Skip to content

the apologetics blind-spot on numerical identity

Listen to this post:

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.

Me_myself_I

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!)
now I get it

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.

Print Friendly, PDF & Email

16 thoughts on “the apologetics blind-spot on numerical identity”

  1. Pingback: Paul Anchor on numerical identity and it’s absence in the same entity, the Word, taken from trinities.org | Badmanna's Blog

  2. It seems to me that the blind-spot belongs to those who call themselves Unitarians.

    John 1 v 1 asserts the numerical identity and the non-numerical identity of the Word with God. Both contraries are asserted to be equally true of the Word in relation to God.

    The Word is God, i.e. numerically identical to God. He is with God, i.e. he is not numerically identical to God.

    If Unitarians ignore this paradoxical revelation of the nature of the true God they are elevating their own mind above the mind of God and denying his revelation, barking up the wrong tree and wasting everybody’s time, including their own.

    1. Paul,

      What you are defining would not be a paradox, but rather a contradiction. The thing with contradictions is that they cannot possibly be true. To assert that contradictory things can be equally true is to throw dialog out the window. You might as well say that you and I are both right, even though we clearly disagree. That would be a contradiction but in your world that’s just a paradox, so why even dialog? Dialog is not possible to have once you throw logic out the window.

      And it is really not charitable to think that John intended to write a contradiction when there are other options. If John did write contradictions then he really wrote nothing at all.

      Here is the statement to which you refer. Maybe a deeper look at it is in order before asserting that it flatly states something clearly contradictory.

      ?? ???? ?? ? ?????, ??? ? ????? ?? ???? ??? ????, ??? ???? ?? ? ?????.

  3. Update: he refuses to argue anonymously here. He’s a Facebook-only type, I suppose. Well, then I cease to care about preserving his anonymity. He doesn’t want to be quoted on the blog, so I continue to engage with him here: https://www.facebook.com/groups/unbelievablejb/permalink/910474702386380/?comment_id=911422565624927&reply_comment_id=911680625599121&notif_t=group_comment_reply&notif_id=1470437200122015

    After a few more rounds, I’ve written him off as a time-waster. Since I’m not parroting the standard evangelical apologetics line, I must be uninformed or wickedly misrepresenting the issue. (facepalm) Bizarrely, he’s convinced himself that this whole “numerical identity” idea is some crazy idea of mine. Oy.

  4. I recently listened to a debate between Buzzard and Fred Sanders. I am shocked as to how fallacious Sanders reasoning is again and again making unwarranted assumptions and building on these. Of course, his big gun is EXACTLY the argument that T displays above.

    Admittedly, this is where it gets a bit frustrating. I am at complete loss why otherwise intelligent men suddenly loose all rational and make blithering statements – and then condescending and arrogantly condemn anyone who does not agree with their nonsense – men who claim the name of Jesus Christ – men who are supposedly “professional” Christians, etc.

    1. Yeah, it’s frustrating. It’s kind of like politics. As long as you’re shilling for the right side, people on that side don’t care how terrible your arguments are. When people on the other side are unmoved – well, that’s just because they are so close-minded and dogmatic in their adherence to the other side. It’s all the worse when the “right” side is a sizable majority, or is thought to be so. Sigh.

      1. Thanks Dale.

        As followers of the Lord Jesus Christ – we are called to “equal weights and measures” – a level of integrity that is unsurpassed. I am happy to see the strengths of others – and weaknesses of my own understanding. In fact delighted… I am looking for that same integrity – and not one who claims “this is orthodox Christianity” all the while sounding like an idiot.

  5. Hi Dale, I appreciate your post while I object that numerical identity is always all or nothing. As you know, I argue for natural law theory examples of impure relative Identity and outline a natural law analogy of the Trinity http://journalofanalytictheology.com/jat/index.php/jat/article/view/jat.2016-4.181919061425a/283 For example, impure relative identity is the same as impure absolute identity. Also, I recently saw that I misused a logical term in that paper that has a simple correction, but otherwise my paper makes a good case. Peace, Jim

    1. I want to clarify my mistake and needed correction. After my paper published, I discovered that I misused *if and only if* in several places of my JAT 4 Trinity paper. For example, *if and only if* is a sentence connective while I used it to connect nouns, except when I correctly used it for my definition of LL.

      Here’s an example of an error on page 136:
      The triumvir was relatively identical to Lepidus, but not the triumvir if and only if Lepidus.

      Here’s the correction for that example:
      The triumvir was relatively identical to Lepidus, but the triumvir was not absolutely identical to Lepidus.

      I asked an editor if the journal will have room for corrections, and I have not yet heard back.

    2. Here are the corrections for my paper:

      The formula indicates the following:
      1. A is relatively identical to the value, but A is not absolutely identical to the value.
      2. B is relatively identical to the value, but B is not absolutely identical to the value.
      3. The value of A is absolutely identical to the value of B.
      4. A is not identical to B.
      (page 135)

      1. The expression 1 + 3 is relatively identical to the value 4, but 1 + 3 is not absolutely identical to 4.
      2. The expression 2 + 2 is relatively identical to the value 4, but 2 + 2 is not absolutely identical to 4.
      3. The value of 1 + 3 is absolutely identical to the value of 2 + 2.
      4. The expression 1 + 3 is not identical to the expression 2 + 2.
      (page 135)

      1. The triumvir was relatively identical to Lepidus, but the triumvir was not absolutely identical to Lepidus.
      2. The pontifex maximus was relatively identical to Lepidus, but pontifex maximus was not absolutely identical to Lepidus.
      3. Natural person Lepidus who existed as the triumvir was absolutely identical to natural person Lepidus who existed as the pontifex maximus.
      4. The triumvir was not identical to the pontifex maximus.
      (page 136)

      Natural persons X and Y become proprietors while forming general partnership C. X is C and possesses the entire authority of C; Y is C and possesses the entire authority of C; X and Y are different natural persons….
      1. X is relatively identical to C, but X is not absolutely identical to C.
      2. Y is relatively identical to C, but noY is not absolutely identical to C.
      3. X’s authority of C is absolutely identical to Y’s authority of C.
      4. X is not identical to Y.
      (page 136)

      1. Octavian was relatively identical to the triumvirate, but Octavian was not absolutely identical to the triumvirate.
      2. Lepidus was relatively identical to the triumvirate, but Lepidus was not absolutely identical to the triumvirate.
      3. Antony was relatively identical to the triumvirate, but Antony was not absolutely identical to the triumvirate.
      4. Octavian’s absolute authority was absolutely identical to Lepidus’s absolute authority.
      5. Octavian’s absolute authority was absolutely identical to Antony’s absolute authority.
      6. Lepidus’s absolute authority was absolutely identical to Antony’s absolute authority.
      7. Octavian was not identical to Lepidus.
      8. Octavian was not identical to Antony.
      9. Lepidus was not identical to Antony.
      (pages 136-137)

      1. The Father is relatively identical to the triune God, but the Father is not absolutely identical to the triune God.
      2. The Son is relatively identical to the triune God, but the Son is not absolutely identical to the triune God.
      3. The Holy Spirit is relatively identical to the triune God, but the Holy Spirit is not absolutely identical to the triune God.
      4. The Father’s divine authority is absolutely identical to the Son’s divine authority.
      5. The Father’s divine authority is absolutely identical to the Holy Spirit’s divine authority.
      6. The Son’s divine authority is absolutely identical to the Holy Spirit’s divine authority.
      7. The Father is not identical to the Son.
      8. The Father is not identical to the Holy Spirit.
      9. The Son is not identical to the Holy Spirit.
      (page 140)

      Thank you for your considerations.

      Peace,
      Jim

  6. David Kemball-Cook

    Great article. Ignorance about numerical identity seems to be very common among trinitarians. See eg this thread I started on Unbelievable last October. We got so many different and competing definitions of what it means to say that ‘Jesus is God’, but a common theme was the reluctance to understand that phrase in terms of numerical ID, despite numerical ID being the obvious interpretation.
    https://www.facebook.com/groups/unbelievablejb/permalink/770377906396061/

Comments are closed.