Thursday, June 30, 2011

The identity of identity


Steve, ah yes... I'm backpedaling... away from someone who is untutorable.
But because hope springs eternal: no, numerical identity doesn't come in kinds. It's the relation that of necessity everything bears to itself. So, it applies to the Trinity, divine persons - anything at all that exists.

Tuggy refuse to follow his own argument. He’s said the following:

i) There is only one kind of identity

ii) Identity is a reflexive relation

And I pointed out that a symmetrical relation is a reflexive relation too. Does he deny this?

Where does that leave him, given how he himself chose to define the issue?

i) If there’s only one kind of identity;

ii) If identity is a reflex relation;

iii) If a symmetrical relation is a reflex relation;

iv) Then a symmetrical relation entails numerical identity

Yet he alleges that when I use enantiomorphism (a type of symmetry) to model the Trinity, this doesn’t qualify.

So his only obvious fallback would be to concede that if there are different kinds of reflexive relations, then there’s more than one kind of identity.

I’m merely following his own argument to its logical conclusion.

Moreover, Tuggy habitually acts as though his own position on identity is indisputable, when, in fact, that’s demonstrably false. To take one example:

Mike Almeida | MARCH 16, 2006 4:34 PM
"The Son is not tripersonal. The Holy Ghost is not tripersonal. Now if two things differ in a property, then they cannot be identical. (This is the irreproachable principle of the Indiscernibility of Identicals expressed in its contrapositive form.)"
I'm always a little suspicious of the application of LL [Leibniz' Law] in abstract metaphysical contexts. For instance, does a proper application of LL really show that a statue *could not* be identical to the bronze that composes it, since there are properties the bronze has that the statue does not? That kind of thing is often said, but why doesn't it just beg the question? Why isn't the reply, "no, the metal does not have the different properties you allege, however much it might seem to". Similarly, why isn't one perfectly good response in this metaphysical situation, "no, there is no distinct being, God, in addition to God the Father, God the Son and God the Holy Spirit. There's just one being"? In this case the alleged difference in properties is what is mistaken. Since they are one in being, each being (F,S, & HG) must be tripersonal.

My point is not whether this is a solution to the “problem” of the Trinity. Rather, my immediate point is to draw attention to the way in which Tuggy knowingly oversimplifies the metaphysical intricacies, as well as glossing over the philosophical controversies, regarding the identity of identity (as it were).


  1. Steve -- I admire your wanting to pursue this.

    The person is a lover of his own wisdom and arguments whether they have any validity at all.

  2. As to standing in the gap until reiforcements arrive you are doing fine.

  3. I'm not sure what you mean by different identity relations (it is necessarily true that everything is identical with itself), but there are different kinds of reflexivity. I think that's the relevant piece. Symmetrical relations are reflex if and only if reflexivity is defined as (x)(y)(Fxy --> Fxx & Fyy). However, they are not totally reflexive: (x)(Fxx).

  4. Great reference from --

    I really fail to see what is left to argue when that reference is given and from what you also wrote.

    However, this Dale, strikes me as one of many who are lovers of their autonomous capacity to reason and derive the truth.

    It does not matter in this day and age if their position is false. The person fully surrendered to the flowering of the autonomous self is not open to being corrected as they themselves decide what is true.


    "I'm not sure what you mean by different identity relations (it is necessarily true that everything is identical with itself), but there are different kinds of reflexivity."

    Try to follow the bouncing ball. I'm responding to Tuggy on his own terms.

    If Tuggy defines identity as reflexivity, then whatever is reflexive is identical.

    If symmetries are reflexive, then symmetries are identical.

    If symmetries are reflexive but not identical, then that's a different definition of reflexivity, which, by Tuggy's equation, commits us to a different definition of identity.

    The "wrong" kind of reflexivity would be the "wrong" kind of identity.

    BTW, why should we define reflexivity by Quine's definition rather than geometry? Do you think one is metaphysically superior to another?

    It's not as if we have a ready-made definition of identity or reflexivity which fell out of the sky. That's not a given.

  6. "iv) Then a symmetrical relation entails numerical identity"

    Steve, it is amazing to me that when I try to un-confuse you on basic logic, I get abused as some kind of arrogant rationalist. But I'll continue, for the sake of the less smug who may read this.

    "iv) Then a symmetrical relation entails numerical identity"

    For a relation to be symmetrical means that if A bears that relation to B, then also B bears it to A. A symmetrical relation doesn't have a direction, as it were.

    Numerical identity (=) is such a relation (if a = b then b = a), but of course there are innumerable *other* such relations, like *being related to. Say we're cousins. Then, I would bear the "relative of" relation to you, and likewise, you to me.

    Likewise, there are other reflexive relations too.

    But what I said, again, is that = is the only relation which is nec. reflexive, symmetrical, and obeys L's Law. See here sections 1&2. This should disabuse you of the notion that I'm pushing some pet theory on you. (Should, but based on what I've seen, probably won't!)

    Is this concept of numerical identity (=) controversial? Yes and no. Yes, in that there have been philosophers, like Geach, who have argued that there's no such relation, and that sentences employing it are meaningless. But it's a lazy sort of pseudo triumph to point out that some philosopher has denied a claim. The problem is, some philosopher or other has denied pretty much every self-evident claim, or any claim you can think of, such that no claim exceeds it in justification. e.g. There are a few out there who think some contradictions can be true! Just google "dialetheism".

    Geach's position is widely rejected, almost universally so, in part because we have such a clean grasp of =, and the logic of = is so obvious that it's taught in all intro to logic courses. Also, the concept of = is closely bound up with our ability to refer to any individual thing. See here for more.

    So no, I don't claim that my views on = are indisputable. But I do claim that it is self-evident that there's such thing as =, and that L's Law is self-evident as well, and that these are part of our God-given common sense, and so, really don't need arguing for, for us to rely on them. And as I've pointed out, there are contexts on which you too will make these inferences.

    On the Almeida quote - he's saying that if someone argues that A and B must be non-id, because they differ qualitatively, one can always get out of that by saying, well, actually, they don't differ! In other words, he's not challenging L's Law there. Pay attention to his last sentence, where he makes an inference based on L's Law - do you see it?

    When interacting with someone holding a Trinity theory, I try not to assume any controversial theory. Sticking largely to matters of = allows me to draw out logical consequences of the theory in question. To get a non-question-begging objection, I can of course add in any premises which my opponent agrees he's committed to. That's what I've done here in my tritheism objection to your theory, such as it is.

  7. Hmmm. I will have to think more about this. My proofs are coming out fine, but the predicate "is a sibling of" doesn't work. That's symmetrical, but not equivalent.