Quantum Infinities Spinning on the Head of a Pin
by Mark Goldblatt (November 2011)
If you like intellectual satire, and don’t mind shooting fish in a barrel, the last four decades in the humanities have been a hunter’s paradise. The advent of postmodern gibberish has given rise to a new and exceptionally preposterous species: the bluff academic. Literature professors, art historians and gender scholars now scatter their conference papers with howlingly nonsensical references to Einstein’s Theory of General Relativity or Heisenberg’s Uncertainty Principle in order to wow their gullible peers. So, for example, the renowned feminist critic Luce Irigaray asks, “Is e=mc2 a sexed equation? Perhaps it is. Let us make the hypothesis that it is insofar as it privileges the speed of light over other speeds that are vitally necessary to us. What seems to me to indicate the possibly sexed nature of the equation is not directly its uses by nuclear weapons, rather it is having privileged what goes the fastest . . .”
For the record, she’s not kidding.
Careers have been made cataloguing and ridiculing the pretensions of humanities professors who wade guilelessly into the jungles of cosmology and quantum physics. Maybe, though, it’s time to consider a related phenomenon: math and science geeks who hurl themselves headlong into ancient epistemological and theological disputes armed with evidence from differential equations, particle colliders and satellite telescopes.
The need to address the phenomenon—let's call it Slide Rule Dilettantism—was driven home recently after Reason.com published an essay of mine titled, “Theology is Dead.” The piece wrestles with a number of gnarly but age-old metaphysical questions: the limits of human reason, the problem of actual infinity and the existence of God. The conclusions, I think, are provocative—click away if you’re curious—but the reasoning isn’t new. I’ve argued the case several times before in specialized philosophical journals. The Reason.com version was an attempt to bring the argument to a wider audience.
Within twelve minutes of its publication, respondents were unloading on the 5000 word tract. That much, I anticipated; I’d been warned by Reason’s editor that it would rile up his readers. What I didn’t expect was that the criticism would center not on the conclusions but on the premises—specifically, on my saying that the laws of identity, non-contradiction, excluded middle and causality were universal: “No human being has ever lived, no human society has ever existed, that did not accept and rely upon the validity of the laws of thought; they are the foundation of reasoning and knowing.”
That statement provoked derision and outrage. By contrast, it would be taken for granted by the vast majority of credentialed philosophers—with the miniscule minority consisting of sad cases who’ve drunk the multicultural Kool-Aid. According to Reason.com readers, however, the laws of thought were decidedly not universal. Their proof?
Many of the more vociferous objections came from respondents who claimed to be well-versed in subatomic physics. Consider the photon, they argued. Observed one way, a photon acts like a particle; observed another, it acts like a wave . . . so there goes your law of identity! Then there’s the matter of particle spin. Until it is measured, every elementary particle has a spin that is both up and down simultaneously . . . so much for your law of non-contradiction! You’ve also got the phenomenon of quantum superposition . . . so wave goodbye to your law of excluded middle! Lastly, there’s quantum entanglement, in which an effect, at least from one perspective, seems to precede its cause . . . so adios to your law of causality!
The naïveté of such responses shouldn’t have caught me by surprise because you do occasionally hear this sort of epistemological hogwash from the halls of science. Take, for example, the recent declaration by Stephen Hawking, the world’s most famous theoretical physicist, that “spontaneous creation is the reason there is something rather than nothing, why the Universe exists, why we exist.” Weaving together the latest insights from string theory, gravitational theory and—wait for it!—quantum theory, Hawking concludes, “The universe can and will create itself from nothing.”
If there’s nothing—to note only the most howling flaw in Hawking’s logic—if there’s literally no thing, then there’s no universe to create itself. But even allowing that a miniscule speck of something, or some thing, ends up big-banging into the universe, you still have to account for that change from speck to world. A speck is what it is, and it will remain what it is absent a causal force acting upon it; so say the laws of identity and causality. Blaming the Big Bang on a quantum fluctuation or a super-string vibration gets you nowhere because you still need a cause for the fluctuation or the vibration. The mathematical peculiarities of theoretical physics do not constitute exceptions to the laws of thought.
There are no exceptions, none whatsoever, to the laws of thought. Nothing—literally, no thing—is exempted. No matter how distant. No matter how exotic. No matter how teensy-weensy. And you don’t have to fill up chalkboards with arcane math to arrive at that truth.
Let’s begin with an observation, which should be uncontroversial: Science is rooted in logic. If you can’t do syllogisms, you can’t do equations. You’re not getting through the front door of the lab unless you realize that if x = z, and y = x, then y = z. Or, as philosophers like to say, if all men are mortal, and Socrates is a man, then Socrates is mortal.
The first three laws of thought—identity, non-contradiction and excluded middle—are even more basic than syllogisms. You can’t deny their validity without assuming their validity. If I say, “The laws are universal” and you say, “The laws are not universal,” is it possible that we’re both correct? (No, and that’s the law of non-contradiction.) Is it possible that we’re both incorrect? (No, and that’s the law of excluded middle.) Is it possible that we’re both saying the same thing? (No, and that’s the law of identity.)
Here’s another way to think about it: Suppose I put forward a truly heinous proposition such as “Hitler was a man who benefited all people.” Your natural response will be to cite the genocidal persecutions of Jews, Slavs and homosexuals waged by Nazi Germany under Hitler’s leadership. You cite those examples in order to establish the contradictory of the proposition I put forward—in other words “Hitler was not a man who benefited all people.” What I assert, you seek to deny. You know instinctively that the two contradictory propositions, the assertion and the denial, cannot be held simultaneously. You’re relying, in short, on the validity of the law of non-contradiction. Thus, the moment you can convince me of that Hitler was not a man who benefited all people, I’m forced to abandon the proposition that Hitler was a man who benefited all people.
The laws of identity, non-contradiction and excluded middle are the in-here laws of rational thought and language. The law of causality, the fourth law of thought, is the link between the in-here laws and the out-there world. The law of causality explains how identities can evolve yet endure as identities, the reason you can step in the same river twice; it says that for every change, or effect, there must be a cause that accounts for it. Things don’t change without something causing them to change. (Indeed, another way to think of the law of causality is as the law of conservation of identity.) The cause of a change may not be known, but it must be supposed; if identities can morph by themselves, then no statement about the extramental world is possible, or even meaningful, because nouns are static and the extramental world is in flux. You cannot talk about things which cease to be themselves as you speak. The only way to account for the endurance of identity is to presuppose that every change is tied to a cause.
None of this is novel. Philosophers have hashed out these issues for millennia, with the last serious challenge coming from Hume, who argued that when we speak of causes and effects we falsely concoct a necessary relationship between things that regularly occur together. Our mind says causality; the world says mere contiguity. Hume’s rejection of cause-effect relationships is flawed—as Kant took great pains to show. For our purposes, however, let’s just say that Hume won’t go over well in the lab since his account of causality would render empirical science null and void.
Which returns us to Reason.com readers’ indignation at my statement that the laws of thought—including the law of causality—admit no exceptions. Without recourse to Hume, the respondents fell back on the alleged topsy-turviness of quantum mechanics to prove that the laws of thought were by no means universal. Here is where Slide Rule Dilettantism comes into play. The problem is that scientists, even brilliant ones, are often bad epistemologists. They tend to climb out on limbs and want to saw off the branches they’re sitting on. It’s true that there’s a raging debate among physicists about whether causality holds in the quantum realm. So let me settle it for them: Yes, it holds. I say this with total confidence because the debate isn’t really about causality but determinism—whether a complete mathematical description, if it were possible, of the conditions of a subatomic particle would allow an observer to predict the future state of that particle. The answer might well be no; there might be no possible mathematics to make such a prediction. But the fact that you’ve hit a mathematical dead end doesn’t mean the change occurs uncaused; there is still some causal force behind it.
Mathematics describes forces but is not itself a force. If I drop a penny from the top of the Empire State Building, mathematical formulae can tell me where it will be and predict how it will behave at a given moment; but mathematical formulae are not causing the penny to fall. Gravity is doing that. We may not know, and may never know, the nature of the force that governs the behavior of subatomic particles—call it the Quantum Fairy if you like—but there is a force operating on those particles, causing those probability equations to work out. There’s a force beyond the law of averages—which, again, is a mathematical description, not a causal agent—ensuring that order emerges out of apparent randomness. You can take that to the bank.
The irony is that physicists are more than happy to reason this way in other contexts. For example, they speculate that “dark matter” must exist to account for the state of the visible universe, and then go looking for it, because they know there must be a cause for every observable effect. Yet utter the word “quantum,” and all bets are off. Ancient priests ridiculed the quest to find causal connections, invoking divine will as the solution to all mysteries—the so-called “God of the Gaps”; modern physicists echo them now with the “Quantum of the Gaps.” Can’t come up with a cause for subatomic behavior? No worries, that’s just quantum strangeness for you! Except causality is science. It is the sine qua non of science. Having shimmied out on the limb of particle physics, physicists want to saw off the branch of causality that got them there.
The same goes for the laws of identity, non-contradiction and excluded middle. These are your axioms, your bedrock certainties. So, for example, saying that a particle’s spin is both up and down until it is measured doesn’t violate the law of non-contradiction. If you said the particle’s spin was both up and not-up simultaneously, that would be a violation . . . but in that case, you’d just be saying something about the particle and then unsaying it. Saying that the spin is up and down until it’s measured just tells me that the spin is temporarily indeterminate—potentially either but actually one. It tells me that the math is still up for grabs. The quantum realm, in other words, isn’t a logic-free zone. “One cannot get around the assumption of reality,” Einstein wrote to Erwin Schrodinger in 1950, and reality is “independent of what is experimentally established.”
Subatomic particles may be paradoxical little devils, fiendishly hard to pin down, but nothing about them rewrites the laws of thought. They are what they are, and they’re not what they’re not. If your equations lead you to the result that they are what they’re not—if, in other words, your conclusions force you to abandon your axioms—you’re screwed. It’s time to climb back down the tree and start over.
Mark Goldblatt teaches religious history at Fashion Institute of Technology of the State University of New York. His lastest novel, Sloth, was published in 2010 by Greenpoint Press.
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