchy is “made of an equality of Nature and a Union of mind, and an identity of motion, and a convergence of its elements to unity… so that though numerically distinct there is no severance of Essence.” God “multiplies Himself without division” and “is divided without being divided,” so that “God is One in essence and energy: the Father, the Son and the Holy Spirit.” Christ is “one and the same Christ… in two natures, unconfusedly, immutably, indivisibly, inseparably.”
In the early modern period, Leibniz partially preserves this insight by casting substance as a complete concept or monad that “involves whatever is sufficient to give a reason for all the phenomena that happen to him.” The individual concept of a person “includes once for all everything which can ever happen to him” and exists as “a complete concept which involves everything that happens to me,” an “idea in the mind of God.” Every monad “expresses the entire universe” and is “like a mirror of God.” Identity here is tightly bound to intelligible structure and divine cognition.
Hume and Descartes, by contrast, dissolve substance and form into bundles of perceptions and aggregates of properties. The self becomes “nothing but a bundle or collection of different perceptions,” and substantial forms are considered “unnecessary” for explanation.
If one returns to Gilson’s “principle of principles,” the classical view seems more faithful to what is “first in reality.” There are real substances that underlie predication, real forms that perfect the whole and each part, real acts of existence that unify composites, and a simple divine act in which all forms subsist and from which all creatures receive their being. Identity, on this picture, is not a primitive given nor a mere summary label.
We can now state the classical insight in more systematic terms.
First, in created things, identity follows upon substantial unity. To say that Callias at one time is the same as Callias at another is to presuppose that there is a single act of being that grounds the various accidents, relations, and changes. Identity is not a bare logical relation between ordered pairs of objects. It is the way we speak when one and the same substance, with one and the same underlying form and existence, persists through time. In that sense, identity is an accomplishment of form and act.
Second, in the human person, identity is the being of the person as that person, grounded in the way the rational soul communicates existence to this body. Personal traits, memories, social roles, and psychological states are real, but they remain secondary expressions of that underlying unity. The human self is not exhausted by any list of predicates, however complete. It is the living “this one” whose being is given and sustained by God and whose destiny is ecstatic union with God.
Third, in God, identity is even more clearly downstream from act. God is not who He is because a primitive identity relation holds between “God” and some underlying this. Rather, He is who He is because He is pure actuality, the Necessary Existent in whom “there is no quiddity other than His individual existence” and who is “one simple substance, without composition or plurality of elements.” Identity language about God is our conceptual echo of that absolute simplicity. It signals, in the thin medium of logical syntax, the fact that there is no distinction between what God is and that God is. In that sense, identity is less fundamental than being in God. It is a way our finite grammar tries to track a reality that surpasses it.
Fourth, all properties and traits, whether in creatures or in God, are expressions and consequences of underlying reality. For creatures, properties express the way a finite essence participates in being, is informed by form, and stands in relation to other things. For God, our talk of attributes expresses analogically the one simple act of pure existence, considered under different conceptual aspects. In neither case do properties or traits serve as the ground of identity. They presuppose identity as grounded in act and form.
We can therefore reformulate the thesis that has guided this essay:
Identity is primordially the being of a thing as that thing, grounded in its essence and existence. In creatures, identity is the accomplishment that results when one substance, with one form and one act of being, endures through time and stands in ordered relations. In God, identity language is our way of confessing, in finite terms, the one simple act of pure being in whom all forms subsist and from whom all things receive their being.
In that sense, identity is an accomplishment on classical grounds. It is the verdict we give when the deeper conditions of unity, act, and origin are in place: in creatures by participation and composition, in God as simple plenitude.
CONCLUSION: THE FATE OF THE SELF
If the classical picture is right, the fate of the self is tied to the fate of substance, form, and act. When substance is reduced to an aggregate of properties and the soul is treated as an unnecessary hypothesis, the self tends to evaporate into a “theatre” of perceptions or a network of functional roles. Questions about personal identity then become puzzles about memory continuity, psychological connectedness, or the sameness of a bundle over time.
The classical tradition offers a different path. A human person is not a bundle of perceptions but a living substance whose soul communicates one existence to “this flesh and these bones,” ordered to a destiny in which, with his body, he “engages in the cognitive reductio that leads to its proper end in the knowledge of God and ecstatic union with God.” Created substances “are what they are by the Forms” and “all beautiful things are beautiful by the Beautiful.” At the summit stands the One in whom “there is no quiddity other than His individual existence,” who “has no essential attribute in any form or in any sense whatever,” who is “an undivided light of pure act.”
To think rightly about identity, on this classical view, is to keep all of that in mind. It is to begin, with Gilson, from what is first in reality. It is to recognise that identity is not the deepest stratum in our ontology. The deepest stratum is act, especially the act of being. Identity is what we say when that act is unified in one substance and one story. The fate of the self, then, is not to dissolve into a passing bundle, but to be gathered, purified, and perfected in the act of the One who is Being itself.
BIBLIOGRAPHY
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Aristotle. De Anima (On the Soul). Translated by J. A. Smith. In The Basic Works of Aristotle. Edited by Richard McKeon. New York: Random House, 1941.
Aristotle. Metaphysics. Translated by W. D. Ross. In The Complete Works of Aristotle, vol. 2. Edited by Jonathan Barnes. Princeton: Princeton University Press, 1984.
Avicenna (Ibn Sīnā). The Metaphysics of The Healing (al-Shifā: al-Ilāhiyyāt). Translated by Michael E. Marmura. Provo, UT: Brigham Young University Press, 2005.
Bonaventure, Saint. Commentary on the Sentences of Peter Lombard (Commentaria in Quatuor Libros Sententiarum), 1250s.
Bonaventure, Saint. Itinerarium Mentis in Deum (The Soul’s Journey into God). Translated by Ewert Cousins. New York: Paulist Press, 1978.
Council of Chalcedon. “Definition of Faith” (451 A.D.). In Decrees of the Ecumenical Councils. Edited by Norman Tanner. London: Sheed & Ward, 1990.
Descartes, René. Selected Philosophical Writings. Translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press, 1988.
Gilson, Étienne. Being and Some Philosophers. 2nd ed. Toronto: Pontifical Institute of Mediaeval Studies, 1952.
Gregory of Nazianzus. “The Third Theological Oration” (Oration 29). In Nicene and Post-Nicene Fathers, Second Series, vol. 7. Peabody: Hendrickson, 1994.
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Gregory Palamas. Dialogue with a Barlaamite, §37. Ed. Panagiotis Christou. See also “The Simplicity of God according to Saint Gregory Palamas.”
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Maimonides, Moses. The Guide of the Perplexed. Translated by M. Friedländer. 2nd ed. 1904. Reprint, New York: Dover, 1956.
Marshner, William H. “The Debate About Universals.”
Plato. Phaedo. Translated by G. M. A. Grube. In Plato: Complete Works. Edited by John M. Cooper. Indianapolis: Hackett, 1997.
Thomas Aquinas. Summa Theologiae. 5 vols. Translated by the Fathers of the English Dominican Province. New York: Benziger Bros., 1948 (Benziger edition).
Primary Sources:
- Aristotle. Metaphysics. Translated by W. D. Ross. In The Complete Works of Aristotle, edited by Jonathan Barnes, vol. 2. Princeton: Princeton University Press, 1984. (Notably Metaphysics VIII–IX on form and unity; X on one and being[1].)
- Aristotle. De Anima (On the Soul). Translated by J. A. Smith. In The Basic Works of Aristotle, edited by Richard McKeon. New York: Random House, 1941. (See II.1 and II.4 on the soul as cause of the body’s unity[3].)
- Avicenna (Ibn Sīnā). The Metaphysics of The Healing (al-Shifā: al-Ilāhiyyāt). Translated by Michael E. Marmura. Provo, UT: Brigham Young University Press, 2005. (Discusses essence and existence distinction; Necessary Existent’s simplicity[31].)
- Maimonides, Moses. The Guide of the Perplexed. Translated by M. Friedländer. 2nd ed. 1904. Reprint, New York: Dover, 1956. (Part I, ch.50–51 on divine unity and simplicity[10].)
- Aquinas, Thomas. Summa Theologiae. Benziger Edition. (See Part I, Q.3 on divine simplicity; Part I, Q.11 on unity; Part I, Q.76, a.1 ad 5 on soul communicating existence[12]; Part III, Q.2–Q.3 on the Incarnation’s unity of person.)
- Aquinas, Thomas. De Ente et Essentia (On Being and Essence). Translated by Armand Maurer. Toronto: Pontifical Institute of Mediaeval Studies, 1968. (Defines essence/existence and the individuation of material substances.)
- Bonaventure, Saint. Commentary on the Sentences of Peter Lombard. (In particular, see Bk II, dist.3, art.2, quaes.1 for exemplar ideas and the Word as form of things[13].)
- Bonaventure, Saint. Itinerarium Mentis in Deum (The Soul’s Journey into God). Translated by Ewert Cousins. New York: Paulist Press, 1978. (Emphasizes that created multiplicity is united in the divine art; e.g., “All creatures are shadows, echoes, pictures… of that Eternal Source and Art”[37].)
- Gregory of Nazianzus. Orations, especially Third Theological Oration (Oration 29). In Nicene and Post-Nicene Fathers, Second Series, vol. 7. Peabody: Hendrickson, 1994. (Monarchy of God: “one made of an equality of nature and union of mind and identity of motion… though numerically distinct no severance of essence”[21].)
- Gregory of Nyssa. To Ablabius: On “Not Three Gods.” In Nicene and Post-Nicene Fathers, Second Series, vol. 5. Peabody: Hendrickson, 1994. (“the divine operation is one, therefore we do not enumerate three Gods”[40][34].)
- Council of Chalcedon. Definition of Faith (451 A.D.). In Decrees of the Ecumenical Councils, edited by Norman Tanner. London: Sheed & Ward, 1990. (“one and the same Christ… in two natures, unconfusedly, immutably, indivisibly, inseparably.”)
- The Holy Bible. (References: Deuteronomy 6:4; John 1:14; John 10:30; Exodus 3:14, etc., as alluded to in theological context.)
Secondary Sources:
- Adams, Robert M. “Primitive Thisness and Primitive Identity.” Journal of Philosophy 76, no.1 (1979): 5–26. (Argues for individual essences (“thisness”) as a way to account for identity of indiscernibles[43].)
- Baker, Lynne Rudder. “Why Constitution Is Not Identity.” Journal of Philosophy 94, no. 12 (1997): 599–621. (Distinguishes the constitution relation between, e.g., statue and clay, from identity, using modal and temporal property differences[42][41].)
- Geach, Peter T. “Identity.” Review of Metaphysics 21, no.1 (1967): 3–12. (Introduces the idea of relative identity, e.g., “the same F but not the same G,” in part to address Trinity paradoxes. Our approach preserves classical absolute identity instead.)
- Gilson, Étienne. Being and Some Philosophers. 2nd ed. Toronto: Pontifical Institute of Mediaeval Studies, 1952. (“The principle of principles is that a philosopher should put first in his mind what is first in reality” – echoed in our method of prioritizing act/unity[38].)
- Hawley, Katherine. How Things Persist. Oxford: Clarendon Press, 2001. (Discusses endurance vs perdurance; our view aligns more with endurance under a unifying principle but with well-defined criteria.)
- Leftow, Brian. God and Necessity. Oxford: Oxford University Press, 2012. (Includes analysis of divine simplicity and identity of indiscernibles in God’s context.)
- Merricks, Trenton. Objects and Persons. Oxford: Clarendon Press, 2001. (Eliminativist view on composite objects; by contrast, we defend that composite unities are real because of unifiers.)
- White, Thomas Joseph. “God and the Trinity.” In The Cambridge Companion to Joseph Ratzinger, edited by D. Cardó and U. M. Lang, 126–142. Cambridge: Cambridge University Press, 2023. (Summarizes Ratzinger’s Trinitarian theology, including the notion of persons as subsistent relations in God[35], which dovetails with our use of origin relations to distinguish divine persons.)
- Wiggins, David. Sameness and Substance Renewed. Cambridge: Cambridge University Press, 2001. (Explores criteria for identity over time, sortal dependence of identity, etc. Our formal approach provides a structure to implement Wiggins’s insight that identity statements are sortal-relative by using kind integrity conditions.)