Friday, September 19, 2014

The Same F

Dale Tuggy has a post in which he puts forward the following argument on the Trinity (see also here for background):

1. The Father and the Son are the same God.
2. For any x and y, and for any kind F, if x and y are the same F, then x is an F, y is an F, and x = y. (x and y are numerically one)
3. The Father = the Son. (1, 2)

(2), however, is false, unless we are making a question-begging assumption, in which case there seems to be an equivocal middle term. To say that something is 'the same F', we usually only require some kind of equivalence relation (a relation that's symmetric, reflexive, and transitive). But identity (represented here as x = y) is only one kind of equivalence relation, namely, the kind with antisymmetry. (Strictly speaking, adding antisymmetry gets you equality -- hence the symbolism. It is in fact not entirely certain that equality and identity are the same relation, since there are accounts you can give of mathematical equality, which is paradigmatic equality, preserving its character as an equivalence relation with antisymmetry, that at least make it seem weaker than what one would want from identity; but this is a contentious issue, and there is no widely accepted view about what you could even conceivably add to equality to make it identity, and people do in general make the assumption that equality is identity, or close enough. It need not make a difference here, since the primary issue turns on identity being an equivalence relation with at least antisymmetry; I mention it only because Tuggy regularly talks as if identity were straightforward rather than something for which there are still many unresolved puzzles. When working with identity, it's wise to go slowly.)

Thus (2) is false in the senses in which we usually talk about things being the same F. If we assume specifically that we are including antisymmetry in 'the same F', then (2) becomes a tautology. But in general the only reason you would ever assume that 'the same F' implies antisymmetry is if you were deliberately doing it in order to get something like (3).

This doesn't even get into the problem of identity across modal domains. Usually when talking about identity we are talking about extensional identity. But we use forms of identity that are not obviously extensional. For instance, if I see someone wearing a hat and then later not wearing a hat:

1. That man with the hat and that man without a hat are the same person.
2. For any x and y, and for any kind F, if x and y are the same F (assuming antisymmetry), then x is an F, y is an F, and x = y.
3. That man with the hat = that man without a hat.

From which you can derive a contradiction (one person being hatted and not hatted), of course, unless one modulates the identity using modal information (that of difference in time). But obviously we do also see immediately that despite being the same person, that man with the hat and that man without the hat differ in properties. Obviously, time is not the only modality that adds this sort of complication. There is no generally accepted account of how to handle identity across modal domains. The three kinds of identity across modal domains most discussed these days are personal identity (i.e., one form of identity through time) and transworld identity (i.e., identity across different possible worlds), and material constitution (if one takes material constitution to be an identity relation; in which case it can involve several different kinds of modal domains). All of them raise remarkably complicated questions, and there is no consensus on the best way of handling any of them.

All three of these, however, require us to recognize that (3) is consistent with x and y also being very different, unless we assume that x and y are not in different modal domains. If they are in different modal domains (different times, different locations, different possibilities, different roles), x can equal y and yet differ from it in quite a few ways (hatted, unhatted; 13,148 days and nine hours old, 13 148 days and ten hours old; etc.). It's pretty clear in context that this is a problem for what Tuggy wants to say, since the point is to press a contradiction on
Bowman rather than just giving a slightly less specific statement of (1), but contradictions can be blocked by difference in modal domain. (This is why the principle of noncontradiction is usually stated as something like 'A cannot be both B and not-B in the same respect', i.e., in the same modal domain.) All of the traditional descriptions of the Trinity, however, and most of the modern 'models', lay out the doctrine in heavily modalized terms, so one would have to rule out, and not merely assume, the possibility that we have different modal domains.

ADDED LATER: James Chastek discusses a counterexample to (2) that is of particular relevance to the question.


  1. Timotheos12:13 AM

    Oy, what's up with all these evangelical philosophers who think they can fiddle around with things like the Trinity, the dual-natures of Christ, etc...?

    Even back in my protestant years, I never would have taken any denials of those doctrines even semi-seriously (now of course I would have taken the fact that so many people were abandoning them seriously; just not their so-called "scriptural" reasons for denying them).

    I feel like so many people have been so well fed with the idea of sola scriptura that they remember the sola part and forget the scriptura.

    Reading scripture is more than just an act of academically analyzing the meaning of the words on the page and seeing what is the "minimal" understanding that is entailed; let the un-believers handle that.

    If one wants to understand scripture as a Christian, then one must approach scripture with humility, prayer, reflection, and of course a LOT of listening to the Spirit; it's him that teaches his Word. (I find it ironic that I sound like an evangelical there, but even though they use such language, I'm not so sure that they know what those words mean...)

    Such was how most protestants used to think about things; if the evangelicals keep this behavior up, they'll all be Unitarian Universalists soon...(or even worse, Episcopalians!)

  2. branemrys9:03 AM

    It does seem to have been a side effect of the sharp upsurge in competent evangelical philosophers (although I think Dale himself might say that he's not quite a typical evangelical philosopher).

    If we talk about the problem in general, I think a lot of the problem arises because this is an area in which the usual method of specialized focus on one problem at a time is simply not the appropriate way to handle things. A lot of people would agree with that, even within the field. And, more controversially, I think a lot of philosophers don't actually have a clear sense of the big picture themselves; which seems to be a root of a problem I've noted explicitly before, that a fair amount of modern philosophy of religion seems to be brilliant and ingenious analysis of doctrines formulated and understood at the level of children's Sunday School. That has some kind of place, no doubt, but it's as if ethics consisted mostly of complicated, technically sophisticated discussions of moral principles understood at the level of Barney the Dinosaur. It's putting means above ends -- a temptation to which academics are already prone in general.

  3. Timotheos2:25 PM

    "I love you, you love me, we're a happy family"...

    Yep, sounds about right...

    All we need to do is make it more rigorous, thus:

    IL iff YL, and if IL, WHF, thus, if YL, WHF...

    Why do I get the feeling that this could actually be the start of a real paper?


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