The Trinitarian Doctrine

My series of posts related to paradox have been using the trinity as an example of a paradox. So this is a good point to clarify what this doctrine is. It is also a good point to distinguish between two different sets of claims regarding the trinity. One set of claims is the actual propositions that make up the trinitarian doctrine. The other set is those claims that enable us to both recognize trinitarian doctrine and indirectly believe it.

One first starts with what trinitarians actually believe about the doctrine of the trinity. First off, all trinitarians are monotheists. They all believe in exactly one God. Therefore they deny any form of polytheism. Second, all trinitarians believe that the historical person of Jesus is God, and that he is God is the same sense that the Holy Spirit and the Father are God. This means that all three are equally God. Therefore they deny any diminishing of the divine status of Jesus or the Holy Spirit. Third, all trinitarians believe that the Father, Son and Holy Spirit are distinct. Each one has a property that the other does not have, and each one is a person. (Both terms were defined by the trinitarian controversies.) These three points define the center of trinitarian doctrine. (I am ignoring the doctrine of procession because some trinitarians reject it.)

Any doctrine of the trinity will be a set of propositions that is the truth-maker of the above positions while not entailing any contradiction. Yet the three points above are not the actual doctrine of the trinity. Consider the Father, Jesus and God. According to the first point, there is one God. According to the second point, the Father and Jesus are both equally God. According to the final point, the Father and Jesus are distinct and have different properties. So the simplest reading of these points generates a contradiction. That means that the three points are not first-order propositions. They must be second-order propositions about unmentioned first-order propositions instead. One does not discuss the meaning of propositions, only whether they are true or false. One discusses the meaning of sentences.

So what are those three points? They are the way to recognize the actual doctrine of the trinity. Since these three points are true of the trinitarian doctrine, they are necessary to recognize that doctrine. Any doctrine these points are true of would be trinitarian, so these points are also sufficient. Therefore, these points are both sufficient and required to recognize trinitarian doctrine and to believe it indirectly.

Sentences and Propositions

At this point, clarity on the nature of both sentences and propositions is required. One cannot speak with clarity on matters of belief (direct or otherwise) while the concepts used to explain it are vague!

The first thing to become aware of is the nature of signs. I am using this word generally to refer to any mark, image, sound or other feature perceived through the senses that represents something. So traffic lights, pictures and words are all signs. Morse code, binary digits, bumps on a CD, and smoke signals are also signs. Signs may represent another sensory feature. This occurs in the case of pictures and recordings of various kinds. Signs may also represent a command: street signs and lights. They may also represent ideas. It is these last kind of signs that we are interested in, for they are the ones that are also known as sentences.

Sentences may be in any language, may be in any medium, and may be written, spoken, demonstrated (sign language) and so on. The unifying feature of sentences is that they express thoughts or ideas. But not every idea is one that can be either true or false. Some sentences are questions, others are commands and still others are declarative sentences. Those sentences that can meaningfully be called either true or false are the bearers of propositions.

A propositions is any thought that can meaningfully be called either true or false. Many sentences may express the same proposition. For example "Snow is white" and "La neige est blanche" (French) both express the proposition that snow is white.

These points apply to belief in a very simple way. One believes propositions, and only propositions. One cannot believe sentences, nor can one believe signs in general. These is because the object of belief is a thought, and belief comes down to whether the thought is thought to be either true or false.

Appearing to Contradict?

In a previous post, I have made use of the idea that some propositions appear to contradict one another. In another post I implied that any appearance of contradiction is identical to an actual contradiction. These two ideas can be explained by explaining what an apparent contradiction is and how it is different from an actual contradiction.

An actual contradiction is simple. A and not-A is a contradiction. Any set of propositions that generate that are also contradictory. So is any set of propositions conjoined with a logically necessary truth, or a conceptually necessary truth. For example, the propositions this square is red all over and this square is green all over form a contradictory set because it is a conceptually necessary truth that no square can be red all and green all over at the same time.

An apparent contradiction cannot be any set of first-order propositions. Any such set would either be contradictory, or it would be consistent. The appearance of contradiction in such a set would be the same as the reality.

Because of this, an apparent contradiction must contain second-order propositions. Not only this, but at least some of them must be about which proposition a certain sentence expresses. Let's consider the example of the doctrine of the Trinity. Any such doctrine states the sentence that "God is one". It also states that "God is three". Any first analysis of these sentences takes them to be stating the propositions God is one unit and God is three units. These propositions form a contradictory set along with the logically necessary truth if something is one unit then it is not three units. So if the doctrine of the Trinity is not a contradiction, then those sentences cannot express the propositions that they appear at first to express. Yet this is a second-order proposition about what propositions are actually expressed by a sentence! In fact, any Trinitarian believer believes that the "is" of the first sentence, and the "is" of the second are not the same relation. This does not tell us what the Trinitarian doctrine is, but what it is not. It is also the second-order proposition used in order to avoid having two sentences express contradictory propositions.

An apparent contradiction is not a contradiction at all. It is a set of sentences that appear to express a set of contradictory propositions, but are believed to express a different set of propositions instead. Without the second-order belief, one would be believing in a contradiction.

On Contradictions, Direct Belief and Tillian Paradoxes

In my previous post I laid out a brief case that Tillian paradoxes cannot be believed directly. In the midst of that argument, I made the assertion that one cannot directly believe a contradiction. Although true as a simple summary, there are some distinctions that need to be made. Under some circumstances it is possible to directly believe a contradiction, and under others it is not. The key difference is immediate awareness of the conflicting propositions.

Let's imagine a situation in which a person believes these four propositions: my computer was not operating at noon, there are only two computers in the house, a computer was in use at noon in the house and the other computer was not at use at noon. The conjunction of these four propositions generates a contradiction. Since these are all propositions, this is a case of direct belief. So all that remains is to imagine a situation in which someone would have all of these beliefs at the same time. Let's suppose that I know that my computer is off and the other computer is only used by others while they are there. I know that there are only two computers in the house because that is all that I see, and I know that the others in the house were away at noon. I later receive an e-mail that indicates that it was sent from an address used by the others in the house. As I think about it, I realize that it could not have been sent unless someone was at home. But until I think about it, I am directly believing a set of contradictory propositions.

Now try to imagine believing a simple contradiction of any kind, such as the sky is blue and the sky is not blue. I can't. I imagine something else: some of the sky is blue and some is not, or the sky is blue at one time and not at another, or I first believe one and then the other. None of these count as believing a simple contradiction. Neither can one believe a set of contradictory propositions while being immediate aware of all of them. Consider the previous example. Once I became aware that the e-mail was sent and focus my awareness on this fact, I believe that someone was home using the other computer. Focusing my awareness on that proposition leads to the belief that the other computer was in use at noon. Yet that is the contradictory of the belief I previously held!

These examples show that immediate awareness is sufficient to dispel any direct belief in contradictory propositions. They also show that lacking such awareness allows for the possibility of such beliefs existing directly. So precision requires that I restate my earlier point on Tillian paradoxes. They cannot be believed directly while bringing such propositions into the immediate awareness. One can believe them directly without doing so.

Believing in the Trinity vs. 'Paradoxing' the Trinity

Is a paradoxical doctrine of the trinity compatible with believing that same doctrine? The answer to that question is the same as the answer to paradox in general. It depends on what one means by paradox.

First off, there are two different ways that one can believe a doctrine. One way is to believe in it directly, by believing a proposition or series of propositions that express that doctrine. Another is to believe indirectly. This way of believing does so not by believing a proposition, but a person or group of people. We believe that the doctrine of the trinity, that those people believe, is true. We trust that these people believe some set of propositions or believe some others who do.

Secondly, there are at least three different senses of the word paradox. One sense is that of contradiction. I am going to ignore that one because it is not compatible with belief in the trinity. The other two senses are different ways of understanding merely apparent contradiction. In one sense, there can be no demonstration that the set of propositions that appear to contradict do not actually contradict one another. In practice, this position is the same as the one I rejected. I am calling this kind of paradox the Tillian paradox. In the other sense, there can be a demonstration that the set of propositions do not contradict one another. I am calling this kind of paradox the Thomist paradox.

Combining these points shows that any Tillian paradox cannot be directly believed, and any such paradox refers to nothing. In the realm of belief, the Tillian paradox is identical to a contradiction. Since one cannot directly believe any contradictions, one cannot directly believe a Tillian paradox. But this creates a problem. For the only way to believe a Tillian paradox is to believe it indirectly. Let's suppose that such a paradox is called X. So I believe X because I believe the doctrine that these other people believe. But then why do these other people believe? They must believe indirectly as well. Since this is an infinite regress, X does not refer to any propositions at all! But in that case, Tillian paradoxes do not successfully reference any paradox of belief at all.

So what does this mean in the end? It means that any attempt to understand theology in a Tillian sense of paradox is doomed to fall into an epistemological abyss. And that includes the doctrine of the trinity.