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Identity is a unique and interesting relation. To understand what modalism is, and in some cases to follow what philosophers who discuss the Trinity are getting so excited about, one needs to be clear about the concept of identity. What follows is a quick primer; for more, see section 2 of this article.
In logic, we express the claim that two (really “two”) things are identical by putting the “=” symbol between their names (here, a, b, c – these are names like “Bob”, not variables that take a numerical value). When “a” refers to George W. Bush, and “b” refers to Koko the Gorilla, these would be true: a=a, b=b. But these would be false: a=b, b=a.
Identity is a relation which is
- transitive. If a = b, and b = c, then also, a = c. (In this, it is like the relations bigger than, or smarter than.)
- symmetrical. If a=b, then also, b=a. (In this, identity is like the relation near to, and unlike the relation father of.)
- reflexive. Identity is a relation that a thing can only bear to itself. Unlike most relations you can think of, then, identity isn’t a relation between two things, but always, between a thing and itself. Thus, sometimes philosophers say that identity is a “one-one” relation.
- Many relations can be reflexive or not. Two men can bear the puncher-punched relation, but then, a man can punch himself. Identity, though, must always be reflexive.
Identity, then, is a relation that everything bears only to itself. It is closely connected with our concept of an individual entity – to have the concept of an individual entity, is to have the concept of a thing which is self-identical.
Closely connected with the concept is what philosophers often call “Leibniz’s Law” (not to be confused with this, which sometimes is also call Leibniz’s Law.) The more proper name for it is “the indiscernibility of identicals”. It says,
For any x and y, they are identical (x=y) only if whatever is true of one is true of the other.
This principle seems obviously true, and it seems to be necessarily true – something which is true, and couldn’t conceivably be false. Moreover, all people implicitly recognize it to true.
- Suppose you just met a new friend, Chelsea. She tells you that her dad used to have an important job, that he likes the ladies, loves McDonald’s french fries, and speaks with an Arkansas accent. You say to yourself, “I wonder if her dad is Bill Clinton?” Then, you find out that her Dad is four foot nine, and has never been taller. Well, you can be sure that her dad and Clinton are not identical. Why? It follows from what you know (based on her testimony) plus Leibniz’s Law.
- Again, suppose you’re on a jury, trying to decide whether or not the defendant Joe Blow is really the Boston Strangler. If you’re certain that the Boston Strangler has a size 9 shoe, and that Joe Blow is a size 13, then “if the shoe does not fit, you must acquit”. Why? If j and b differ with respect to anything at all (including, of course, shoe size), then it is false that j=b.
When it is true that a=b, we can say “a is b”. But that can be misleading, as that little word “is” can express many different ideas. (e.g. “Sally is pretty.” “This sculpture is ice.” “New England is Connecticut, Massachusetts and a few other small states.”) Sometimes philosophers say “a just is b” to express a=b.
OK – the above is mostly common sense, just spelled out with unusual precision. Of course, everything is itself, and not something else. And of course, nothing can differ from itself. So what is the payoff, when it comes to the issue of the Trinity?
Many Christians go around saying things like “Jesus is God“, “Jesus just is God”, or “Jesus is God himself”, etc. And the Father? “He’s God too, of course.” Now, what is being said here? If they’re saying that j=g, and f=g, then it follows (by Leibniz’s Law, or by the transitivity and symmetricality of =) that f=j and that j=f – that Jesus just is the Father, and vice-versa. But if that is so, then “Jesus”, “God”, and “the Father” are three co-referring names – those “three” entities are in fact identical. And thus, whatever is true of one, will be true of the others as well. So we get:
- The Father was born of Mary, and was later crucified.
- Jesus sent his only Son into the world, to redeem humankind.
- There are three persons within the Father.
- Jesus is a Trinity.
Yikes – looks like some ill theology. Where did we go wrong? Each different developed version of the doctrine of the Trinity has an answer to this question. Some have gone so far as to deny that there’s any such relation as identity. That, however, seems nuts – we all know there’s such a relation, and that it’s ubiquitous. It would seem better understand the truth that “Jesus is God” in some way other than “Jesus is identical to God” (j = g). But how exactly? And will this compromise the claim that Jesus “is fully God”?
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and one last thing
about jesus being fully god and fuly man
now i think the biggest problem is in the trinity for if the trinity is false than no reson going to the fully god fully man
but the trinity is correct then a nother question needs to be asked can god put all of earth inside a small egg while still preserving there size?
if god is almighty i think he can doesn’t need logical explanation
what needs logical explination is that i think god would present himself to us in a logical non contradital way thanks
dal i am looking frw for what every you have to say …
hey Dale
i know that i may have entered this debate a little bit too late but i wanted to add something listin…what you are stating as a formula of contradiction is true but you made an error allow me to redemonstrait your formula
father = f
son = s
holy spirit = h
f not= s not= h
and taking god = g
we have f=g , s=g ,h=g
contradiction
okay this is wrong for one reson lets examin your fields if you pick a variable wich is x this means that there is one answer for god and you limited a god to any answer so to say father = f is false father is not one solution he is and all the infinity of solutions so then you have the following formula
father = infinty – 0
son = infinty – 1
holly spirt = infinity – 2
now-0 -1 and -2 are not acurate i’m just elimnating a digit i might as well said infinity -8 same thing
now infinty is not equal to infinaty -1 and not equal to infinty – 2 “think of it as a set”
but in essense we all know that infinty -231234 is still infinty so you get the final result
father = infinty
son = infinty
holly spirit = infinaty
infinaty = god
father is god
son is god
holly spirt is god and all are the same god
same infinty
but they are not equil to each other
hope you reply thanks
ps : sorry for spelling mistakes i’m not that good in english
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and one last thing
about jesus being fully god and fuly man
now i think the biggest problem is in the trinity for if the trinity is false than no reson going to the fully god fully man
but the trinity is correct then a nother question needs to be asked can god put all of earth inside a small egg while still preserving there size?
if god is almighty i think he can doesn’t need logical explanation
what needs logical explination is that i think would present himself to us in a logical non contradital way 🙂 thanks
dal i am looking frw for what every you have to say …
hey Dale
i know that i may have entered this debate a little bit too late but i wanted to add something listin…what you are stating as a formula of contradiction is true but you made an error allow me to redemonstrait your formula
father = f
son = s
holy spirit = h
f not= s not= h
and taking god = g
we have f=g , s=g ,h=g
contradiction
okay this is wrong for one reson lets examin your fields if you pick a variable wich is x this means that there is one answer for god and you limited a god to any answer so to say father = f is false father is not one solution he is and all the infinity of solutions so then you have the following formula
father = infinty
son = infinty – 1
holly spirt = infinity – 2
now -1 and -2 are not acurate i’m just elimnating a digit i might as well said infinity -8 same thing
now infinty is not equal to infinaty -1 and not equal to infinty – 2 “think of it as a set”
but in math we all know that infinty -231234 is still infinty so you get the final result
father = infinty
son = infinty
holly spirit = infinaty
infinaty = god
father is god
son is god
holly spirt is god and all are the same god
same infinty 🙂
but they are not equil to each other
hope you reply thanks
ps : sorry for spelling mistakes i’m not that good in english 🙂
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Hi Joel!
As I see it, there’s a theological problem here, and a philosophical one. The theological one is this. According to Chalcedon and the mainstream tradition, the Word (the Son) was “hypostatically united” to a complete human nature, body and soul. On this doctrine, it may be natural to call this complete human nature Jesus, or (more usual) to reserve the name “Jesus” for this new thing with two natures. If one says either thing, then even if the Son has always existed, clearly “Jesus” did not.
However, part of the idea of the Incarnation, one would think, is that the Incarnated Son retains his personal identity through the taking on of flesh – i.e. numerically the same person – Jesus/the Son – was once in heaven, and is now walking around in Galilee healing people.
This raises the strictly philosophical problem of intrinsic change. Given Leibniz’s Law, how can, say, the two year old Joel be numerically identical to the twenty-five year old Joel? (Many things are true of one but not of the other.) Generally, how can anything have different intrinsic properties at different times?
Now there are a number of standard philosophical solutions to this. I believe that the controversial doctrine of “presentism” best solves it, but perhaps anyone should say at least this. We know (from our own case) that intrinsic change happens. Ergo, it is possible – even if we can’t show how. So, I don’t see any particular problem for christology here.
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Hey Dale,
Here is a question I have been wrestling with for 3.5 hours tonight (putting off sleep and study) but have raised in a couple of settings more than once:
Was the Son of God always Jesus? Or to use Johannine language: Was the Word always Jesus?
“In the beginning was the Word. “And the Word became flesh.” Jesus had a birthday way after ‘the beginning’…
Does the identity equation ‘Word (or the Son) = Jesus’ violate Leibniz’s Law?
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Hi Christian,
You raise a number of interesting issues! The three “whatevers” is a real can of worms.
I should probably hold off on them, though. I’ll probably post on Merricks some time. All I’ll say now is that I wasn’t convinced by his paper that we don’t know what a person is.
And you do raise an important question: Why does the NT characterize Jesus and God’s “Son”? That has always proven very offensive to Muslims, for one.
The claim is of course to be taken non-literally. The concept of sonship seems two-sided to me: part of it is functional. Being a full-fledged son means relating in a certain way to one’s parent(s). Another aspect of it is origin. A son is in some sense from his parents. This latter aspect is perhaps the more troubling one when it comes to trinitarian doctrine. Both aspects it seems to me, require that the son not be identical to either parent, as you point out.
D
Dale,
First, I agree. I don’t like this option.
However, it does raise an issue worth exploring in the debate.
The modal objection says the trinitarian cannot make sense out of the claim there is one god, but three distinct persons in a sense in which the claim “there are three persons” is consistent with what we mean by ‘person’.
This is bad because trinitarians seem to think that there are three persons in the trinity. The claim is one they are committed to.
Another objection is the one above. Trinitarians cannot make sense out of the claim that there is one God and yet two distinct “whatevers” such that one whatever sent the other whatever to do something.
I don’t know how committed to this claim a trinitarian is, as opposed to a person who believes claims expressed in the bible or claims associated with the Jesus story.
But the idea is that the claims are different and one claim might be easier to reconcile with the claim that there is one God. But that needs to be shown. Perhaps the claim that Jesus is son of God is harder to make any sense of than the claim that there are three persons in God.
One reason might have to do with the following kind of consideration: we don’t know what it takes to be a person, that’s a real tough question! Trenton merricks has recently written a paper on the trinity that to my mind exploits this fact.
But, we do have a pretty good grasp on the the ‘son of x’ relation and it is one that requires numerically distinct relata to be instantiated. So, the idea is that one can object to the trinity not by talking about the personhood claim, but by talking about some oher claims that attribute, say, asymmetric relation or intransitive relations to its members.
Hi Christian,
I guess I think that this approach is pretty hopeless, on New Testament grounds. Jesus talks about being sent, not about sending himself, or just up and coming on his own. And the one who sent him is the Father, and Jesus in the gospels says and does many things that presuppose or straight up imply that he’s not identical to the Father.
A particularly vivid example is the Garden of Gethsemane, where Jesus basically prays – “I don’t want to do this. Can I not? But if you want me to, I will.” However you make sense of this episode, it’s going to involve attributing a feature to Jesus, or to his Father, which one denies of the other – such as: knowing that God’s will is for Jesus to be crucified. So, on any such reading, it will be false that Jesus just is his Father.
Ole Leibniz’s Law is pretty hard to get around…
Dale
Hi Dale,
Here is a rough sketch of the idea.
First, accept monotheism.
Second, infer from this that Jesus is identical to the Father and the Holy Spirit.
Third, explain away claims that purport to show these claims are false.
There are a variety of ways to do this. One way to do this is to argue that ‘Jesus’ carries with it information like the individual who is the son of God. Suppose one also believes that if x is the son of God then x is not identical to God. From this it follows that ‘Jesus’ carries with it, together with background beliefs, the idea that Jesus is not identical to God.
But since Jesus is identical to God, it follows that either Jesus is the son of Jesus or that Jesus is not the son of God.
One then argues that one of these claims is true despite the fact that both seem false. We then explain away intuitions to the contrary by noting the fact that a false claim, for example, Jesus is the son of God, is associated with ‘Jesus’ and we are lured into thinking that the claim is true.
More generally, the reference of a name can be fixed by a description some of which is false. This happens with ‘Jesus’.
Now, I know the response is “Well, Jesus is the son of Jesus is false.” What is the argument to the contrary?
Suppose one uses the inconsistency of the trinity as such an argument.
The question is then: why is it false that Jesus is the son of Jesus?
Let me just pose that question for now. I’m curious whether the reasons offered in support of this claim will be more reasonable for a theist to believe than the view that the trinity is coherent.
“the details are somewhat obvious”? 😉
I guess I haven’t thought too much about any Christian biting the bullet, and saying all those claims are true.
Is your idea something like this? Suppose you’re OJ Simpson’s daughter, and you hate your mother’s killer, and you think OJ ain’t the real killer. And, let’s suppose, as.. ahem, a few have maintained, that OJ just is the actual killer of Nicole.
So a lot of philosophers would say, that it’s true that his daughter hates her mother’s killer, but it’s false that she hates OJ.
On the other hand, some would argue, that she does in fact hate her father, though she doesn’t presently realize it, and would answer “no” if asked, “Do you hate your father?” I kind of like this answer.
But I guess I’m not really grasping your suggestion. Can you say more about how it would work? I guess I’m not getting how descriptivism about names is supposed to help…
Dale, so you give these examples:
The Father was born of Mary, and was later crucified.
Jesus sent his only Son into the world, to redeem humankind.
There are three persons within the Father.
Jesus is a Trinity.
You point out that trinitarians typically take these claims to be false, thus motivating the need to understand the ‘is’ in the relevant statement of the trinity to express some relation other than identity.
A different attack would be to systematically deny the claims above are false. One approach would be to endorse a descriptivism about names (even if not their semantic values, but at least about some information the names carry) and then to explain away the appearance of falsity to the claims above. In fact, the story would go, the claims are true, but we take them to be false because the names that occur in them carry information about the relationships between the member”s” of the trinity that is false.
For example, in “The Father was born of Mary, and was later crucified” the name ‘The Father’ may be thought to convey the “false” information of “the god that is the father/begettor of Jesus who was the only individual that was both a son of Mary and crucified.” Together with background beliefs like ‘Jesus’ is the name of the son of Mary that was also crucified and if x is the father of y and y is the only son of z, then x is not the only son of z, and…I hope the details are somewhat obvious.
Anyway, I’m not endorsing this position, but it is one that should be objected to. I also suspect that there is room for the common arguments for the failure of substitutivity of co-referring names in opaque contexts that might come into play here in exlpaining away the intuitive data the claims abocve are supposed to provide.
What do you think?
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