Substitutivity

I'll comment on Tuggy's attempted reply to me:

http://trinities.org/blog/hayss-self-inflicted-dental-injury/

I'd like to single out this particular line of argument:

Generally, when Hays, in interacting with me, starts riffing on the metaphysics of time or personal identity, it is because he wants to deny this:Things which differ are two (i.e. are not numerically identical)
which is premise 2 in this argument, an argument to which McClatchie and Hays seem to lack any good reply. To put it differently, nothing can, either at one time or in eternity, be and not be some way. Ridiculously, Hays denies this. Why? Because his confused, pop-evangelical theology says that Jesus just is God and vice-versa. And yet all Christians think, on scriptural grounds, that God and Jesus have differed. So this self-evident truth, Hays reasons, has got to go!
Epistemically, this is indefensible. The above principle is just as evident to Hays as it is to me. It has the same epistemic status as countless other principles he’d insist on, like the validity of modus ponens. He employs it all the time without realizing it. It’s probably unfortunate for him that he heard it from me. If he’d heard it from someone on his theological team, his head would immediately nob. “Yes, that is obvious.”But coming from me, it just must be the product of some ungodly speculations. It must be, ’cause it helps to make a problem for my obviously-correct theology!
Well, no, it’s not. Basically every one of these worked out Trinity theories is designed to be consistent with the indiscernibility of identicals. That’s because these philosophers (with the exception of the logically idiosyncratic Geach) see that it is self-evident that if some x and some y actually differ (or have differed, or will differ, or even just could differ) that it is false that x = y. Understanding this is just part of understanding our concept of (numerical) identity. Many times, a philosopher will explain identity as that relation whichnecessarily: is reflexive, transitive, and symmetrical, and which forces absolute indiscernibility.

1. Let's compare that to a recent exchange that Tuggy and I had on my blog:

Tuggy

In the NT, 'the Son' and 'Jesus' are co-referring terms. That is to say, it is assumed that Jesus just is the Son, and vice-versa. In plain English, these are not two characters, but one. You just asserted that one existed before the other; but that requires them to be two."

Hays

Norma Jeane and Marilyn Monroe are coreferring terms. Does that mean Norma Jeane was always a movie star, Playboy centerfold, wife of Arthur Miller and Joe DiMagio? Things can be true of the same individual at one stage of life, but false at another stage of life. 

Tuggy then admits that my example "is obviously true". But obviously true in reference to what? The reality of change, or the indiscernibility of identicals? 

Continuing the exchange:

Hays

That's why your invocation of is the indiscernibility of identicals is arbitrary. You yourself make that consistent with change. But in that event, you're not using the the indiscernibility of identicals as your standard of comparison. Rather, you are using your theory of personal identity as your standard of comparison, and then adapting the indiscernibility of identicals to accommodate the reality of change in reference to the same individual. So you're very flexible in how you apply the indiscernibility of identicals in that case, but very inflexible in how you apply to the Trinity or the Incarnation.

Tuggy

We know that things change.

Hays

True, but what this means is that you're not using the indiscernibility of identicals as your standard of comparison. Rather, you begin with the experience of time as your standard of comparison. You then reformulate the indiscernibility of identicals to accommodate the experience of time.

Time is change. Change is difference. How is that consistent with the the indiscernibility of identicals? Not consistent if you absolutize the indiscernibility of identicals.

You're not using a necessary truth (indiscernibility of identicals) as your criterion. Just the opposite: your using a contingent truth (the experience of change) as your criterion. So you prioritize truths of fact over truths of reason. 

2. Compare Dale's methodology to John McTaggart. McTaggart denied the reality of time, based on the very same principles that Tuggy invokes: the dissimilarity of the diverse (i.e. identity of indiscernible) and the diversity of the dissimilar (indiscernibility of identicals).

Unlike Tuggy, he actually begins with that "self-evident" truth of reason, which he applies with ruthless, fanatical consistency. By contrast,  Tuggy approaches the issue from the opposite end of the spectrum. Tuggy begins with the self-evident truth of time. 

So there's a choice of starting-points. Do we, like McTaggart, take a necessary truth like the law of identity as our standard of comparison, and then disallow change because that conflicts with the law of identity? Or do we take a contingent truth like the experience of time, and allow that to qualify the law of identity? 

The same issue crops up in the case of transworld identity. On the one hand, it seems natural for us to make counterfactual claims. For instance, if I had a brother, I'd be somewhat different than if I didn't have a brother, or vice versa. For one thing, some of my memories would be different, and memories are an element of personal identity. 

But how can I be the same individual if something about me is different, especially something as significant as personal memories? So what gives? Do we deny the truth-value of counterfactuals? Or do we qualify the law of identity?

One move is to distinguish between intrinsic and extrinsic properties. I don't object to that distinction, but that's drawn in spite of the indiscernibility of identicals. 

Tuggy's dilemma is that he careens between two divergent "self-evident" principles. He absolutizes the law of identity when attacking the Trinity and the Incarnation, but he makes exceptions when the topic is diachronic identity or transworld identity. He exempts them from his strictures. So Tuggy's appeal is selective and arbitrary. 

3. Finally, let's take a comparison. Do symmetries satisfy the principle of substitutivity (i.e. indiscernibility of identicals)? What makes them symmetrical is one-to-one correspondence. That's a rigorous criterion. 

But consider mirror symmetries. What makes them symmetrical is that you can place them in a relation of one-to-one correspondence.

Yet because they have the property of chirality, they are nonsuperimposable. Left-handedness is not interchangeable with right-handedness. 

So that's where Tuggy's false dichotomy between strict identity and strict alterity breaks down. Not everything is reducible to his binaries.