the apologetics blind-spot on numerical identity

Here’s part of a conversation I had recently with a guy in a Facebook group who when it comes to theology consumes almost only evangelical apologetics sources. I’m going to call him “Tim” here. The conversation illustrates a blind spot that I often run into, a blind spot which results from people who study apologetics being insufficiently trained in logic. All the non-theological points I make in this post are things one learns in a first deductive logic class; more on this at the end.

I had observed that the New Testament identifies the Father with the one true God. Tim replies:

But then you have things that ONLY God can do Jesus doing. That is the rub.

Tim implies here that the New Testament also identifies Jesus with the one God. So, he’s meaning to argue like this:

1. Only God can do X.
2. Jesus did X.
3. Therefore, Jesus just is God.

1 says that God can do X, and that anyone who can do X just is God himself (i.e. is numerically identical to God); more concisely: only God can do X. And so the conclusion 3 is that Jesus is numerically identical to God – that Jesus and God are one and the same, numerically one thing, a point much emphasized by apologists, despite obvious and deep problems.

Of course, the argument is valid (that is, 1 and 2 imply 3). But I point out that (for a Protestant) there’s no justification for 1, and that the case of Jesus in the NT seems to imply that 1 is false. I said,

No rub. It’s only an assertion of catholic traditions that only God can e.g. forgive sins, be called “Lord”, be worshiped, etc. Such claims are unsupported by reason or scripture. In fact, the case of Jesus shows such claims to be false. To see this, you need to get clear on identity, and the importance of God and Jesus undeniably differing in the New Testament. All clearly laid out here.

Now, I know Tim is not going to want to work through a lecture, but experience has taught me that people who read a lot of apologetics have been programmed to not understand the above sort of argument, or just, the logic of identity. So, I try. Tim eventually replies:

I started to watch that video, every time you say numerical one, I shutter. That I can tell, you haven’t defined what you mean by “one”. Can you help me with that?

OK, so maybe he watched a few minutes. Great! I reply with a link to a detailed blog post about the concept of identity, saying

I mean this.

Now, either Tim didn’t read that, or he didn’t comprehend it. In truth, the concept of numerical identity can’t be analyzed in terms of more basic concepts. It is a basic, rock-bottom concept that everyone has and often employs. Of course, we can make certain observations about it, like I do in the linked post.

But Tim moves on to address an example I use in the video, saying

Dale, in your example in the video you said Saul=Paul. Sure in all senses that is true.

Tim is right, because Saul just is Paul – they’re the same thing. (The “in all senses” is not needed, though, as the statement is unambiguous.) But he’s thinking that the sentence “Paul=Saul” says that Saul and Paul are very similar or totally similar. Well, they can’t ever differ in any way, given that they’re one and the same being. Everything is, at any given time, perfectly similar to itself!

But of course two different beings can also be very similar, such as twins. To say Saul = Paul is to say a lot more, so to speak, than that they are similar. It’s to say that if you’re counting realities, you don’t count Saul and Paul individually, as that would be over-counting. Rather, the words “Saul” and “Paul,” in this context, co-refer. We’re referring to the same thing twice using different names.

Numerical identity is a relation that something can only bear to itself, never to another. And unlike similarity, it doesn’t come in degrees. It’s all-or-nothing.

But with his misunderstanding in place – that “Saul = Paul” in my example means only that those two are qualitatively similar, Tim continues, saying

Now what if we said Saul=human, this would also be true. We would also say that there is only one human nature, all humans have that nature, or anything that has that nature is human.

Again, Tim thinks “Saul = Paul” is merely describing Saul (as being Paul?), and so he compares it to the statement that “Saul is human.” “Saul = human” is nonsense if the word “human” here is a predicate (that is, a description); only referring terms like names can go on either side of “=” in logic. Of course, there is a human with whom Paul is identical – Paul (aka Saul). In any case, he means to say that “Saul is human” and that this is true because Saul has the universal essence humanity or human nature. That’s a controversial piece of metaphysics, but let it slide for now. Tim continues,

Then if we said that Saul=Tim, you would have to ask, what do you mean by that. If you mean they share the common trait of being human it is true, but I don’t share ALL of the qualities of Saul, just the one that all humans have in common.

“Saul = Tim” is not vague in meaning, and it is false, because Saul is one thing, and Tim is another. These are not numerically the same, but are two things. Again, “Saul = Tim” doesn’t say that Saul and Tim are similar, but rather that they’re numerically the same thing. Sure, both are humans, whether or not there’s such a thing as the Platonists’ universal property called humanity. But what does this have to do with theology? Tim gives what he thinks is the payoff, saying

When Trinitarians say that Jesus=God, it is saying they share a common nature.

Well, that’s what they often mean. But clearly, many apologists mean the argument above; they often assert the numerical identity of Jesus and God, and not only their co-essentiality or nature-sharing or equal divinity.

But perhaps Tim all along meant this argument instead, and/or was confusing it with 1-3 above:

4. Only a being with a divine nature can X.

5. Jesus can X.

6. Therefore, Jesus has a divine nature.

Again, X might be, “have the authority to forgive sins,” or “be called ‘Lord’,” or “fulfill prophecies about Yahweh,” be called “God,” etc. And this argument 4-6, like the first one (1-3) is valid; that is to say that if each premise is true, then the conclusion must be true too. And for many Xs, the New Testament will directly assert that Jesus can X. (e.g. be worshiped)

BUT, 4 has the same problem as 1: it is provable neither by reason nor by scripture. And, for many Xs, we have scriptural examples of people who can X but we don’t think that they have a divine nature. (e.g. Jesus’s followers forgiving sins, various beings other than God being called “gods”) Thus, catholic traditions seem to conflict with the Bible in these cases. Most Protestants are in denial about this.

But to return to my main point, 1 and 4 say different things, and have different truth-conditions.

Also, the conclusions 3 and 6 are very different.

• The trinitarian should deny 3 (that Jesus just is God – that “they” are one and the same), because any Trinity theory has it that the one God just is (is identical to) the Trinity, and that Jesus and the Trinity are two, so that the one God can’t also be identical to Jesus. It is obviously impossible that anything be numerically identical to two different, i.e. non-identical things. If a = b, and a = c, then it follows that b = c. And if the one God is the Trinity, and the one God is Jesus, then it follows that Jesus just is the Trinity, and vice-versa, which is patently false. That Jesus and the Trinity can’t be numerically one follows from the fact that (if both are real) they differ in various ways, e.g. the Trinity is tripersonal and Jesus is not tripersonal, or Jesus died and the Trinity has never died. Since 3 follows from 1 and 2, the trinitarian must also deny 1 and/or 2. I recommend denying 1 – that only God can X.
• In contrast, a trinitarian should want 6 to be true; 6 – that Jesus has a divine nature – seems a way of expressing the main claim about Jesus in the catholic creed of 381. Of course, many will not be convinced by the argument for it. (And rightly so!)

In sum, note to apologists: study standard first-order predicate logic with identity. Never mind that some of your apologetics heroes don’t know it; you will need to. Any naturalist, Muslim, etc. who’s majored in Philosophy knows this, as well as many other well-educated people. It’s not enough to learn about some informal fallacies (e.g. begging the question, ad hominem), so as to accuse your opponents. Invest in your own reasoning abilities. Then, on the Trinity and the Incarnation, you’ll see what all the hubub among Christian philosophers and theologians trained in philosophy has been about. These are people who’ve all been trained in this way, and they build their theories, in most cases, on the assumptions that there’s such a thing as numerical identity, and that the indiscernibility of identicals is true. The few that aver know what they’re getting into.

And you don’t need an undergrad degree in Philosophy; any high school freshman can learn this logic – it’s no harder than year 1 Algebra. Here’s a good book, by a trinity of accomplished Christian philosophers, no less.

Learning about identity will also help untangle some common confusions about John 17 – but that’s another story.