Monday, November 22, 2010

The Trinity, Marriage, and Relative Identity

Submitted for your reading pleasure, for Thanksgiving break...

So, let’s go back to two earlier issues that have arisen in this blog. Let’s also do this by way of a common path in addressing the matter of relative identity. Because if it is true that the relation of identity is not absolutely subject to the rule of transitivity, and if it is true that it is possible for objects X and Y to be the same object F but not same object G, then certain matters of Christian and biblical theology just became that easier to grasp.

To establish some context, the reader may recall the following past blog entries:

Monday, April 19, 2010
“Challenge for Trinitarians”

(Cf. Monday, April 26, 2010
“Challenge for Anti-Trinitarians, Part 1”

Monday, May 03, 2010
“Challenge for Anti-Trinitarians, Part 2”

Saturday, October 02, 2010
“About David's Census”

Linked to:
SEP: “Relative Identity¨
First published Mon Apr 22, 2002; substantive revision Mon Nov 5, 2007

Wednesday, October 27, 2010
“A Difficult Teaching”

The two issues in question are: 1) the supposed logical and metaphysical impossibility of the biblical teaching of the divinity and co-distinctiveness of God the Father, the Son, and the Holy Spirit; and 2) the bodies of a man and his wife being one in number. The would-be downfall of the doctrine of the Trinity and of the difficult marital teaching was this: the Rule of Transitivity of the relation of identity.

The Scriptures apparently hold that each of the Father, the Son, and the Holy Spirit (the names of whom we will abbreviate as F, S, H, respectively) is distinct from the other and that each is God, where the noun phrase “God” is a subject complement and not a camouflaged adjective of any sort. What do we know about identity? If an A is C, and if B is C, then A is B. Again, if les États-Unis are the United States and if los Estados Unidos are the United States, then les États-Unis are los Estados Unidos: this is something which is perfectly clear to see. So where we abbreviate the name “God” with “G,” if F is G and if S is G--and don’t lie to yourself--then F is S according to the transitivity rule of identity.

The same problem arises with married couples. Christ said that a man and wife are no longer two but one, and if we are to take the words of Christ at face value or are to take his words literally--as is required in any hermeneutic enterprise until the possibilities that words were meant to be taken literally are exhausted--then we have a problem. For it is clear that when the body of Barack Obama stands behind a teleprompter to give a speech while the bodies of wife and children have every appearance of being located elsewhere on the stage or on the earth, there are two distinct objects involved, even two distinct bodies. Leibniz’s Law of the Indiscernibility of Identicals creates the problem, because if Barry is Michelle and if Barry is behind the teleprompter, then according to the rule it must be that Michelle is behind the teleprompter. However, we will see later that the law is quite possibly defeasible in instances of this sort if we want to hold to the idea that the bodies of a man and his wife are one in number and not two.


So once again, what are some facts of identity or something’s being identical with something else?

(1) A is A.
(In other words, everything is identical with itself.)

(2) If A is identical with B, then every property of A is a property of B, and vice versa.
(In other words, if A and B are the same thing, then whatever is true of A is true of B, and vice versa; likewise, whatever quality A possesses is also possessed by B, and vice versa.)

(3) (Except where subject to qualification) The relation of identity is transitive. If A is C, and if B is C, then A is B.
(In other words, if Jesus’ Father is God, and if Jesus is God, then apparently Jesus is Jesus’s Father.)

(1) is the Law of Identity and its validity is incontrovertible. (2) is pretty much Leibniz’s Law of the Indiscernibility of Identicals and it supports (3). (3) is the rule of transitivity which is thought to bind or govern the identity relation.

The validity of the transitivity rule is to be granted. For starters, remember that language is a matter of the signifier and the signified. With that said, consider the statement “A is B.” If the name “A” refers only and precisely to an object φ and if the name “B” refers only and precisely to an object φ, then there just is only one denotation of the two names: φ. In other words, A necessarily is B and B necessarily is A since A and B are I-related (i.e., identity-related) in that there is precisely, only, and commonly one object which they denote.

Because the transitivity rule of identity is to be granted, guess what you get with the following sentences:

(4) The Father is God.
(5) The Son is God.
(6) The Spirit is God.

Or if any trinitarian will not admit that there is trouble for trinitarianism here, let’s reduce those sentences to symbolic logic, with the attendant reminder, for example, that the Bible apparently affirms not merely that Jesus and the Spirit of Jesus are equal with God but identical, as in John 1.4 or Acts 5.3-4:

(4') F = G
(5') S = G
(6') H = G

On the transitivity rule, F = S = H, which clearly is not orthodox.


In philosophy it is often useful to examine language and the ways in which we speak of different matters of ontology, mereology, epistemology, and so forth. In fact, it is useful to think of the identity relation as being a linguistic or semiotic relation, but only up to a certain point. The foregoing account of trinitarian doctrine and the transitivity of identity is a semiotic one, and there are shortcomings in a mere semiotic account of identity.

[DB, Semiotics contrasts with semantics in being the study of the words and such that convey meanings or connotations. ;) ]

Number one, how does a mere semiotic account explain the Law of Identity? After all, when we stop to contemplate the Law of Identity and affirm it we are not asserting that a name, N, refers to what it refers to. To the contrary, it is clear that in those instances what we have in mind is that an object, φ, is φ--our concern is one of raw metaphysics and not language.

Number two, suppose you point at two physical objects (such as two coffee mugs) resting on your desktop and assert that one is the other. Regardless of whether your assertion is veridical or jibes with reality, it is clear that your concern in this case is not a semiotic one and also that you are not employing any novel or unconventional concept of identity in the process.

Number three, a mere semiotic account of identity reduces the Father, Jesus, and the Holy Spirit to mere names of a common object, something which is hardly supported by the entirety of the Scriptures.

Having considered these problems, what would it mean to point to a physical object with your right hand and to assert that it is another physical object that you point out with your left hand? Transitivity could not begin to apply to the two physical objects, as it were, or to any additional and third object if the assertion were true. This is because Leibniz’s law, which is metaphysical and concerned with the properties of objects, still holds true such that you have no diversity or plurality of objects to which transitivity could apply.

What all of this means is that the transitivity rule of identity apparently holds in language and symbolic logic, but not beyond language and symbolic logic. In terms of the realities of raw metaphysics or ontology, which are the foundation of language in the first place, the rule binds nothing.


So the transitivity rule of identity apparently cannot rightly be used to deny the doctrines of the Trinity. It remains entirely possible that F = G and S = G while F ≠ S. Of course, if one affirms that F = G and S = G while F ≠ S then he affirms the idea of relative identity, according to which X and Y can be the same φ though not the same ψ. Someone might invoke Occam’s razor to claim that the Scriptures themselves are proof that relative identity exists, at least in the case of the Father, Son and the Holy Spirit. Apart from that, strong proofs of the existence of relative identity seem rather elusive. However, a tentative case can be made with the paradox of constitution.

Take a piece of clay that has no remarkable or special shape or form. Now take that entire quantity of clay and fashion it such that the piece of clay that now has a shape exactly like that of a man, with various constituent atoms or matter in various locations relative to one another: the piece of clay is now a statue. Now take a mallet and smash the statue. By doing so, you will have destroyed the statue, but it bears noting that at the same time you have not destroyed the piece of clay.

The piece of clay is the piece of clay. The statue is the piece of clay. The piece of clay is the statue. The statue is an object, O, which the piece of clay is not. Stated in another way:

C = C
S = C
S = O
C ≠ O


F = G
S = G
H = G
F = O1 (“O1” meaning an object which S and H are not)
S = O2
H = O3
F ≠ S; S ≠ H; F ≠ H

Notice that the thought experiment of the piece of clay is carefully worded. The piece of clay does not merely take the form of a man or of a statue. To the contrary, in virtue of the piece of clay’s having a shape exactly like that of a man it just is a statue. Meanwhile, it is clear that a statue is destroyed when it is smashed with a mallet. At the same time, it bears noting that in the thought experiment the piece of clay begins as an object which has no remarkable or special shape or form and persists even after it obtains a special shape. Therefore, the piece of clay is not destroyed by any stroke of a mallet, though the statue is. Consequently, it seems difficult to conceive that the thought experiment or its conclusions suffer from some sort of language defect or some sort of “vague” or “misleading” use of vernacular speech. No, the vernacular means of speaking of destruction and constitution seems quite straightforward in this instance, and so there seems to be at least one intuitive example of relative identity.

So with a dismissal of the transitivity rule of identity in matters of metaphysics or ontology, we discovered what we already knew to begin with: that it is entirely possible that each of F, S, H is G while F, S, H are distinct from each other. With the would-be paradox of constitution, we see again that it is entirely possible that each of F, S, H is G while F, S, H are distinct from each other. Of course, no one believes that either F, S, or H is a physical or mental construct of any sort, yet the paradox only bolsters and supports the re-evaluation of the transitivity rule.

Now let’s see what happens if we try to account for trinitarian proof texts by means of the concept of relative identity. In the ontological realm, when two objects are I-related--and let’s stop right there, because there can be no naïve relation of identity between two distinct objects in extra-linguistic world; instead, identity by definition means having only one object in question though it may carry two different names. Then again, in the ontological realm when objects are R-related (i.e., when the relation of relative identity obtains between the objects) A and B will be the same X, but not the same Y. Again, A and B will be the same X, but not the same Y.

A and B will be identical with some common object (this object perhaps being either A, or B, or some third object), though at the same time there is at least one object A is though B is not or at least one object B is though A is not. In the case of the piece of clay, the piece of clay was the statue and vice versa, though apparently the statue was something which the piece of clay was not, for one object was destroyed while the other was not destroyed. Therefore, the piece of clay and the statue are R-related to each other while there is yet a third object somewhere in the picture, regardless of whether or not it is readily discernible. In the case of F, S, and H, it is likewise the case that certain objects (e.g., S and G) apparently are identical while there is a third object which one of the two is while the other is not (cf. the doctrines that G is F though F is not S).

So, relative identity is possible, and it appears to support the propositions that each of God the Father, the Son and the Holy Spirit is the one god that exists while each is also distinct from each other.


If a piece of clay and a statue are R-related in the paradox of constitution, then it follows that such may well be the case with human beings. Consider a human body for example. It seems entirely fair (though every matter of philosophy is doomed to remain forever controversial to some degree) to say reductionistically that a zygote is a particular amount or body of matter, regardless of its being a vessel of a soul or spirit. This zygote, or rather this body of matter, will undergo radical changes in its career. If all goes normally, the body of matter will increase in size over the course of nine months and its shape will undergo radical changes of shape, but the body of matter persists nonetheless as opposed to ceasing to exist upon any would-be change that it undergoes.

Now suppose the worst and that this body of matter perishes at an age of ten months and is later incinerated. The human being is destroyed in the process, but that particular amount or body of matter is not. Come rain or shine or fire or any other condition, all the constituent atoms of that body of matter persist, even if their locations relative to one another become as counterintuitive or as strange as the relative locations of the United States or the minuscule letter “i,” which both consist of disparate parts. What follows from our thought experiment is that the body of each of us is never alone; instead, it may well be that we have two of them even if one of them is not readily discernible.

With that said, let’s revisit some texts that we earlier looked at. It is written:

1 And he arose from thence, and cometh into the coasts of Judaea by the farther side of Jordan: and the people resort unto him again; and, as he was wont, he taught them again. 2 And the Pharisees came to him, and asked him, Is it lawful for a man to put away [his] wife? tempting him. 3 And he answered and said unto them, What did Moses command you? 4 And they said, Moses suffered to write a bill of divorcement, and to put [her] away. 5 And Jesus answered and said unto them, For the hardness of your heart he wrote you this precept. 6 But from the beginning of the creation God made them male and female. 7 For this cause shall a man leave his father and mother, and cleave to his wife; 8 And they twain shall be one flesh: so then they are no more twain, but one flesh. 9 What therefore God hath joined together, let not man put asunder. 10 And in the house his disciples asked him again of the same [matter]. 11 And he saith unto them, Whosoever shall put away his wife, and marry another, committeth adultery against her. 12 And if a woman shall put away her husband, and be married to another, she committeth adultery. (Mark 10.1-12)


3 The Pharisees also came unto him, tempting him, and saying unto him, Is it lawful for a man to put away his wife for every cause? 4 And he answered and said unto them, Have ye not read, that he which made [them] at the beginning made them male and female, 5 And said, For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh? 6 Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder. 7 They say unto him, Why did Moses then command to give a writing of divorcement, and to put her away? 8 He saith unto them, Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so. 9 And I say unto you, Whosoever shall put away his wife, except [it be] for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery. 10 His disciples say unto him, If the case of the man be so with [his] wife, it is not good to marry. 11 But he said unto them, All [men] cannot receive this saying, save [they] to whom it is given. 12 For there are some eunuchs, which were so born from [their] mother's womb: and there are some eunuchs, which were made eunuchs of men: and there be eunuchs, which have made themselves eunuchs for the kingdom of heaven's sake. He that is able to receive [it], let him receive [it]. (Matthew 19.3-12)

So Matthew 19 and Mark 10 speak of acts of remarriage which constitute acts of adultery. The texts also raise the following question: How does remarriage constitute adultery since the divorced person presumably is no longer married? For the time being, let’s try to answer this question with the naïve set of assumptions which most of us have concerning the texts: that the identity relation is always transitive and that the word “one,” as used in the texts above of a man and his wife, is merely figurative in meaning.

On the naïve view, remarriage or acts resulting from remarriage can be adultery only in virtue of the following: either a divinely irrevocable married status or a divinely irrevocable oneness of married couples. The former disjunct seems not to be an option, since it seems as though people who divorce do end their marriages and are unmarried right after they obtain a divorce. John 4.1-18 also seem to support this assessment (just as it is entirely unlikely that the Samaritan’s five former husbands were all dead at that time).

So marriages apparently end even when neither a husband nor a wife dies, and that means that adultery in this case must be a violation of oneness of an earlier marriage, which is a problem. It is a problem because the naïve view treats the word “one” in this case as being figurative in meaning: it ends up meaning close instead of one. Yet people who divorce each other clearly are no longer close in the sense of the Mt 19 and Mk 10 passages; they are neither physically nor emotionally nor sociologically close in whatever sense could exist in these passages. So the naïve view on the one hand must treat the adultery problem as a violation of erstwhile oneness while on the other hand it cannot possibly affirm that such oneness is possible. Therefore, the naïve view must be incorrect and cannot account for all the details of Mt 19.3-12 and Mk 10.1-12.

However, you get a solution to the problem if you assume that some particular relation of relative identity exists between married couples. The piece of clay and the statue overlapped in space and time, and perhaps two bodies for every human person also overlap in space and time. When someone marries, one of those two bodies ceases to be distinct in quality or in number from a body of another person who has just experienced an analogous change of being. In the case of the piece of clay and the statue, there turned out to be a third object which one object was while the other was not and which was meanwhile more or less indiscernable. In the case of married couples, some more or less indiscernable objects are those which become one in number while the two distinct bodies which we all see with our own two eyes are analogous to the piece of clay and the statue which we likewise see with our own two eyes. Consequently, it would have to be the case that the kind of people that Christ speaks of in Mt 19.3-12 and Mk 10.1-12 is not that which we see with our own eyes but rather the “hidden” physical bodies; otherwise, the appeal to relative identity is thus far ineffective.

So there it is: a bunch of things to consider, along with possible implications of 1 Corinthians 6.15-17. Food for thought and grounds for further research, to borrow from Emory.

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