In the beginning was the Word, and the Word was with God, and the Word was God...And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father...No one has ever seen God; the only God, who is at the Father's side, he has made him known (Jn 1:1,14,18).He is the image of the invisible God (Col 1:15).He is the reflection of God's glory and stamp of his nature (Heb 1:3).
What these passages share in common is the principle of resemblance. The spoken or written word is the audible or visible counterpart to interior monologue or silent thought.
No one is more like a father than his son, and vice versa.
An image of something invisible. A bit paradoxical.
Heb 1:3a could either mean reflection or radiance. It is probably trading on connotations of the Shekiah, which was an outward manifestation of the invisible, aniconic God.
A "stamp" (Heb 1:3b) is a facsimile or replica, indistinguishable from the original, archetype, or exemplar. A duplicate.
The principle of resemblance is a useful way to model the Trinity. Let's explore that.
Suppose you're standing in front of a mirror, which reflects the room behind you. A mirror looks like a window. The room appears to be in front of you rather than behind you, as if you're peering into another room.
Suppose you could pass through the mirror to the room on the other side of the mirror. Suppose the mirror was a portal, and you could walk into the counterpart. What would you find?
In one respect, everything would be identical. By walking through the mirror you enter a parallel universe. Same dimensions. Same furniture. Same size, shapes, and relative position.
Suppose you went to bed in one world but woke up in the bedroom of the parallel world. Could you tell the difference?
There'd be a subtle difference. Suppose you were transported from a right-handed room to a left-handed room.
If you looked more closely, differences might be more dramatic. A reversal of the Coriolis effect as sink water drains. A piano keyboard with with a left-handed layout. Books with words and sentences written backwards. Cars with the steering wheel on the righthand side. There might be inverted color spectra.
Would you notice the difference? That depends. Suppose, in passing from our world to the twin world, you undergo a psychological shift. For instance, mirror-writing is natural for southpaws. Likewise, I once read Paul Davies describe the Big Crunch, where, as cosmic expansion contracts, time reverses itself, and mental processes run in reverse. That depends on your theory of time and philosophy of mind, but if that was feasible, the difference would be indetectable.
A pair of butterfly wings exhibits reflection symmetry. In plane geometry, they're nonsuperposable, but in solid geometry, they're superposable by rotating the orientation. Changing from two-dimensions to three dimensions makes them isomorphic. So the same thing can be symmetrical and asymmetrical depending on one's perspective. Likewise, Father and Son can be interchangeable from one perspective, yet distinct from another perspective.
Amazing analogies here Steve.
ReplyDeleteVery thought provoking. Great post.
ReplyDelete"So the same thing can be symmetrical and asymmetrical depending on one's perspective. Likewise, Father and Son can be interchangeable from one perspective, yet distinct from another perspective."
ReplyDeleteRight, things can be *qualitatively* similar (even in a sense indistinguishable) in one respect, and yet qualitatively different in another respect.
A truism, really.
A pair of 2D butterfly wings share *qualitative* identity while a pair of 3D butterfly wings share *quantitative* identity (i.e. superposable). What's the difference between a left-handed wing and a right-handed wing? Interchangeable if you turn it over.
DeleteDale, try to think for a change. Reflection symmetry is stronger than *similarity*. Rather, it entails point-by-point correspondence. And that's a definition of numerical identity:
DeleteThe Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y.
http://plato.stanford.edu/entries/identity-indiscernible/
LOL. Yeah, I should think once in a while.
ReplyDeleteYour blind spot here is interesting. If you're talking about *correspondences between* the points on A and the points on B, this presupposes that A and B are two.
"Likewise, Father and Son can be interchangeable from one perspective, yet distinct from another perspective."
As stated before, this is a trivial truth, that things can be the same in one respect and different in another. So loosely, we can say that qualitative sameness can be perspective-relative.
But numerical identity can't relative in that way - otherwise, what things there are would be perspective relative. Basically no one wants to say that, including trinitarian theologians. They want to say it is a perfectly objective matter that Father and Son are the same god, or that they are both "Persons" within the one god.
Because you hope this line of speculation will help somehow with the Trinity, you're not seeing this. You *need* this to be a kind of numerical identity, and not merely qualitative identity, but it is not, and this is obvious that it is not. This sort of sameness is just an extreme case of similarity.
The indiscernibility of identicals (basically: numerical sameness entails indiscernibility) is self-evident, and is widely deployed in metaphysics, e.g. in discussions of mind and body, or of mental and physical properties.
The identity of indiscernibles is a different principle, and I believe has always been controversial, since Leibniz formulated it. As summarized in the piece you cite: "no two distinct things exactly resemble each other" - that is, things which don't differ have to really be one and the same thing (so, not thingS at all).
To be clear, Leibniz accepted both, and both are sometimes called "Leibniz's Law," as is the combination of the two (a biconditional). But the two seem to have very different epistemic statuses.
What you're trying to argue is that this sort of similarity entails numerical sameness. But your examples all involve multiple things, not one thing. And unfortunately, the identity of indiscernibles is a thin reed on which to build a doctrine of the Trinity. To my knowledge, no one has tried - you're alone in this suggestion - or at least, no one in the recent analytic theology literature. And further down in the piece you cite, they argue that your principle is false!
Again, Dale, try to think. Is a left-handed butterfly wing the same or different from a right-handed butterfly wing? Depends. In 2D, different–in 3D, the same.
DeleteDale, comparing A to B is used to formulate identity. For instance:
DeleteThe Indiscernibility of Identicals (Roughly, if a = b, then whatever is true of a is true of b, and vice versa.)
http://maverickphilosopher.typepad.com/maverick_philosopher/2011/07/leibnizs-law-a-useless-expression.html
Yes, "a" and "b" may be co-referring terms - two ways to refer to the same thing. That is how one must be using them when a sentence like "a = b" is true. In any statement of *numerical* identity, if the two terms don't co-refer, then the statement is false. Do you see why?
DeleteBut this post was about the Father and the Son. As I've pointed out many times, in *your* view, some things are true of one but not of the other. So by the indiscernibility of identicals, in *your* view, this will be false: f = s. But then, being numerically two, they can't be the same god.
They might still be two somethings somehow within the one god. On this view, neither is a god, but only the Trinity is - the triune god is the only god - like W.L. Craig thinks.
This sort of Trinity theory runs afoul of the NT, though, in which the Father just is the one God himself, the one true God.
At least you're trying to focus on *numerical* identity now; to the extent that you do this, you'll see the problems that all the analytic theologians build their Trinity theories in order to get around.
"If you're talking about *correspondences between* the points on A and the points on B, this presupposes that A and B are two."
DeleteCompare that to a standard definition:
Indiscernibility of identicals: The principle that if A is identical with B, then every property that A has B has, and vice versa. This is sometimes known as Leibniz's law. The Oxford Dictionary of Philosophy.
"But your examples all involve multiple things, not one thing."
What's the relationship between a left-handed butterfly wing and a right-handed butterfly wing? One thing, two things, or both (in different respects)?
"You *need* this to be a kind of numerical identity, and not merely qualitative identity, but it is not, and this is obvious that it is not."
Once again, Dale, you keep intoning the same formulaic claims without bothering to ask what constitutes numerical identity. What's the criterion?
Definitions of Leibniz's law typically appeal to one-to-one correspondence, where A and B can be set in systematic point-by-point correspondence. Well, Dale, reflection symmetries satisfy that condition. An exact match. And yet they remain distinct due to chirality.
Steve, you're quoting me a standard definition thinking that I disagree with it. But I don't - I would formulate it slightly differently, but the underlying intuition is the same.
Delete"What's the relationship between a left-handed butterfly wing and a right-handed butterfly wing? One thing, two things, or both (in different respects)?"
It's your example. If you're talking about two individual wings, the answer is: non-identity, numerical distinctness. Now if you're thinking that one wing can be viewed as either right-handed or left-handed depending on the perspective from which it is viewed - well, sure. But now we're talking about objectively one thing, self-identical.
"What's the criterion?"
Of numerical identity? Like, what other concepts can it be defined in terms of? I think, none. It is a basic concept, like existence. If you're asking for criteria in the sense of necessary conditions or sufficient conditions - it is necessary than numerical identity is reflexive, transitive, and symmetrical - if the relation you're thinking of is not one of these, it is not = (as used in logic) that you have in mind. It (=) also forces absolute indiscernibility at a time (or in timeless eternity). If you discover simultaneous differences between any A and any B, that suffices for their being non-identical (not numerically identical). The distinctness of discernibles is as obvious as is the indiscernibility of identicals.
This is fairly standard stuff.
"Definitions of Leibniz's law typically appeal to one-to-one correspondence, where A and B can be set in systematic point-by-point correspondence. Well, Dale, reflection symmetries satisfy that condition. An exact match. And yet they remain distinct due to chirality."
I think that by "Leibniz's Law" here you must be the identity of indiscernibles. Then you give what you take to be an example of indiscernible pairs. The conclusion (by id of ind) would be that the apparent pair is *really* one and the same thing ("they" are really =). But you say this pair remains distinct, due to their being mirror images of one another. This doesn't make sense, Steve. You seem to be fishing for something where, Trinity-like (in your view), a pair of somethings remains distinct while also being in some sense the same. But in these cases there *is* some sense in which the things are the same - they are similar to a high or even (arguably) a maximal degree. But as I said at the outset, you are now just making a point about the qualitative sameness of numerically distinct things. How is this supposed to help a trinitarian state his view?
In this, you've not advanced a step beyond Basil of Caesarea c. 370 - three beings, each of whom is divine, amounts to three gods. His catholic, non-Nicene opponents constantly pointed this out. That they are indistinguishable in respect of their divinity is surely interesting, but does not soothe the concerns of those wanting to insist on biblical monotheism - then, and now. His example of same yet different things was three men sharing the universal humanity. So with the Trinity - the universal divinity, and three... gods. Yikes. Your analogy or model is just different things which are so similar that all their intrinsic features can be put in one to one correspondence. In either case (yours or Basil's) the one might be mistaken for the other - but it has been specified that they are not =, by Basil, and by you, in your own way.
"It's your example. If you're talking about two individual wings, the answer is: non-identity, numerical distinctness. Now if you're thinking that one wing can be viewed as either right-handed or left-handed depending on the perspective from which it is viewed - well, sure. But now we're talking about objectively one thing, self-identical."
DeleteYou keep swinging and you keep missing. A 2D left-handed butterfly wing is *objectively* distinct (nonsuperposable) from a 2D right-handed butterfly wing while a 3D left-handed butterfly wing is *objectively* interchangeable (superposable) with a 3D right-handed butterfly wing. So the distinction is not between objective and perspectival. Hence, there are cases in which a pair can be objectively/numerically the same in one respect but objectively/numerically distinguishable in another respect.
"it is necessary than numerical identity is reflexive, transitive, and symmetrical"
By definition, reflection symmetries are…symmetrical.
"Then you give what you take to be an example of indiscernible pairs. The conclusion (by id of ind) would be that the apparent pair is *really* one and the same thing ('they' are really =). But you say this pair remains distinct, due to their being mirror images of one another. This doesn't make sense, Steve. You seem to be fishing for something where, Trinity-like (in your view), a pair of somethings remains distinct while also being in some sense the same. But in these cases there *is* some sense in which the things are the same - they are similar to a high or even (arguably) a maximal degree."
Dale, you're trapped in a false dichotomy, as if every relation is reducible to absolute identity or absolute alterity. You need a blood transfusion. You need to expand your conceptual scheme.
In a reflection symmetry, the pair is the same thing vis-a-vis point-by-point correspondence but distinct vis-a-vis chirality. You keep falling back on "similarity" as your default explanation, but that's too weak to capture systematic, one-to-one correspondence between A and B.
"Your analogy or model is just different things which are so similar that all their intrinsic features can be put in one to one correspondence."
Once again, the law of identity is typically formulated in terms of systematic, one-to-one correspondence between A and B. That's not just "similarity".
"but does not soothe the concerns of those wanting to insist on biblical monotheism - then, and now."
The Bible doesn't have a philosophically rigorous definition of divine unicity. The comparison with reflection symmetries is already more rigorous than what you find in Scripture, which merely involves a contrast between Yahweh and pagan polytheism.
"Hence, there are cases in which a pair can be objectively/numerically the same in one respect but objectively/numerically distinguishable in another respect."
ReplyDeleteThis again makes clear that you have in mind similarity, not identity. But you're not willing to see it for some reason.
"By definition, reflection symmetries are…symmetrical."
Sure. But symmetry is only a necessary condition for identity, not a sufficient one. Many relations are symmetrical.
"You keep falling back on "similarity" as your default explanation, but that's too weak to capture systematic, one-to-one correspondence between A and B."
Nonsense. Similarity comes in degrees. Arguably, two things might be maximally similar, i.e. have *all* their properties in common - if id ind is false.
You're hunting, for trinitarian reasons, for something in between the concept of identity and the concept of similarity. But you've not found any such thing. You're fixated on special cases of similarity. That word *sounds* too weak to you for what you have in mind, but necessarily, everything is similar to itself, and again, arguably two things might be indistinguishable - similar to a maximal degree.
It'd be nice to expand my conceptual scheme, Steve, but you're not helping.
"The Bible doesn't have a philosophically rigorous definition of divine unicity."
It doesn't need to. It explicitly says and everywhere assumes that the Father (aka YHWH, Adonai, God) is the one true God. That is analyzable as a conjunction of two assertions, one of which employs the plain vanilla concept of =, as I've been explaining. To put it not in symbols, but in quasi-English: the Father is true God and for anything whatever if it is true God then it just is (=) the Father. This is part of what Jesus is saying in John 17:1-3. And the analysis is what is given in any deductive logic class for any statements of the form "X is the only F."
The Bible's sort of monotheism doesn't require any abstract speculations about "divine unicity."
"[Dale Tuggy] Erm… you think this is important to consider here? https://en.wikipedia.org/wiki/Bilocation OK, nothing I have said rules this out a priori. You seem to want to make the concept of numerical identity, or the indiscernibility controversial points of speculation - but that is a patently wrongheaded move, as best I can tell, motivated by our own desire to defend your confused views on God and Jesus."
Deletehttp://triablogue.blogspot.com/2018/04/bilocation.html?showComment=1523798869703#c1939318974839000221
Since, by your own admission, numerical identity is consistent with bilocation, you have a pretty flexible notion of numeral identity. As Stephen Braude points out, bilocation seems to require a doubling of body and also a doubling or bifurcation of consciousness.
"This again makes clear that you have in mind similarity, not identity. But you're not willing to see it for some reason."
DeleteOnce again, Dale, what makes a lefthanded butterly wing merely similar rather than identical to a righthanded butterly wing?
"Sure. But symmetry is only a necessary condition for identity, not a sufficient one. Many relations are symmetrical."
You're understanding is always skin deep. But what makes symmetries symmetrical? What makes A and B symmetrical is the fact that they share everything in common. Well, if they share everything in common, aren't the identical?
But there's a twist because some kinds of symmetries are chiral, so even though A and B are completely symmetrical with each other, they're not superposable. Or they're superposable in 3D but not 2D.
"Nonsense. Similarity comes in degrees. Arguably, two things might be maximally similar, i.e. have *all* their properties in common - if id ind is false."
That's you trying to squeeze my categories into your categories, but they don't fit. That similarities come in degrees is a red herring. Who denies it?
"You're hunting, for trinitarian reasons, for something in between the concept of identity and the concept of similarity."
No, I'm not hunting for something in-between.
"You're fixated on special cases of similarity."
Once again, that's you laboring to repackage my examples into your conceptual scheme.
"arguably two things might be indistinguishable - similar to a maximal degree"
Indistinguishable but not identical. Where is that distinction in Leibniz's law?
"It explicitly says and everywhere assumes that the Father (aka YHWH, Adonai, God) is the one true God."
Yes, I've heard your stump speech many times before. Repetition doesn't make it true.
"This is part of what Jesus is saying in John 17:1-3."
Been there, done that. Once again, this is Dale Tuggy as a tape recorder on replay.
"The Bible's sort of monotheism doesn't require any abstract speculations about 'divine unicity.'"
Which is why coarse-grained biblical monotheism disallows pagan polytheism but allows for the Trinity.
Too much point-missing and silly posturing here. You would profit from a standard class, or a standard text book, on deductive logic, one that includes quantification. Here's an excellent one, by three Christian metaphysicians: https://www.amazon.com/Power-Logic-Frances-Howard-Snyder-Dr/dp/0078038197
DeleteThanks for your backdoor admission that you can't refute my response.
DeleteLol!
Delete