Wednesday, August 4

Thoughtful Thursday: A Close Shave with Occam’s Razor


One of the most useful, but also one of the most neglected, principles in the practice of theology is Occam's (or Ockham's) Razor. Occam's Razor is usually credited to William of Occam, a nominalist Franciscan monk of the early 14th century.  There are several mutually equivalent ways, in both Latin and English, of expressing the principle. One of the more common Latin versions is Pluralitas non est ponenda sine necessitate:  "Plurality is not to be posited without necessity". Much less laconic, but more colloquially accessible, is my favorite English version: "Hypotheses / suppositions / premises that contribute no expository power should be deleted from any proposed explanation".


In the early 1300s, classical Scholasticism began to wane as theologians, William of Occam among the most vocal, began to lose patience with the vast and complex conceptual edifice of the dominant, primarily Thomist, theology of that day. So much of the intellectual and discursive energies of the Schoolmen seemed to the nominalists to be consumed in sterile speculation about matters that seemed completely untethered to reality, e.g., the precise difference between instrumental and efficient causality.  To the rising school of post-Thomist theologians, an inordinate amount of time and energy were devoted to mere haggling about words ... words, words, words, and more words! So a school of theology arose that emphasized minimizing speculation about matters that had no correlates in the real world. Beyond this reality, they said, we have, not actually existing things, like clouds and trees and God and the Sacraments, but only empty words, only names. Hence the name of the movement:  "nominalism" from the Latin nomine (name). Nominalists strove to divest theology of all conceptions and terms that were superfluous in the sense that they did not contribute to the understanding and elucidation of faith and doctrine. Hence Occam's Razor.


To get a better intuitive grasp of how Occam's Razor works in practice, consider the following (admittedly simplistic) thought experiment. I drop a pencil to my desk. The pencil falls down. Now suppose I ask "Why did the pencil fall?"  At least two explanations for the fall of the pencil are possible. The first explanation says the pencil fell for two reasons: (1) the earth's gravity  attracted the pencil and pulled it down, but also (2) there was a "pencil demon" hovering just above the pencil and pushing the pencil toward the desk. Between (1) and (2), the pencil, pulled from below and pushed from above, had to fall down. The second possible explanation just appeals to the laws of gravity cited in (1). The second, gravity-only, explanation seems to exhaustively account for the motion of the pencil, in the sense that it explains everything there is to know about the motion of the pencil. There is no explanatory "work" left to be done by the pencil-demon hypothesis / premise in (2). Consequently, Occam's Razor says we may safely omit the latter hypothesis.

(A real-world analog of the pencil-demon thought experiment is the  (possibly apocryphal) story that tells of the great 19th-century mathematician and theoretical astronomer Pierre Simone, Marquis de LaPlace, giving Emperor Napoleon a copy of his [LaPlace's] great work on celestial mechanics, Mechanique Celeste.  Napoleon probably didn't understand the math.  I dunno ... maybe he looked at the pictures.  Anyway, some days later, Napoleon remarked to LaPlace "M'sieu, I noticed that nowhere in your great work did you mention God".  Replied LaPlace:  "Ah sire!  That was a hypothesis of which I had no need". LaPlace was citing his paraphrase of Occam's Razor.)


In considering the use -- and the misuse -- of Occam's Razor, it is important to bear in mind a couple of points. First of all, the Razor is completely "agnostic" about whether superfluous entities like pencil demons actually exist or not. They may. They may not. Occam's Razor is concerned exclusively with what you might call the "forensics" of scientific explanation:  what can be said, and what needs to be said, by way of explanation and understanding -- no less, but also no more. (This reticence about pronouncing on extraneous issues of pure metaphysics, untethered to actual reality, is characteristic of the nominalist approach to theology.  In fact, nominalism can be accurately seen as a 14th-century precursor of the phenomenology of Edmund Husserl and of the analytic school of philosophy exemplified by P. F. Strawson, A. J. Ayer, and Gilbert Ryle.  The Razor itself is also strongly reminiscent of Ludwig Wittgenstein's famous maxim:  Woruber Mann kann nicht sprechen, daruber muB Mann schweigen -- "Whereof one cannot speak, thereof one must be silent".)  Early in the 20th century, it was believed that, just as ocean waves propagate through water and sound waves through air, so also electromagnetic waves -- light -- propagate through an all-pervading medium termed the "luminiferous ether". Michelson and Morley set out to measure the effect of this "ether" on the speed of light. They reasoned that the speed of light, measured in the same direction as the flow of the "ether" (basically the direction of the earth's motion around the sun) would be greater than the speed of light measured in the opposite, or some transverse, direction. Light emitted in the same direction as the "ether" would benefit from the "ether tailwind", and would slow down if emitted into an "ether headwind". Despite repeated and exhaustive measurements of the speed of light emitted in many different directions, no difference in the speed of light was detected. (It remained for Albert Einstein's special theory of relativity to account for this result in terms of the universal invariance of the speed of light.) The by-now-classic Michelsom-Morley experiment did not prove that the "luminiferous ether" does not exist, but it did demonstrate that the hypothesis of the "luminiferous ether" is of no explanatory or "forensic" consequence.


The second point to be borne in mind regarding Occam's Razor is that which hypotheses "count" as superfluous depends on the context, which, in turn, depends on the kinds of questions one is dealing with. Consider a Schubert string quartet. There are a couple of different ways of considering a Schubert string quartet. I can consider it just as a collection of sounds -- that is, sonic vibrations in the air -- each member of the collection having a certain frequency, amplitude, and duration. I can even consider the silences between the notes as a kind of "non-sound" in an analogous way, having duration but no non-zero frequency or amplitude.

I think it is safe to say that, if we were to compile a complete account of a Schubert string quartet as an elaborate sequence of sounds of a certain frequency, amplitude, and duration, interspersed with a set of silences of a certain duration, and if we were to present this account as a "complete" and "exhaustive" account of the piece in the sense of leaving nothing unexplained, most people, probably even people completely tone-deaf, would react with incomprehension, probably followed by pity. They would think we missed the whole point -- which was beauty. And if we invoked Occam's Razor for the omission of considerations of beauty and aesthetics -- which, after all, have no explanatory utility for music as an acoustic phenomenon -- they would pity us even more.


But if we play a different game with our Schubert string quartet and consider the aesthetics of the music as a work of art, the situation is much the opposite. Now beauty, far from being a superfluous appendage, becomes instead an absolutely essential hypothesis. A consideration of beauty includes and yet transcends the mere acoustics of the music. So we would have a hierarchy of explanation and understanding.  The purely acoustic understanding would not be wrong, but it would be included "inside" the aesthetic explanation, much like a set of those little Russian matryoshka dolls nest inside each other.  Considerations of beauty, superfluous in the case of music-as-mere-acoustic-phenomenon, now become utterly essential in the case of music-as-a-work-of-art. Why Franz Schubert wrote the music he wrote, why he wrote it as he did with that particular acoustic sequence of sounds and silences, why that sequence is considered "beautiful" within a certain culture's aesthetic canon, etc., all these issues depend critically on the hypothesis of beauty. Even if we don't care for Schubert's music, we will almost certainly articulate our distaste in terms of our personal aesthetic canons of beauty. Considered from this perspective, beauty becomes something essential, not a mere expendable whisker to be shaved away by Occam's Razor.

So, with all the foregoing as context, we may ask:  what of God? what of religion? From what standpoint -- playing what kind of "forensic game", if you will -- does the hypothesis of God become essential, or at least meaningful? What (kinds of) explanations does the hypothesis of God support?  Well, for the last 500 years or so – that is, ever since the advent of science – the role of God as an explanatory construct has been diminishing. God no longer “explains” anything.  Despite the desperate rear-guard action being fought in the courts and in the media by advocates of creationism and intelligent design, the usefulness of God as a non-superfluous (in the Occam-esque sense) scientific hypothesis has diminished to zero.  God is nothing like the inflation that occurred during the “Planck time” at the Big Bang.  God is nothing like plate tectonics.  God is nothing like natural selection.  God is nothing like the double helix of DNA.  Furthermore, attempts to dragoon God into explaining the remaining gaps in our knowledge, the interstices in the scientific understanding of the world have always and without exception turned out, in the end, to subvert the very attempt itself to render God scientifically relevant by feeding into the “God-of-the-gaps” process, whereby God is invoked to explain an at-the-time unknown phenomenon – only to be supplanted a year or two, or a generation or two, later when a scientific explanation is found. God then – again – becomes one of William of Occam’s superfluous hypotheses.


The conclusion we are left with is this:  God tells us nothing about the external / objective world.  Of what possible relevance, then, is God?  Perhaps the best way to understand the relevance of God in the contemporary world is by recurring to our previous account of the Schubert string quartet.  We can look at the quartet from (at least) two different and complementary perspectives:  as a sequence of sonic vibrations of different frequencies, amplitudes, and durations; and from an aesthetic perspective as a work of art.  From the former perspective, all considerations of “beauty” are indeed superfluous hypotheses to be shaved away by Occam’s Razor.  In fact, strictly from that perspective, one cannot even talk meaningfully about “beauty”.  Considered as a sequence of sounds, saying that, say, Schubert’s String Quartet No. 3 in B-flat Major is “beautiful” is a category mistake, like saying the square root of two is green. But if we consider the B-flat Major quartet as a work of art, then the attribution “beautiful” is anything but superfluous. In fact, in those terms, beauty becomes not only relevant, but the final cause of Schubert’s work:  Schubert created the String Quartet No. 3 in B-flat Major because he wanted to create a beautiful work of music.  Beauty, in those terms, far from being superfluous, becomes the very raison d’etre of the B-flat Major quartet.  From this latter, aesthetic, perspective, everything we said about the quartet as an acoustic phenomenon – frequency, amplitude, duration, etc. – is true, but, absent beauty, these assertions are … well … pointless, vacuous.  Much the same is true of God:  without God, the world is just noise, William James’s “blooming, buzzing confusion”, but add God to the mix and the world, the entire universe, becomes … music ...

… at least for many people.

And in those last five words lies an absolutely critical qualification that must not be overlooked.  To some people, Schubert’s string quartets are indeed “just noise”, considerations of beauty notwithstanding.  They prefer, say, Stan Getz (whom I also admire) and Benjamin Britten (whom I don’t).  Please understand now:  my own personal preferences aside, no one is “right” and no one is “wrong”.  It is all, indeed, just a matter of preference.  So also with God.  The relevance or God, or lack thereof, is determined on a purely personal, individual, idiosyncratic basis.  The most we can say – but this is pretty important – is that, for many people, the existence and character of God – or, rather, how they conceive God’s existence and character – are critical, sometimes even literally life-and-death, issues.  I have never heard of anyone descending into black clinical depression or committing suicide because their estimate changed of Franz Schubert or Stan Getz or Benjamin Britten as artists.  religious_tolerance symbol startBut I do know of people – in fact, I am one – who did struggle for many years with severe, even pre-suicidal, levels of depression as a result of an existential crisis – a “dark night of the soul”, if you will – precipitated by a changing perception of and belief in / about God.  I doubt that anyone ever entered a “dark night of the soul” because they stopped liking or became bored with Stan Getz’s tenor-sax riffs.  From that standpoint, and for them, God is anything but one of William of Occam’s superfluous hypotheses.  Why?  Because, unlike people like me, for whom God is indeed thus superfluous, they are playing an altogether different “forensic game”, a game called “staying alive and healthy”. That is why an attitude of religious tolerance is absolutely critical, not only to the health of individuals but to the health of entire societies.  For the sakes of others, if not just for our own sakes, we would be well advised to be sufficiently skeptical or our own religious convictions to allow others room to exercise their own.  God may no longer be critical to ensuring the coherence of the world, but God is very often critical to ensuring the coherence of others' worlds.  Occam's Razor counsels us to dispense with superfluous hypotheses.  But it does not give us a universal rule for determining, on the basis of each individual life, which hypotheses are superfluous and which are essential.

(c) 2013 James Cowles



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