Identity is a unique and interesting relation. To understand what modalism is, and in some cases to follow what philosophers who discuss the Trinity are getting so excited about, one needs to be clear about the concept of identity. What follows is a quick primer; for more, see section 2 of this article.
In logic, we express the claim that two (really “two”) things are identical by putting the “=” symbol between their names (here, a, b, c – these are names like “Bob”, not variables that take a numerical value). When “a” refers to George W. Bush, and “b” refers to Koko the Gorilla, these would be true: a=a, b=b. But these would be false: a=b, b=a.
Identity is a relation which is
- transitive. If a = b, and b = c, then also, a = c. (In this, it is like the relations bigger than, or smarter than.)
- symmetrical. If a=b, then also, b=a. (In this, identity is like the relation near to, and unlike the relation father of.)
- reflexive. Identity is a relation that a thing can only bear to itself. Unlike most relations you can think of, then, identity isn’t a relation between two things, but always, between a thing and itself. Thus, sometimes philosophers say that identity is a “one-one” relation.
- Many relations can be reflexive or not. Two men can bear the puncher-punched relation, but then, a man can punch himself. Identity, though, must always be reflexive.
Identity, then, is a relation that everything bears only to itself. It is closely connected with our concept of an individual entity – to have the concept of an individual entity, is to have the concept of a thing which is self-identical.
Closely connected with the concept is what philosophers often call “Leibniz’s Law” (not to be confused with this, which sometimes is also call Leibniz’s Law.) The more proper name for it is “the indiscernibility of identicals”. It says,
For any x and y, they are identical (x=y) only if whatever is true of one is true of the other.
This principle seems obviously true, and it seems to be necessarily true – something which is true, and couldn’t conceivably be false. Moreover, all people implicitly recognize it to true.
- Suppose you just met a new friend, Chelsea. She tells you that her dad used to have an important job, that he likes the ladies, loves McDonalds french fries, and speaks with an Arkansas accent. You say to yourself, “I wonder if her dad is Bill Clinton?” Then, you find out that her Dad is four foot nine, and has never been taller. Well, you can be sure that her dad and Clinton are not identical. Why? It follows from what you know (based on her testimony) plus Leibniz’s Law.
- Again, suppose you’re on a jury, trying to decide whether or not the defendent Joe Blow is really the Boston Strangler. If you’re certain that the Boston Strangler has a size 9 shoe, and that Joe Blow is a size 13, then “if the shoe does not fit, you must acquit”. Why? If j and b differ with respect to anything at all (including, of course, shoe size), then it is false that j=b.
When it is true that a=b, we can say “a is b”. But that can be misleading, as that little word “is” can express many different ideas. (e.g. “Sally is pretty.” “This sculpture is ice.” “New England is Connecticut, Massachussets and a few other small states.”) Sometimes philosophers say “a just is b” to express a=b.
OK – the above is mostly common sense, just spelled out with unusual precision. Of course, everything is itself, and not something else. And of course, nothing can differ from itself. So what is the payoff, when it comes to the issue of the Trinity?
Many Christians go around saying things like “Jesus is God“, “Jesus just is God”, or “Jesus is God himself”, etc. And the Father? “He’s God too, of course.” Now, what is being said here? If they’re saying that j=g, and f=g, then it follows (by Leibniz’s Law, or by the transitivity and symmetricality of =) that f=j and that j=f – that Jesus just is the Father, and vice-versa. But if that is so, then “Jesus”, “God”, and “the Father” are three co-referring names – those “three” entities are in fact identical. And thus, whatever is true of one, will be true of the others as well. So we get:
- The Father was born of Mary, and was later crucified.
- Jesus sent his only Son into the world, to redeem humankind.
- There are three persons within the Father.
- Jesus is a Trinity.
Yikes – looks like some ill theology. Where did we go wrong? Each different developed version of the doctrine of the Trinity has an answer to this question. Some have gone so far as to deny that there’s any such relation as identity. That, however, seems nuts – we all know there’s such a relation, and that it’s ubiquitous. It would seem better understand the truth that “Jesus is God” in some way other than “Jesus is identical to God” (j = g). But how exactly? And will this compromise the claim that Jesus “is fully God”?