Is the Trinity Logically Impossible?



One of the various disagreements I had with IM Skeptical regarding my recent post, "Should Philosophy of Religion Be Ended?", concerned whether there are possible worlds in which the laws of logic do not hold. I maintain that the laws of logic must hold at every possible world if the very concept of "possible worlds" is to have any meaning whatsoever. Once it is permitted that the rules of logic are not themselves necessary truths, we are left with no means to distinguish possible truths from necessary truths, let alone possible worlds from impossible worlds (e.g., worlds that both exist and do not exist at the same time). Skeptical, in order to refute arguments for God from logic – like the "Lord of Non-Contradiction" paper by Anderson and Welty – to the contrary contends that there may be possible worlds in which rules of logic do not in fact hold.
 
Skeptical then suggested that despite their appeals to logic theists make special exceptions for theism, and asked me this: "Do you believe that the doctrine of the trinity is true? If you do, then how does that square with the rules of classical logic?" Now I believe that question is worthy of a considered reply. For clarity's sake my own reply to the first part of the question is simply "Yes" But of course what skeptics are more interested in is the second part: why Christians like me believe in the Trinity, especially when we claim to place such a high premium on the validity of logic in understanding God and the world he created.
 
Theologians have written volumes on the Trinity as a church dogma, as a description of divine ontology drawn from biblical statements, and as a model of divinity that lends itself to the activity of securing human redemption. Apologists, however, are the most interested in whether or not the Trinity is actually, or least potentially, coherent. That issue in turn concerns the logical relations among Father, Son and Spirit. According to Wayne Grudem, the set of propositions underlying the doctrine of the Trinity can be stated succinctly as
 
1. God is three persons [hypostases].
2. Each person is fully God.
3. There is one God. 
 
…the problem being that these appear inconsistent. However, there are no explicit contradictions here. Additional premises would be required to create an explicit contradiction, such as
 
4. God is not three persons.  – or –
5. Each person is less than fully God.  – or –
6. There are many Gods (gods). Etc.
 
Now I have already mentioned Plantinga's free will defense in the context of my ongoing discussion with Skeptical, but I believe it bears mentioning again. The free will defense appears analogous to a defense of the Trinity, in that the one who argues that the problem of evil renders God's existence impossible, like the one who charges that the Trinity is illogical, bears the burden of proving that the initial set in question is formally inconsistent and not merely counterintuitive. 
 
Clearly it would be logically problematic to say that the one God is actually three separate beings. After all, that seems to be directly translatable to 1 = 3, which is contradictory (in that something, God, is said to be both one and not-one at the same time). At issue, though, is whether the relations among the members of the godhead are absolute reflexive identity relations. To put it another way, we need to ask ourselves: what exactly does it mean to say "God is Father, Son and Spirit," and to also say, "Father, Son, and Spirit are God"? If it's right to say that God is strictly equal to – nothing more and nothing less – all three members of the godhead, and vice-versa, then we are saying that one equals three and effectively speaking nonsense. But I don't think it's necessarily true that the relations among the members of the godhead are absolute reflexive identity relations.
 
Some theologians, for example, have suggested these are "relative identities," wherein identity relations are still logically valid but in terms other than shared properties. Deutsch comments in the Stanford Encyclopedia: "It is possible for objects x and y to be the same F and yet not the same G, (where F and G are predicates representing kinds of things (apples, ships, passengers) rather than merely properties of things (colors, shapes)). In such a case ‘same’ cannot mean absolute identity. For example, the same person might be two different passengers, since one person may be counted twice as a passenger." Now this "passenger" analogy, like most other analogies, does not apply all that well to the Trinity, but for present purposes the fact that relative identities are possible is enough to undercut the argument that the Trinity is explicitly illogical. 
 
While analogies proposed for the Trinity are typically imperfect (as analogies are generally), they do often serve to underscore that the Trinity is a mystery in need of an explanation rather than an example of explicit illogic. It should not surprise anyone that there are few, if any, applicable worldly analogies for a spiritual reality. And skeptics, at least those familiar with scientific theories, should know that on naturalism, nature houses numerous mysteries of its own: How an entropic universe can come into existence unaided; how quantum mechanics can be reconciled with general relativity; how chemical evolution can take place apart from replicators that only operate within living systems. Etc. Meanwhile there are some serious Trinitarian models that purport to provide solutions – or at least potential solutions – beyond merely pointing out that the Trinity is not formally contradictory. Those will have to be addressed by someone else, or at least at some other time.
 
 

Comments

BK said…
Very well done, Don. I tend to believe that most people who reject the Trinity do so because they have bought into the 1=3 argument without really stopping to consider that 1=3 is not what Christians are saying. The remainder of the people who reject the Trinity as "logically inconsistent" have heard the arguments that Christians use to show that it is not logically inconsistent or impossible, but reject them because they really don't want to listen to the Christian explanation (especially because it may be true and therefore make sense of the Trinity).

As far as the analogy, I always refer people to the blogpost that I wrote a few years ago entitled "A Simple Illustration of the Trinity" that provides two illustrations that actually meet the Biblical definition of the Trinity of being three yet one. Of course, as you point out, it isn't a perfect analogy (that would be an identity), but it does illustrate quite clearly how the concept is not logically impossible or inconsistent.
Joe Hinman said…
The allegation of being illogical based upon the numbers, 3 in 1 iw dispelled by understanding Platonic notion of essence, i';ts not three perons in one person it's three identities persona) in one essence,
Joe Hinman said…
btw great article Don good going!
Don McIntosh said…
Thanks for the comments fellas!

I haven't studied theology proper in a long time but felt challenged by Skeptical to explore the Trinity again. I was happy to get back into it, though, because it's not just a fascinating topic, but spiritually edifying.
Jason Pratt said…
I'm okay with people rejecting the Trinity if they think the idea is illogical -- I think they're wrong about it being illogical, but in principle they're doing the right thing. Accepting something as true that they think is illogical can only result in bad habits at best, and maybe in disaster later. And after all, historically there has been a lot of attempts at shielding trinitarian doctrine from critique by snorfing at "human reasoning" and "human reason"; in recent years I had one fellow apologist (not on this site) declare me a heretic specifically because I was using my "human reason" to defend the Trinity as reasonable which he declared to be impossible (and, as noted, even heretical).

Well yeah, that kind of thing would (and I think should) set off any careful person's bull$#1^ meter! -- just as much as a sceptic trying to avoid logical conclusions in favor of religious faith by appealing to imaginary realities where logic simply might be void! In my experience, dedicated anti-theists pull this once the implications of human reason itself start to point toward theism instead of atheism being true. A related move is to try to utterly denigrate human reason to the point of non-existence, although of course they themselves don't want to be treated as equivalent to spambots, furbees, or other illusions of conscious will. But then I've seen theists (including Christians) go that route, too, when implications of free will and/or logic go against what they currently prefer to believe.

Matters can get pretty embarrassing and crazy on any side. {g}

Anyway. The largest book I've ever posted to the Cadre (over 850 pages) was on a systematic logical progression to trinitarian theism (and thence to an expectation of historical Christianity). And the second largest section of chapters is the first section, on how I should be a logical sceptic (but not a sceptic about logic in principle!) http://christiancadre.blogspot.com/2010/10/jrps-sword-to-heart-contents-page.html

JRP
BK said…
Jason, that's an interesting comment. Are you saying that a person can be a Christian and not believe in the Trinity, or are you saying that you prefer to work with a skeptic who honestly believes the Trinity to be illogical (even though it isn't) than a Christian who won't permit attempts to understand the Trinity, or what? Not sure I understand where you were attempting to go.
im-skeptical said…
It is clear that there is no agreement among Christians about whether the Trinity doctrine makes logical sense. The catechism of the Catholic calls it a "mystery" without providing a cogent logical explanation.

I think BK's treaty analogy doesn't work, and here's why: There is one treaty. It is an agreement between nations. The treaty may be expressed in many different ways (spoken, written, digitized, in any number of languages), and each of those is a physical representation of the treaty itself, which is still an agreement. The physical expression, regardless of its form, still has the same content and the same meaning. It is a representation of the agreement. While it might be correct to say that a particular piece of paper is not identical to another piece of paper on which the treaty is written, it would not be correct to say that the agreement is different, just because it is expressed or represented in a different way.

Yet the trinity doesn't appear to be like that. The Trinity doctrine holds that the three persons are substantively different. They are not merely expressed in a different way - they are actually different things (while still being the same thing - namely, God).
Joe Hinman said…
t is clear that there is no agreement among Christians about whether the Trinity doctrine makes logical sense. The catechism of the Catholic calls it a "mystery" without providing a cogent logical explanation.

Know why that is a silly opinion? Because the guys that say t can be understood are also Catholic or basing it on Catholics. They are the same guys as those who say it is a mystery.Because it's a mystery in other ways than the one's that can be explained. Some aspects of it are explained and some are mysterious.

I think BK's treaty analogy doesn't work, and here's why: There is one treaty. It is an agreement between nations. The treaty may be expressed in many different ways (spoken, written, digitized, in any number of languages), and each of those is a physical representation of the treaty itself, which is still an agreement. The physical expression, regardless of its form, still has the same content and the same meaning. It is a representation of the agreement. While it might be correct to say that a particular piece of paper is not identical to another piece of paper on which the treaty is written, it would not be correct to say that the agreement is different, just because it is expressed or represented in a different way.

Yet the trinity doesn't appear to be like that. The Trinity doctrine holds that the three persons are substantively different. They are not merely expressed in a different way - they are actually different things (while still being the same thing - namely, God).

they share one essence that what unifies them as one, Essence is that which makes a thing what it isl So sharing one essence means they are the same thing, but they don't share tyhe same persona.
I
I do not speak for Bill.I respect his intelligence he can answer for himself and I really don't know how he sees it. I know some don't like dealing with Platonic essence for waht ever reason but that's what the doctrine is based upon.


1/12/2017 12:42:00 PM Delete
im-skeptical said…
they share one essence that what unifies them as one

Yes. That's what I said. It is one treaty.
Joe Hinman said…
you got it half right, that's not a proof that one essence cam't be shared by three identities.
Jason Pratt said…
BK: {{Jason, that's an interesting comment. Are you saying that a person can be a Christian and not believe in the Trinity...}}

Not sure I said that, but since you bring it up, yes. I'd _rather_ they were trinitarian, because I think that's both true and importantly true, but I'm not going to spit on someone who is trusting Jesus Christ as Lord of their lives, much moreso trusting Jesus as the authority to save them from their sins. Moreover, if Jesus says some people are faithful members of His flock and servants of His, whom He accepts and rewards as such, even though they're surprised to learn they've been serving Him at all, _I'm_ not going to complain! (My business is to make sure I'm not one of the baby goats He's sending to the eonian fire prepared for the devil and his angels!) This is probably worth a detailed post in itself.

{{...or are you saying that you prefer to work with a skeptic who honestly believes the Trinity to be illogical (even though it isn't) than a Christian who won't permit attempts to understand the Trinity...}}

If I _had_ to choose between one or the other, I'd choose the former. I can work with both, but obviously there are some large difficulties either way. (The latter is a main stumbling block for me ever joining the Eastern Orthodox communion, for example -- although a Calvinist apologist whose ministry I support was who I had in mind. Obviously I think he still does good work in other regards, but srsly?? {smh})

JRP
Jason Pratt said…
Skep: {{The Trinity doctrine holds that the three persons are substantively different.}}

Nope, personally distinct, but same unique substance: the one and only self-existent reality upon which all reality depends for existence. Not different things (one Person being this and other Persons being creatures for example); and not different instances of the same thing (three independently existent facts, much less three IFs grounding all reality).

I know it's a complicated and difficult doctrinal set, but getting the details right is important if you're going to critique it. Critique unitarian Christologies (where the 2nd Person is a super-angel or a human hero, and the Spirit either also is a super-angel or is only a mode of one of the other persons fully divine or otherwise), or critique Tri-theism (three distinct Gods Most High), as much as you like, but we aren't either of those. Even if you decide we don't even make as much sense as they do (proponents of those positions would themselves agree with that {wry g}), it's still worth aiming at the intended target.

JRP
im-skeptical said…
you got it half right, that's not a proof that one essence cam't be shared by three identities.

OK, Joe. Try to understand this. If I write the treaty on a new piece of paper (in Greek), does that become a fourth "identity"? Has it become a Quaternity? No. It's just paper with the treaty written on it. The paper is not the treaty. The treaty is still the treaty, and it hasn't changed, no matter how many times I write it down, or even if I destroy all the paper copies of it. It is an agreement between nations.
im-skeptical said…
Jason,

getting the details right is important if you're going to critique it

The question at hand is How do we make logical sense of this doctrine? Do all Christians agree about it? No, they don't. And that's precisely because it is not logically possible to interpret the doctrine in a coherent way. Look at the picture at the top of the post. You see "est" and "non est" linking all the elements. It would not be unreasonable for someone to think that the outer elements are different in some substantial way, if they are related by "non est". To say that they are three different persons is a confirmation of that. But at the same time, they are all the same thing.

You can try to rationalize it in your own mind, but there is no guarantee that other reasonable Christians will agree with you. So how exactly do we get the details right?
Joe Hinman said…
OK, Joe. Try to understand this. If I write the treaty on a new piece of paper (in Greek), does that become a fourth "identity"? Has it become a Quaternity? No. It's just paper with the treaty written on it. The paper is not the treaty. The treaty is still the treaty, and it hasn't changed, no matter how many times I write it down, or even if I destroy all the paper copies of it. It is an agreement between nations.

do you have any idea what the hell you are talking about? no you do not. identity is not an essence, Identities can share in essence with one another. the original word, persona, meant the masks worn by an actor. But has to do with the need to reflect the Hebrew concept through Greek terms, There was a Hebrew idea thyat was barrowed, That is more complex
Joe Hinman said…
Se my Trinity pages especially the one;s on Hebrew

Trinity pages
Joe Hinman said…
The importance of my answer for your argument Skep is that it points up the confussion of your argument. You think the trinity the Trinity is derived from a logical deduction based upon the need to inconsiderate three different entities into one; ny point is the concept aroizes from revelation given though the prophets and that revelation was voiced in Hebrew form, The gentile church didn't' understand it,forgot it,and tried to translate it into Greek concepts. I(t's not just derived from seeming logic,
BK said…
Just a quick reaction to im-skeptical's reaction to my illustration. He said, "There is one treaty. It is an agreement between nations. The treaty may be expressed in many different ways (spoken, written, digitized, in any number of languages), and each of those is a physical representation of the treaty itself, which is still an agreement. The physical expression, regardless of its form, still has the same content and the same meaning. It is a representation of the agreement."

Actually, that's not accurate. He is right that a treaty is an agreement between nations, but legally speaking, once the treaty is put into written form the writing becomes the treaty. You cannot go behind the treaty and say, "Here's what we agreed to...." because the treaty replaces all prior negotiations and parol agreements. So, the treaty is not merely the physical expression of the agreement -- it becomes the treaty itself. So, when you have three treaties in three different languages, they are all different treaties, but still one treaty. So, im-skeptical's criticism fails.
Joe Hinman said…
I'm sure you are right about treaties BK but theological doctrines are not treaties.
im-skeptical said…
once the treaty is put into written form the writing becomes the treaty

To illustrate how this is wrong, let me go back to your original example, where the treaty is written in three different languages. Let's say the translation was faulty, and nobody recognized the problem before they were signed. Now we have three papers that don't all agree with one another. What should we think of that? Does it mean that all three versions are the official treaty? And if so, what have the nations agreed to? There are different ideas expressed on paper, but clearly, the nations involved didn't agree to three different things. When the mistake is recognized, the proper course of action would be to correct the mistakes so that the words on the paper conform to the idea that was agreed upon. It's that agreement that is that essence of the treaty, as Joe puts it.
BK said…
Joe, theological issues are not mustard seeds either, but it can be used to make a point by analogy.
BK said…
im-skeptical, you are arguing against International Law. Of course the parties can go back and try to amend the treaties so that they more closely match what the parties intended, but until they do so the writing(s) (however, flawed and however inconsistent in the multiple translations) is the treaty. I am not sure why you are arguing about this. I have simply shown something that is one thing but also three things using a well-settled principle of International Law. I am not arguing for the wisdom of the system.
im-skeptical said…
BK,

I am certainly not arguing against international law. I understand that a treaty or a contract, as written on paper and duly signed, is legally enforceable. The paper holds a record of the agreement, and the signatures are proof that the parties assent to making the agreement legally binding. The paper is merely a medium that holds that record. What is enforceable is the agreement that is recorded on the paper. I don't think this is so hard to understand.
Joe Hinman said…
BK said...
Joe, theological issues are not mustard seeds either, but it can be used to make a point by analogy.

;-)
im-skeptical said…
Joe, theological issues are not mustard seeds either, but it can be used to make a point by analogy.

It's interesting that you make this comment. If something is described in words written on paper, those words are a representation of that thing. They are not the thing itself. If what you claim is true, then I can write down a description of my dog, and then the piece of paper with those words on it would become my dog. And if I made another written description like that, I'd have a Trinity. There would be three things, all sharing the same "essence", as Joe says.

But one of them is different from the others. One of them is the actual thing, and the others are only representations of the real thing.

A legal document is the same thing. It is a description of an agreement. It has to be written down, because without the document, there would be no proof of what that agreement was. Nevertheless, the document is not the agreement - it is a description of the agreement.

Now, using this as an analogy for the Trinity only serves to illustrate the opposite point from what you intended (at least to people who have a modicum of logical sense). The three things are not one and the same, despite your ill-conceived efforts to make something illogical appear to be meaningful. What you have done is to show how absurd it is.
im-skeptical said…
I know. Trying to get a Christian to acknowledge things like logic and common sense is like talking to a brick wall. Yawn.

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