SUFFICIENT & NECESSARY?

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Scientists, philosophers and even theologians build models in an attempt to explain phenomena they’ve observed, whether results of laboratory tests, recurrent patterns in nature or prayer experience. The first test of any such model is whether it actually succeeds in accounting for the phenomena it seeks to explain: Does it work?

If a theory does indeed account for the phenomena in question, we say that it is “sufficient”, i.e. it is sufficient to explain the phenomena. But the Holy Grail for model builders is to create models that are not only sufficient but also ‘necessary’.

Consider the Ptolemaic model of the Solar System. Within a certain tolerance, it was sufficient to account for the motions of the Sun and its planets. But was it necessary? Galileo and Copernicus showed that it was not. They built an alternative model that accounted even more closely for the same phenomena but that differed in fundamental ways from the Ptolemaic model.

Of course, the Copernican model is not necessary either. There may be an unlimited number of ways to explain the motions of the planets. We tend to favor the Copernican model, not because it is necessary but because it is relatively simple and aesthetically pleasing. (Model builders believe that simpler, more elegant models are superior to tortured, ugly Rube Goldberg contraptions.)

In another essay in this collection, Beauty and Truth, we accept the conventional view that no model can be proven to be ‘necessary’ if it references any real world phenomenon, i.e. if it contains ‘synthetic propositions’. Models that do not refer to real world phenomena but only to themselves are said to consist entirely of ‘analytic propositions’. A model is analytic if its truth value relies entirely on an understanding of its terms. For example, “a square has 4 sides” is an analytic proposition. 4 sides is part of what makes a square a square. It doesn’t tell us anything about the actual world.

This conventional view sets a significant upper bound to our ability to assign truth value to the models we create. However, in Beauty and Truth, we ‘got around’ this limitation by invoking a new criterion, Beauty, as a substitute for Necessity when evaluating a certain family of models, i.e. models that propose to be universal in scope, so-called ‘theories of everything’ (or TOEs). Essentially, we took the model makers’ relative preference on aesthetic grounds for Copernicus over Ptolemy and made it an absolute preference when the model in question is a TOE. We posited that the most beautiful model, provided it is sufficient, is functionally ‘necessary’.

In this essay, we will reconsider the conventional view that models containing synthetic propositions cannot be necessary. Is that view even correct? Or are there models that contain synthetic propositions but are in fact ‘necessary’? Once again, we will limit our attention to models that are ‘theories of everything’ (TOEs). The best place to find candidate models for our inquiry is the field of theology. Theological models are by definition TOEs; furthermore, they all purport to say something true about the real world.

The First Letter of John in the New Testament ends with a model that attempts to account for nothing less than the most fundamental phenomenon: existence. I perceive that something exists; how do I account for that? (And when I say “something” I don’t just mean some particular something; I mean any possible something.) To put the matter traditionally, and more eloquently, 1 John asks, “How is it that there is something rather than nothing?”

Outrageously, the author of 1 John does not just propose an answer to this ancient conundrum, he proposes the answer. In the nomenclature of this essay, 1 John is not satisfied to offer a model that is sufficient to account for the phenomenon of existence; it seeks to develop a model that is necessary to account for existence.

What does it mean to say that a model is necessary? It means that there is no alternative way to account for the phenomena in question or, to be more precise, that any model that does account for those phenomena must turn out upon analysis to be structurally equivalent to the initial model.

Let’s begin with the text itself (1 John 5: 1-13) and then reframe that text more explicitly in the form of a model:

“Everyone who believes that Jesus is the Christ is begotten by God…(and) whoever is begotten by God conquers the world. And the victory that conquers the world is our faith…that Jesus is the Son of God. This is the one who came by water and blood, not water alone but water and blood. The Spirit (wind/breath) is the one who testifies and the Spirit is truth. So there are three that testify, the Spirit, the water and the blood, and the three are of one accord…Now the testimony of God is this: that he has testified on behalf of his Son. Whoever believes in the Son of God has this testimony within himself…And this is the testimony: God gave us eternal life and this life is in his Son. Whoever possesses the Son has life…I write these things to you so that you may know that you have eternal life, you who believe in the name of the Son of God.”

The ontological model proposed in 1 John, Chapter 5, verses 1 -12 (1 John 5: 1-12) consists of just seven propositions:

(1)   Everyone who believes that ‘Jesus is Christ/Son of God’ is ‘begotten by God’.

(2)   Everyone who is ‘begotten by God’ ‘conquers the world’.

(3)   The conquest of the world is the faith that ‘Jesus is Christ/Son of God’.

At first glance, it seems that the author of 1 John might just as well have written the tautology, “Everyone who believes that Jesus is Christ/Son of God believes that Jesus is Christ/Son of God.” But this is not the proposition that the author is setting out to prove and, as we’ll see below, the two middle terms (‘begotten of God’ and ‘conquers the world’) play a crucial role in the overall proof.

(4)   There are three witnesses on earth: Spirit (wind/breath), water and blood and the three are of one accord (i.e. give common testimony).

(5) The testimony of God is (a) that he testified on behalf of his Son, (b) that God gave us eternal life and (c) this eternal life is in his Son.

(6) Whoever believes that ‘Jesus is Christ/Son of God’ has this testimony within himself.

(7) Whoever possesses the Son has life!

The author places a helpful summary sentence at the end of this sequence of propositions. It is the theological equivalent to QED in logic: “I write these things to you so that you may know that you have eternal life, you who believe in the name of the Son of God.”

Hold on! What does ‘eternal life’ have to do with ‘existence’? Only everything!  If you have eternal life then you exist and if you exist then other persons and other things may exist. Potentially, 1 John does account for the phenomenon of existence.

Did the author succeed? Did he build a model with the 100% truth value required for the reader to “know” that the propositions are true?

The proof pivots on the 4th proposition. Fortunately, it’s relatively easy to understand so let’s begin our analysis there. The 4th proposition sets forth the testimony from the witnesses on earth, Spirit (breath/wind), water and blood. Spirit (breath/wind), water and blood symbolize the essential nature of the world (cosmos): Change. As such, they do indeed give testimony that is “of one accord”; it could not fail to be given its content. All you can ever say of change is that it is, well, change. But why does this testimony matter?

To understand, we need to step back. The Apostle John, founder of the Johannine school, was also the Bishop of Ephesus in Asia Minor. 1 John, traditionally attributed to the apostle himself, is almost certainly the work of someone from that school. As it happens, Ephesus was also home to another famous philosopher, Heraclitus, almost 500 years earlier. The Biblical writings attributed to the Johannine school show a thorough familiarity with Heracletian ideas. For example, the concept of logos, so central to the Gospel of John, is a fundamental Heracletian category.

The central thesis of Heraclitus’ teaching as we know it is the concept of ubiquitous change. His ideas have been summarized on a bumper sticker, “Everything flows”, and on a billboard, “No one can step into the same river twice.” As far as we know, Heraclitus never actually made either statement but they are reasonably accurate popularizations of his views.

Therefore, the testimony on earth, i.e. Spirit (breath/wind), water and blood, is testimony of change: Spirit, the life force (or breath, the rhythm of life or wind, Gaia’s breath), water, the unceasing flow of events, and blood, the ultimate and inevitable morality of all that is.

But the doctrine of continuous change has a flaw. If everything is in constant flux, how can we say that anything actually is? If everything flows, what is it that flows?

Consider the problem in terms of time. If time is a continuum (or nearly so), then everything is either past or future; nothing is ever truly present. But past and future exist in memory and imagination only and memory and imagination can only actually exist in a present. But if there is no real, actual present, then what is there?

Again, according to the doctrine of universal process, there is no room for a beginning or an end. Unless process is infinite (or at least unbounded), the doctrine lacks internal consistency. But if change is infinite, do the accidental, finite structures that seem to crop up along the way have any real value…or even existence. If I die, did I ever really live?

But human experience is quite different from this Heraclitean model. The world of our experience is made up entirely of discrete events and these events all have extension in space and/or time (duration). Such discrete events are apparently impossible inside Heraclitus’ model. So the testimony on earth, as related by the author of 1 John, is inconsistent with the actual data of experience. It fails radically to account for the phenomenon of existence; it is not sufficient, much less necessary.

Yet the author of 1 John accepts the testimony on earth as valid (“the Spirit is truth”). After all, who can find something in cosmos that is not subject to cycles, to ongoing change, to death? So we have a paradox. The testimony is true but the verdict is false. The propositions are true but the model is neither necessary nor sufficient.

This paradox cannot be resolved inside the Heracletian world view; in the words of Gödel, the Heraclitean model is “incomplete”. There are self-evident truths (e.g. “something exists”) that cannot be deduced form the Heraclitean model and that, in fact, contradict that model. Something beyond the Heraclitean model is required. So the author of 1 John posits something Heraclitus never dreamed of: another dimension to reality, an atemporal/aspatial dimension, a dimension in which process is not change but emanation (‘begetting’).

The author of 1 John adds a ‘divine dimension’ (at right angles so to speak) to the ‘cosmic dimension’ of Heraclitus.  In the divine dimension, process is not about differentiation but about harmonization, identification, and inter-penetration. The divine dimension negates the cosmic dimension but it negates it without cancelling it. A is conserved in Not-A. In fact, A is an improper subset of Not-A. To put that another way, all elements of A belong to Not-A and vice-versa. We are not talking about two realities, two sets of entities, but one reality, one set of entities, two sets of dimensions.

A contemporary of Heraclitus, Parmenides, spoke of two “ways” in Nature: ‘the way of truth’ and ‘the way of appearance’. Parmenides’ way of appearance has something in common with the Heracl1tean model while his way of truth has something in common with the divine dimension proposed by the author of 1 John.

Now let us apply these insights to the main argument. The unanimous testimony on earth is perpetual and ubiquitous change. The testimony of God directly contradicts the testimony on earth. The testimony of God is “eternal life”. Yet the author of 1 John suggests that we accept both testimonies as true. If the world is change then there must also be a real present (a here-now outside the spatiotemporal continuum) if we are to account for the phenomenon of existence; we need a ‘way of truth’ as well as a ‘way of appearance’. Or, in the words of Ezra Pound, “the grove needs an altar”.

In the cosmic dimension, ‘events’ are related according to the mode of succession (we sometimes call it ’cause and effect’). Relation in the mode of succession is a process of decay and eventual death. Process in the mode of succession is entropy. Heraclitus was in fact the first philosopher to propose an entropic model of reality.

In the divine dimension, however, all events co-exist in a common, eternal now. Therefore, there can be no decay and certainly no death. Events cannot be related by succession because there is no such thing. Nothing comes to be, nothing ceases to be. Instead, events are related to one another according to the mode of emanation.

Relation in the mode of emanation is a process of growth and generation (vs. decay and death). Events are embedded in other events and ultimately, all events are embedded in the whole, itself an event. When one event emanates from another, it retains that other within it; and when one event begets another, it is immanent in that other. Emanation and begetting are flip sides of the same coin, they are templates; where there is one, there is the other.

According to the testimony of God, the divine dimension, eternal life, is “in the Son”. To believe that Jesus is ‘Christ/Son of God’ is to believe the testimony of God on behalf of his Son that eternal life is “in the Son”, i.e. in Christ Jesus.

So far so good…bet we’re not home yet. There is still one hurdle we have to overcome. There is eternal life and it is in the Son of God, Christ Jesus, but what does that have to do with us? We seem to live in the world according to the mode of succession; we see ourselves aging and we expect to die. Perhaps there are two worlds, one eternal, one transient, and we have the misfortune to live in the later. If so, what is Christ/Son of God to us?

He is precisely “the one who came through water and blood…not by water alone but by water and blood”, that’s what Jesus Christ, Son of God, is to us! Jesus is a product of the same ever changing cosmos as we are. Yet Jesus is begotten (Son) by God. Therefore, Jesus links the cosmic dimension and the divine dimension.

And further (and this is why the first three propositions are important after all), believing that ‘Jesus is Christ/Son of God’, we too are begotten by God. And by the nature of begetting (see above), God is therefore in us and we are therefore in God.

So we conquer the world: we are not doomed to perpetual change and ultimate death; we have eternal life. We have God’s testimony to that effect because God testified on behalf of his Son and that testimony is actually within us; and God’s testimony is that eternal life is “in the Son”.

The virtuous noose is tightening but it’s not yet taut; something is still missing from the model. God testified on behalf of his Son that eternal life is in his Son and we have that life if we possess the Son. But we have not demonstrated yet that we do in fact possess the Son.

To close this gap, we need once again to understand the context of the argument. Today, we viciously segregate the speaker from the speech and the speech itself from its denotational content (if any). This epistemology was unknown, or at least unaccepted, by the members of the Johannine school. Thinking according to the mode of emanation, they understood the speaker to immanent in the speech and they did not separate the speech itself from its denotational content.

Consider the opening verses from the Gospel of John: “In the beginning was the Word and the Word was with God and the Word was God…and the Word became flesh…and we saw his glory as of the glory of the Father’s only Son…” Clearly, God is one with his Word (testimony) and that testimony (Word) is one with the Son.

Now apply this to our argument. The testimony of God, given on behalf of his Son, is within us and that testimony is eternal life and that eternal life is in the Son. We possess the testimony (word) both on behalf of the Son and in the Son and therefore we possess the Son as well. Therefore we have eternal life.

We have constructed a logical system capable of demonstrating what we already know experientially, namely that ‘something is’ (e.g. that we are, the we really and truly exist, that we are not just an eddy in a whirlpool of perpetual change). We have solved the paradox of existence; we have demonstrated how it is possible that things that perpetually change can yet exist.

So 1 John is undoubtedly sufficient to account for the phenomenon of existence. But is it necessary? Or is it possible that another model could equally well account for this same phenomenon? Of course it is! But would that other model be structurally different from the model set out in 1 John? Or will it turn out that any possible alternative model is the same as our model?

Let’s strip the model of its First Century theological vocabulary and distill it down to its essential components: (1) Things that exist must emerge from the flux of perpetually change (succession, entropy). (2) Things that exist must exist atemporally (i.e. eternally). (3) Things that exist atemporally must be related to one another according to the mode of emanation (rather than succession). (4) Relations in the mode of emanation are characterized by mutual immanence (otherwise succession would enter back through a back door). (5) All entities that exist in the mode of emanation must together constitute an entity, a whole. (6) That whole must be immanent in each of its parts (elements).

I propose that this model accounts for the phenomenon of existence (‘sufficient’), tells us something meaningful (‘synthetic’) about the totality of its universe of discourse (i.e. it is a TOE) and that any model that similarly accounted for the phenomenon of existence would have to include the same elements and structure as this model.

Let’s test our theory. Let’s examine three classes of alternative models and see how they stack up.

The first class consists of models designed to prop up Heraclitus and explain away the apparent short comings in his theory. The first person to engage in this enterprise was none other than Heraclitus himself: “World…an everliving fire, being kindled in measured and put out in measures.” (Fragment 30)

According to this model, and all others like it, the discrete entities we experience are actually the result of variations in the rate of change in various spatiotemporal regions. At first glance, this seems attractive. Entities obviously have varying extension in space and time relative to one another yet ultimately all must pass away. But is this model internally consistent and, if so, is it really sufficient?

First, it is not consistent. Hawking proposed that time and entropy are synonymous. If so, local variations in the rate of entropy would have to correspond to deformations of the temporal dimension. According to Einstein, such deformations, while possible, can only be a function of variations in mass/energy density (or acceleration). However, it is not our experience that greater mass corresponds perfectly with larger spatial volumes or slower rates of decay.

Second, it is not sufficient to account for the phenomena in question. Relative variations in the rate of change are not the same thing as absolute suspension of the phenomenon of change. Real entities require a real Present without past or future. A slower transition from past to future does not a Present make. Ultimately, rate of change is absolutely irrelevant to our critique of the Heraclitean model.

The second set of models we will test purport to account for existence via a totally different framework. For example. British philosopher and mathematician, Alfred North Whitehead addressed exactly the same issues as 1 John. He developed a model based on ‘actual entities’. Each actual entity inherits an actual world consisting of other actual entities. It aims (‘subjective aim’) to transform that actual world consistent with freely chosen values (‘eternal objects’) and a freely chosen objective (‘proposition’). Accordingly, it prehends the entities that constitute its actual world and through a process of concrescence transforms those entities into a novel entity (‘satisfaction’) which thereby becomes an entity (‘superject’) in the actual worlds of other actual entities.

Through prehension, the entities in an actual world are immanent in the novel entity that prehends them and that novel entity is immanent in the actual entities that prehend it. The entire process constitutes a single actual entity which Whitehead calls “God”. While each actual entity is entirely free to select its own values and shape its own objective, it is through God that values are available and objectives are possible.  God, the totality, is present in every actual world and in the subjective aim of every novel entity. Every novel entity prehends God in its inheritance and in its satisfaction. Therefore, God is immanent in every actual entity just as every actual entity is immanent in God. No God, no entities; no entities, no God.

What can we say about this model? Is it sufficient? Definitely! Is it necessary? Possibly! Then does it disprove the necessity of the model we found in 1 John? It does not…because Whitehead’s model is fundamentally (structurally) the same as the model from 1 John. In a surprising way, it demonstrates the argument that any model that succeeds in accounting for existence, no matter how imaginative and complex, must ultimately boil down to a restatement of 1 John.

Finally, let us consider a third set of models that invoke a singularity to explain existence. The first chapter of Genesis provides us with just such a model: “…Earth was without form or shape, with darkness over the abyss and a mighty wind sweeping over the waters. Then God said, Let there be light and there was light…”

Is this model sufficient? Definitely. It is necessary? Perhaps. So what’s wrong? The model set forth in Genesis does not contain synthetic propositions, only analytic propositions; it doesn’t tell us anything about its universe of discourse. How can that be? In the history of Western civilization, no passage has been more controversy than Chapter One of Genesis. How can it possibly be that so much heat has been generated, and so much ink spilled, over mere analytic propositions. Not since first grader Sally O’Leary told the class that 2 + 2 = 5 has an analytic proposition generated so much angst.

The problem is that the first term of the argument, God, is an undefined term. As the old Baltimore Catechism states, “Who is God? God is the Supreme Being who made all things.” So the Genesis model simply states that the being who made all things made all things. (Please be careful not to misunderstand this argument. Genesis gives us an immense amount of information about the process of creation;  but it tells us nothing about creation, i.e. existence, per se.)

I can hear you, dear reader: “Genesis, really, can’t you find something more contemporary…and relevant?” Ok, how about the Big Bang Theory (the theory itself, not the lame TV show by the same name); does that work for you? Same problem: it describes, beautifully, the process of creation…but it doesn’t account for it. BBT is just another name for God…an undefined term.

So now that we have successfully defanged three groups of alternative models, have we then established the necessity of the Johannine model? Of course not! Can we? That question is beyond the scope of this essay and well above the pay grade of this essayist. But I think we have at least made the case that a certain class of model (TOE) may be relevant to the actual world (i.e. contain synthetic propositions) and still stake a claim to ‘necessity’.