BEAUTY AND THE TRUTH

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“Beauty is truth, truth beauty, that is all

Ye know on earth and all ye need to know.”

 

In high school, if not before, most of us were introduced to these famous lines from John Keats’ Ode to a Grecian Urn. Of all the poems to present to an adolescent audience, none could possibly be more ridiculous than this one. At that age, we are all busily learning the Correspondence Theory of Truth. Sometimes at that age, it seems as though that lesson is our life’s work and beauty has no place whatsoever in such a theory.

“Who broke that vase?” my mother shouts. If I answer, “I did”, I am perceived to be ‘telling the truth’ since I did in fact knock it over while tossing a baseball in the air. Likewise, if I answer, “The wind blew it over,” I am not telling the truth because that is not ‘what happened’.

(Please don’t argue that ‘I’ didn’t knock it over, because it was knocked over by my overly active pubescent hormones or by an angry carelessness springing from the deprivations of my childhood or by bourgeois society that cruelly places fragile vases in little boys’ living rooms; we don’t have time for that!)

At that age, we learn that ‘Truth’ is the correspondence between verbal formulations and actual events. ‘Beauty’ has nothing to do with it. More often than not, the consequences of ‘truth’ are anything but ‘beautiful’. One might even argue that childhood, at least in bourgeois Western culture, is the process of learning to separate truth from beauty, ‘what it is’ from ‘what I wish it were’.

But as we grow older, some of us discover problems with the Correspondence Theory. We know what verbal formulations are (“I broke the vase”) but where are the historical events to which those formulations are supposed to apply?

“I broke the vase” corresponds with the perception of scattered shards on the living room floor or with the video footage secretly recorded on the nanny-cam no one knew existed or with a neighbor’s report of a crashing sound followed by a shriek and then deafening silence. But none of these correspondences actually constitutes the imputed historical event itself.

About all we can say about the verbal formulation, “I broke the vase”, is that it is consistent with a number of other ‘formulations’ (mother’s visual formulation of the shards, the camera’s video formulation of the vase toppling in the vicinity of me…and my baseball, and the auditory formulation in the memory of prying neighbors). None of these formulations is the event itself. Which begs the question: Is there an ‘event itself’?

Of course, this simple question is at the core of who we are as philosophers: idealists, empiricists, materialists, realists, etc? Kant, for example, would undoubtedly argue that there was an ‘event itself’, that it was the noumenon behind the phenomena that make up the various formulations. Plato would probably agree: the ‘event itself’ would be the confluence of several Platonic Ideas.

But these arguments are not helpful. We only know noumena through the related phenomena and we only know the Ideas from their shadows. We may choose to believe that noumena or ideas lie behind our perceptions, but that belief is not itself a perception; it is just another theory.

Consider another example: an explosion. Several people witnessed it, it was recorded on a traffic cam, it was measured by a seismograph, a satellite in space noted the light burst, etc…

There will be no end to the number of formulations related to this event: stories in the local papers, a segment on the nightly news, a poem submitted to a literary journal, several paintings, a chemical formula for explosion scribbled by a chemistry teacher on a high school blackboard, a list of bomb ingredients found on the internet, etc…

But where is the event? It appears after all that Truth is not measured by the correspondence of a symbolic formulation with an actual event; rather it is a measure of consistency among multiple symbolic formulations. Gradually, we move from a Correspondence Theory of Truth to a Consistency Theory of Truth.

The American legal system is an excellent illustration of the Consistency Theory at work. Cock Robin has been murdered and I have been accused of the crime. But I am presumed innocent until proven guilty. The prosecution goes to work gathering ‘evidence’, symbolic formulations that provide information about the event. They are especially keen to find formulations that are consistent with the statement, “David Cowles killed Cock Robin.”

Prosecutors will interview potential witnesses to see if anyone ‘saw’ me kill Mr. Robin (knowing that such eye witness testimony is prone to error). Detectives will see if they can find my fingerprints on the victim or on objects of interest in the area. Police will confiscate CCTV tapes to see if there are images of me striking the victim or fleeing the scene.

The objective is to build a dossier of symbolic formulations consistent with each other and with the charges against me. As far back as Mosaic Law, there has been a principle of jurisprudence that a man cannot be convicted on the testimony of a single witness (i.e. on a single piece of evidence); guilt requires confirmation. The charge against me cannot be ‘true’ unless it is consistent with multiple symbolic formulations.

At the same time, my attorneys are also looking for symbolic formulations – formulations that are inconsistent with the charges against me. Someone saw me across town at the time the crime was committed. My doctor testifies that I am not strong enough to inflict the wounds in question.

In the end, all of these formulations are submitted to the jury. Now the real work begins. The jurors have to try to construct the most probable theory of what ‘actually happened’. They will decide which formulations are credible and patch those formulations together. Can they build a consistent picture of what happened and is that picture consistent with the charge against me?

This is phase one: yes, we are convinced by the preponderance of the evidence that David Cowles did kill Cock Robin. But now comes the harder part of the process: how certain is the jury of its conclusion? If they think that I probably killed Cock Robin but they’re really not sure, they must acquit.

In order to convict, they must be sure ‘beyond a reasonable doubt’. So we learn that the truth value of a symbolic formulation is analog, not digital. It is not just a matter of T/F, 1/0. Propositions have a truth value that can range from near 0 to almost 1 (assuming no non-analytic proposition can ever be true or false beyond any doubt whatsoever).

This is very different from the ‘black and white’ Correspondence Theory of Truth we learned as children. Truth can be grey after all.

Things are no different, by the way, in the more exacting realm of science! A conclusion drawn from a single experiment in a single laboratory can be interesting but it still lies in the realm of theory. Only when the experiment has been performed again, and again, and again in independent labs with similar results do those results become part of our map of reality.

So far we have dealt with truth as it relates to imputed events, the stuff of everyday life. But what if I am looking to account, not for an event among events (a vase break, e.g.), but rather for the set of all events or for the nature of an ‘event’ or for the phenomenon of ‘event-ness’ itself? None of these is an ‘event’ per se, yet we would very much like to be able to make true statements about them. What if I want to make a true statement, not about something, but about everything? How do I do that? How can we talk about Truth in the context of a ‘Theory of Everything’?

Like the megalomaniacs that we are, living in shadow of the millennium, we imagine that we discovered the notion of a Theory of Everything. We’ve even given it a cute nickname, “TOE”. But what we usually mean by this enormous concept is ‘merely’ the harmonization of General Relativity with Quantum Field Theory.

A Theory of Everything can go much further even than that…and our generation is not the first to attempt such a synthesis. In fact, human beings have been generating TOEs since the dawn of recorded thought. From Lao Tzu’s Tao Teh Ching in the East and Parmenides’ On Nature in the West through the works of Plato and Aristotle, John and Paul, Augustine and Aquinas, to the great systematic philosophers of the modern era (Hegel, Marx, Whitehead, Heidegger and Sartre) and to the two great epic ‘poets’ of the 20th century, Joyce and Pound.

How does one evaluate Truth in the context of a Theory of Everything? We certainly cannot speak of Correspondence since now we are all in agreement that there is no event for our formulations to correspond with. This, by the way, is where the Logical Positivists and even Wittgenstein went wrong. The lack of an event does not necessarily mean that no meaningful formulation with a truth value is possible.

Nor can we settle for consistency among formulations, though this can be tempting. Often similarities among formulations abound. But such similarities are accidental and have no meaning. Theories of Everything, if they are to be successful at all, must be organic wholes. Their parts must derive 100% of their meaning from the relationship each has to its whole. Superficial similarities among the parts of disparate TOEs, while intriguing, are absolutely meaningless.

Consider the letters of the English alphabet. The letter “t” appears twice in both “tautology” and “tantrum”. A cryptographer from another galaxy might theorize that some connection existed between these two words because of the appearance of two “t’s” in each; but we know that no such connection exists (does it?). The common element between the two words is an ‘accident’ and effectively meaningless.

Likewise, we note that two paintings by different artists on adjoining walls of a museum are both dominated by the color red. Are we then to conclude that these two works or art are communicating a similar message? Of course not! The elements of a painting derive their meaning from their relationship to the whole. Superficial similarities between paintings are meaningless.

When we speak of a Theory of Everything, we don’t actually mean “everything”, of course; we mean everything in a certain ‘universe of discourse’. For example, if physicists do succeed in combining General Relativity and Quantum Field Theory into a single TOE, that will not tell us who won last night’s baseball game or why Americans’ taste in movies is so bad. These matters, while interesting in their own right, are not part of the physicists’ universe of discourse.

So how do we evaluate the truth of a TOE? We cannot rely on the touchstones of Correspondence or Consistency; we must apply a new standard: Completeness.

Completeness (Truth in the context of a TOE) consists of two things: Sufficiency and Necessity. The process of determining the Truth value of a TOE is therefore a two-step process:

(1)   Is the Theory ‘sufficient’ to account for all of the phenomena in our universe of discourse? In other words, does the Theory work?  This is a relatively easy test to apply…and to pass.

The problem with this test, if there is one, is a problem of ‘scale’. Genesis, for example, accounts for the creation and evolution of the universe and life on Earth; but it does not have very much to say about galaxy formation, natural selection or the workings of DNA. Does it therefore fail the sufficiency test?

I don’t think so. I think it is permissible for the TOE to specify not only its universe of discourse but also the scale at which the TOE is meant to apply.

(2)   Is the Theory ‘necessary’ to account for all the phenomena in our universe of discourse? Or is there a different way to account for the same phenomena? This is an extremely difficult test to apply…or to pass. In fact, it’s not clear whether it’s even possible to pass such a test conclusively because it requires us to prove a ‘synthetic negative’ (a negative statement outside the realm of logic, i.e. about the real world.)

If you claim your TOE is ‘necessary’ as well as ‘sufficient’, you must maintain not only that it works but that no other non-equivalent explanatory framework can possibly account for the same phenomena. If someone else comes up with a theory that works, sue that man; he must have violated your patent!

Newton’s physics was sufficient to explain the cosmic phenomena in his universe of discourse, and for a time many took it as necessary as well. But it wasn’t! Einstein accounted for the same phenomena using a radically different theory.

The problem here, and there definitely is one, is really twofold: (1) On the one hand, how can we be sure that some new theory will not emerge someday to shatter our claim of necessity? (2) But on the other hand, how can we be sure that any two theories are really different theories? How do we know that they cannot somehow be shown to be equivalent to one another?

Example: when physicists began to consider the possibility that space-time might not be 4 dimensional, it seemed that they were making great discoveries. But later it was shown that phenomena modeled in n-dimensions are often mathematically equivalent to phenomena modeled in (n-1)-dimensions. The disparate dimensional theories were not really different theories after all. They both accounted for the same phenomena because they were in fact the same theory, expressed differently.

Necessity is more difficult to establish than sufficiency because we impose on it a very different standard. Sufficiency can be established by simple demonstration: “See, my contraption works!” Of course, in real life such a demonstration might be immensely difficult but at the core it is just this simple.

Sufficiency, a positive, can be ‘proven’ by demonstration. On the other hand, a proof of necessity, a negative, requires rigorous logical deduction; it is not at all clear that any such proof is even possible.

So if necessity is logically required to establish the truth of a TOE, but if it is also an impossible standard to meet, where does this leave us? Must we give up our quest to make true statements beyond the realm of everyday events? Must we surrender to the Logical Positivists after all? Or is there a way around this impasse?

Sufficiency is a binary variable, it either works or it doesn’t, yes or no. But must necessity be binary as well? Is it possible that sufficient Theories of Everything might exhibit relative degrees of necessity? Between two sufficient TOEs, both addressing the same universe of discourse, is it possible for one to be more or less necessary than the other? If so, then it would also be possible to assign a relative truth value to each of those two TOEs.

Earlier, we saw that symbolic formulations about events exhibit truth values that are not binary (1/0); they exist in a range. Why should this not also be true for the truth values of TOEs?

Here is where Mr. Keats comes in…at long last! It turns out that the ‘necessity’ of a sufficient TOE is directly proportionate to its ‘beauty’. Its beauty is its truth.

Physical scientists are way ahead of us in this regard. It is a commonplace principle in science that a more beautiful theory is to be preferred over a less beautiful one. Although few scientists would admit to being theists, most practice a kind of ‘closet theism’: they assume that for some reason the universe prefers beautiful solutions over less beautiful ones (which was, essentially, Einstein’s test for the existence of ‘God’).

Copernicus’ model of planetary motion triumphed over Ptolemy’s, not because one was sufficient and other wasn’t (they both ‘worked’), but because it was simpler, more beautiful.

Among sufficient theories, the more beautiful theory is always to be preferred over the less beautiful. If there were such a thing as an ultimately beautiful theory, and maybe there is, then no other theory would be possible. And if there were more than one ultimately beautiful theory then those theories would have to be identical.

Beauty is the new Necessity!

According to the Completeness Theory of Truth, a proposition must be sufficient and necessary. Its sufficiency may be established by demonstration and its necessity by aesthetic valuation.

Now, let’s apply this Completeness Theory of Truth to some real life Theories of Everything. How do they fare? Earlier, we said that TOEs could be divided into three classes:

(1)   Theories about the set of all events in a given universe of discourse. The set is not itself an event but it is the common subject of every TOE in this class. Perhaps the best possible example is James Joyce’s Ulysses. The subject of this novel is literally the set of all human experiences. Joyce demonstrates that there is such a set, he explains how such a set comes to be, and most amazingly, he shows how the set itself influences the content of the events that make it up. And he does all this in one of the most beautiful works in all of literature. Ulysses demonstrates its own sufficiency and its incredible beauty constitutes its necessity.

(2)   Theories about the nature of ‘event’ itself. An excellent example in this class of TOE is Alfred North Whitehead’s Process and Reality. Whitehead’s theory assumes that events (he calls them ‘actual entities’) are the ultimate stuff of reality. His book identifies the features and processes that all events share in common. He answers the question, “What is an event?” His theory is undoubtedly sufficient…and very beautiful (necessary).

(3)   Theories that account for the phenomenon of ‘event-ness’ itself. These theories address the most fundamental questions of all: “Why is there something rather than nothing?” and “What a thing is universe that it should happen to be populated by events?”  An example in this class is the Gospel of John. John presents a theory of creation, incarnation and salvation that rigorously accounts for the fact that we live in a world populated by events. And because of its air-tight organization and the soaring lyricism of its language (this is probably the most beautiful book in the entire Judeo-Christian cannon), it can claim necessity as well.

We began this essay examining our childhood theory of truth: Correspondence. We then identified the Consistency Theory of Truth as a superior way to assess truth value in the context of events. Finally, we developed a Completeness Theory of Truth as a way to assign truth values to ‘Theories of Everything’, theories not about events per se but about event-ness.

In the context of ‘meta-events’, we recognized that Completeness requires a theory to be both sufficient (an easy test to meet) and necessary (an apparently impossible test to meet). However, we discovered another way, outside the rigors of logic, to establish the necessity of a theory. We discovered that we could approach the question of necessity not only through logic but through aesthetics.

And so we return once again to Mr. Keats. Beauty is truth and truth beauty, indeed. And in the context of Theories of Everything, that is all ye know on earth and all ye need to know.