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Sunday, June 26, 2011

Defining identity

Dale Tuggy thinks the Trinity is self-contradictory because it (allegedly) violates numerical identity. And Tuggy defines numerical identity according to Leibniz law, viz. the identity of indiscernibles.

I suppose that’s adequate as a preliminary definition, but it’s a rather vacuous definition. A tautology, where you define identity by indiscernibility or vice versa.

There’s nothing inherently wrong with a circular definition, but by the same token, a circular definition isn’t terribly informative.

Tuggy also defines identity somewhat paradoxically by suggesting whatever is true of A is true of B. I say paradoxical since, in that event, you wouldn’t have A and B. For the definition collapses the comparative relata.

One problem with Tuggy's appeal is that Leibniz was a 17-18C philosopher. But philosophy often relies on math and science to provide conceptual models, and a lot has happened since Leibniz kicked the bucket.

I’m been defining identity in terms of symmetry, self-similarity, equipollence. If A maps onto B in one-to-one correspondence, then isn’t that a pretty tight definition of identity? Indeed, I think that marks an advance over Leibniz law inasmuch as it explicates the principle by giving us a procedure for determining what constitutes identity. A more rigorous definition of identity than Leibniz law.

Yet here’s the catch: it’s possible for A and B to be equipollent even though A and B are not mutually reducible, if the relation is enantiomorphic.

If Tuggy deems that definition to be defective, he needs to explain why. It won’t suffice for him to repeat Leibniz law, for I’ve already discussed the limitations of that definition, as well as how my definition improves on his definition by giving us a procedure to determine when that condition is met. That's more exacting. 

3 comments:

  1. Well Done Steve,

    A more rigorous definition indeed.

    Had to look up the term enantiomorphic though. And tell spell check to recognize it as well.

    It seems I posted on a similar enantiomorphic recently (http://brandatthebrink.blogspot.com/2011/05/not-so-wright-on-hawking.html)without knowing it.

    And criticized Scot McKnight on the same enantiomorphic here- http://www.koinoniablog.net/2011/06/scot-mcknight-on-heaven-and-hell.html

    But your enantiomorphic defence of the Trinity is far more fundamental.
    And considerably less vacuous.

    Soldier on Steve...

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  2. "Dale Tuggy thinks the Trinity is self-contradictory because it (allegedly) violates numerical identity."

    No - this is not what I say. First, I don't grant that there is *a* Trinity theory. The creedal formulas are too vague to be inconsistent. Hence, I do not and have never made the above charge. Second, it is wrong to suppose that I reject Trinity theories because I think they're patently self-contradictory. For one thing, *most* of them are not - at least, not obviously so. But the main point is that I think a unitarian view better explains what the Bible says.

    About identity, you ought to read some standard work on predicate logic. If you did this, you'd find that my def. is neither circular, nor vacuous, nor outdated, nor unclear. You're objections show that you are simply not clear on the concept.

    = is a relation which necessarily whatever there is bears only to itself, and not to anything else. So it is a relation which must be reflexive. Like *larger than* it is transitive. And, it is the relation that obeys, as it were, Leibniz's Law, aka the indiscernibility of identicals.

    No, there's no paradox in the definition; L's Law simply uses two terms for one thing, much as we might refer to you by either "Steve H." or "Mr. Hays".

    No, this is in no way confined to Leibniz's other (very controversial) views, or two late 17th or early 18th c. philosophy. This is still taught in logic books, e.g. The Power of Logic.

    More importantly, this is a principle of common sense. If the Boston Strangler is known to have feature X (at time t) and we know Steve to have lacked X at t, then we're *sure* that Steve is not the Stangler. This discovery completely exonerates you. This, even if we know nothing else whatever about the Strangler, or indeed, about Steve! A thing can't (at some one time) differ from itself.

    By "identity" you mean qualitative similarity (not numerical identity), perhaps to a high degree. And maybe sameness in terms of structure specifically (hence, your talk of mapping). This is no advance over L's Law - it merely changes the subject to a different idea of sameness, or to a different meaning of "same."

    Nor have you provided any objection whatever to L's Law, or to using the concept of =. I have no doubt that you regularly assume L's Law, in fact.

    Suppose you meet a dude named "Dale" and wonder if he's the trinities guy. You know the latter teaches philosophy. So you ask this Dale if he has ever done so. He says no, and so, to the degree you trust him, you're sure that he ain't me. Because this one guy - Dale Tuggy - can't be such that both of these are true of him: he has taught philosophy, he has never taught philosophy. Thus, you too know L's Law to be true, even though you think good theology requires you to deny it.

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  3. Dale said...

    "About identity, you ought to read some standard work on predicate logic. If you did this, you'd find that my def. is neither circular, nor vacuous, nor outdated, nor unclear. You're objections show that you are simply not clear on the concept. = is a relation which necessarily whatever there is bears only to itself, and not to anything else. So it is a relation which must be reflexive."

    Symmetries are reflexive relations too. Hence, symmetry is, by your own definition, a model of identity.

    So I guess your objection goes to show that you are simply not clear on the concept.

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