3. Philosophical Puzzles and Solutions
For Christians, at least in the West,
Quincunque Vult, commonly known as the Athanasian Creed, defines Trinitarian orthodoxy as follows:
We worship one God in Trinity, and Trinity in Unity, neither confounding the Persons, nor dividing the Substance
For there is one Person of the Father, another of the Son, and another of the Holy Ghost…
Such as the Father is, such is the Son, and such is the Holy Ghost…
[T]he Father is God, the Son is God, and the Holy Ghost is God.
And yet they are not three Gods, but one God
Christians are thus committed to the following claims:
(1) The Father is God
(2) The Son is God
(3) The Holy Spirit is God
(4) The Father is not the Son
(5) The Father is not the Holy Spirit
(6) The Son is not the Holy Spirit
(7) There is exactly one God
a. Trinity and Identity
Can one consistently believe (1) – (7)? It depends on how we read the “is” in (1) – (6). If we read it throughout as the “is” of strict identity, as “=” the answer is no. Identity is an equivalence relation: it is reflexive, symmetric and transitive, which is to say, for all
x, y and
z the following hold:
Reflexivity:
x =
x
Symmetry: If
x =
y then
y =
x
Transitivity: If
x =
y and
y =
z then
x =
y
In addition, identity is an unrestricted indiscernibilty relation for all properties, which is to say it obeys Leibniz’ Law, understood as the Indiscernibility of Identicals:
LL: If
x =
y then for all properties,
P,
x has
P if and only if
y has
P
This is bad news. Suppose we read the “is” as “=” in (1) – (6). Then it follows from (1) and (2), by symmetry and transitivity, that the Father is the Son, which contradicts (4). Put another way, given LL, (1) entails that God has all the same properties as the Father, including the property of
being identical with the Father insofar as everything has the property of self-identity. (2) says that the Son likewise has all the same properties as God. It follows that, since God has the property of being identical with the Son, the Son also has the property of being identical with the Father, which contradicts (4).
These formal features of identity are non-negotiable in the way that the four-sidedness of squares is: God cannot evade them any more than he can make a square with only three sides. God can make triangles—and pentagons, chiliagons or figures with any number of sides he pleases—but he cannot make such things
squares. So, assuming that “God,” “Father,” “Son” and “Holy Spirit” don’t change their reference, the “is” that figures in (1) – (6) cannot be the “is” of strict identity.
b. The "Is" of Predication
In English, most of the time the word “is” occurs it does not express an identity. The “is” that occurs in (8) and (9) is the “is” of predication: it is used to ascribe a property to an object:
(8) Ducati is a dog.
(9) Ducati is canine.
(8) is not an identity statement because “a dog” does not pick out a particular object. Identity is a relation between objects; in particular, it is the relation that everything bears to itself and to no other thing. In a true identity statement the nouns or noun phrases on either sides of the identity pick out the very same thing. (10) and (11) are true identity statements:
(10) Ducati is the chocolate Lab at 613 Second Avenue.
(11) Ducati is Britynic Cadbury of Bourneville
“The chocolate Lab at 613 Second Avenue” and “Britynic Cadbury of Bourneville” each pick out particular dog, as it happens, the same dog that “Ducati” picks out but “a dog” does not. (8) in fact says the same thing as (9)—it says that Ducati has the property of being a dog, that is the property of being canine. The “is” in (8), like the “is” in (9) is therefore, the “is” of predication.
Now consider (1) – (3) understanding the “is” that occurs in each sentence as the “is” of predication to yield:
(1') The Father is a God
(2') The Son is a God
(3') The Holy Spirit is a God
The “is” of predication does not express an equivalence relation and, in general, “
x has P” and “
y has P” do not imply “
x is identical to
y.” Ducati is a dog and Riley is a dog but it does not follow that Ducati is (identical to) Riley—in fact they are not. Similarly, (1') and (2') do not imply that the Father is the Son so there is no contradiction.
However, (1') – (3') just say that the Father, Son and Holy Spirit are each divine, in the way that (8) just says that Ducati is canine, and this leaves open the possibility that there are two, or three Gods involved. They do not explain what makes the Persons one God or provide any rationale for (7). Furthermore, together with (4) – (6) it seems to follow that there are indeed three Gods, just as it follows from “Ducati is a dog,” “Riley is a dog” and “Ducati is not Riley” that there are (at least) two dogs.
This is the concern Gregory of Nyssa addressed in his response to Ablabius, who worried that understanding the unity of Trinitarian persons in terms of their sharing the property of divinity implied Tri-theism:
The argument which you state is something like this: Peter, James, and John, being in one human nature, are called three men: and there is no absurdity in describing those who are united in nature, if they are more than one, by the plural number of the name derived from their nature. If, then, in the above case, custom admits this, and no one forbids us to speak of those who are two as two, or those who are more than two as three, how is it that in the case of our statements of the mysteries of the Faith, though confessing the Three Persons, and acknowledging no difference of nature between them, we are in some sense at variance with our confession, when we say that the Godhead of the Father and of the Son and of the Holy Ghost is one, and yet forbid men to say “there are three Gods”? The question is, as I said, very difficult to deal with. (Gregory of Nyssa, “To Ablabius”)
This is a difficult question indeed.
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