by Arthur Boyer
By this, I don't mean flaws in reason or to demean the value of rationalism. My intention is only to point out a fatal flaw in purely formal rationalistic thought. My thesis here is that, sometimes, pure rationalism can lead us to absurd conclusions, which must be discarded if we cannot correlate them to physical reality as we know it. I will refer to Zeno's Paradoxes and Parmenides' doctrine of the unchanging nature of being as erroneous results of this kind of reasoning. My argument is that rationalism must always be balanced by a respect for empirical observation.
As an example, consider the way we use mathematics to solve a problem. The following problem makes use of the real–world application of quadratic equations, taken and paraphrased from a standard algebra textbook Intermediate and Advanced Algebra (p. 913):
Instead of using the hallways, students are wearing a path though a planted quad area to walk 195 feet directly from the classrooms to the cafeteria. If the length of the hallway from the office to the cafeteria is 105 feet longer than the hallway from the office to the classrooms, how much walking are the students saving by taking the shortcut?
The two hallways and the shortcut form a right triangle with a hypotenuse 195 feet long. We will use the Pythagorean theorem to solve this problem.
If we let x = the length (in feet) of the hallway from the classrooms to the office, then let the length of the hallway from the office to the cafeteria = x + 105 feet. Substituting these lengths into the Pythagorean theorem, we have:
a2 + b2 = c2
Substitute x for a, (x+105) for b, and 195 (feet) for c we have: x2 + (x + 105)2 = 1952
The textbook proceeds to solve this problem after finding the value of (x + 105)2 using the quadratic formula. At the end of all this calculation, we arrive at these two solutions:
x = 75 and x = –180
But since the length of the hallway can’t be –185 feet, this solution is obviously discarded.
This happens often when using quadratic equations to solve real–world problems. Our mathematics, though flawless because it follows formal rules of mathematical logic, leads us to one conclusion that is impossible when we try to relate it to the physical world. We cannot have a negative number of something (some actual object). Because there is no physical referent for this value, we must discard it; it is nonsense.
My conjecture is that this can occur in any formal science/philosophy that is purely rational. How do we discriminate between real and absurd solutions? We relate our solution to the external realm. This allows us to eliminate untenable ideas. The same could be said for Zeno's Paradoxes, one of which being that motion is impossible. His formal rationalist method leads him to this conclusion. However, because it does not relate to the physical world as we experience it, the conclusion must be discarded. What is the nature of these inherent flaws? Why do formal systems produce these? I wouldn't venture at an explanation now—I'd rather leave the issue to greater minds.
But it is incontrovertible, I think, that formal reasoning can lead to nonsense. In such cases, we reject conclusions uncorroborated by external reality. For this, we must give in to realism when it comes to the external world, as opposed to idealism or subjectivism. The world cannot be in our minds, but possesses a reality distinct from us. Otherwise, we cannot discern facts from opinions and to do this we must take for granted an independent external reality.
Now I am curious of something else. How often is Quantum Theory guilty of mistakes like these? When one interpretation claims a malleable reality determined by us, is it perhaps guilty of failing to eliminate the untenable solutions? The ones that do not correlate to the physical world? Does it mistake abstract concepts without physical referents as having empirical content when they don't? The Many–worlds interpretation posits an existing universe for every possible event. A parallel universe is unverifiable and unfalsifiable. The concept of a parallel universe has nothing existent to refer to. If it exists, it must be of the universe and presumably, this universe. Of what else that "exists" could we possibly conceive? Immanuel Kant (rightly) acknowledged the limits of human knowledge, when he said in his Critique of Pure Reason that an object outside of time and without spatial properties cannot be meaningfully conceived of. A parallel universe separate from our own falls under the category of meaningfully inconceivable things. If our formalism leads us in this direction, are we not then to discard the conclusion in favor of a better one?
I cringe every time I read an article about “observer effect” or potential realities, or a subjective universe generated by our mental faculties. Why? Because this all seems like the thinking of a purely mathematical mind. Instead of rejecting the untenable solution that we cannot correlate to observable reality, they drift off into imaginary worlds doing metaphysics, where every possible solution is a separate reality in itself, and equally plausible. This leaves the door open for physicists (who are so mathematically inclined) to believe that the observer him/herself must be the one to determine which reality is “true.”
“Truth” then becomes a subjective idea, relative to the observer. This relativistic doctrine results as a rationalistic failure—the failure to objectify our rational conclusions by relating them to empirical observation—the real scientific method (not the sorry state of metaphysics to which some of our present day “physicists” have succumbed). Our mathematics is only as valuable as its empirical content, when it comes to describing the physical universe. Now, I am a firm admirer of mathematics and its ability to deduce truths unempirically as well as its power to describe the physical universe. In no empirical science can we claim that proof is possible for our theories, yet in math we find razor sharp logical proofs everywhere. That is amazing to me. Einstein expressed this sentiment when he said:
One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
(1923, Geometry and Experience)
Einstein knew that mathematics, as a formal science, contains no empirical content. As a formal science, this elevates above the empirical science in terms of verifiability and proof. The laws of math never change, regardless if empirical facts do.
However, we must remember that math—in and of itself—is independent of empirical facts. All mathematical statements are analytic—meaning we do not have to relate them to experience to verify or validate them. (I am rejecting Kant's assertion that mathematics are based on synthetic a priori reasoning, a priori reasoning that is somehow related to experience.) We do however have to relate these statements to empirical facts when we are using mathematics as a tool, an accessory, to explain them. If the error is not in the math, it may be in how we interpret that math. We use experience, for example, to determine that we cannot have a negative number of something. And so we discard the solution.
I read this article in the Huffington Post recently and was amused by the M.D. who likes to play philosopher. He writes:
There is no way to remove the observer—us—from our perceptions of the world ... In classical physics, the past is assumed to exist as a definite series of events, but according to quantum physics, the past, like the future, is indefinite and exists only as a spectrum of possibilities."
If we, the observer, collapse these possibilities (that is, the past and future) then where does that leave evolutionary theory, as described in our schoolbooks? Until the present is determined, how can there be a past? The past begins with the observer, us, not the other way around as we've been taught.The observer is the first cause, the vital force that collapses not only the present but the cascade of past spatio–temporal events we call evolution.
“The past begins with the observer, us.” Forgetting the fact that I nearly choked on my banana and peanut–butter snack when I read this, I wondered in what sense Dr. Robert Lanza is using the word “past.” I wonder, too, if he is even aware of what sense he is using the word in. By “past” does he mean actual physical events that took place on this earth before Homo sapiens?
The word “past” can potentially refer to two things: a concept, as in a mental record of events; or the actual events themselves. In either case, the events no longer exist presently (since they are not occurring at this moment). An event is not the same as a physical object—it is defined according to the time at which it occurs and usually has a defined beginning and an end. Physical objects in science are defined by their visible physical boundaries, and can exist across time. If an event, by contrast, is not currently occurring at exactly the moment it is being observed, we can’t rationally state that it “exists.” Past events do not exist. We may be tempted to say that the nonexisting past is determined by the observer—and in some sense, we may be correct in saying this. However, we cannot confuse the concept of past with actual events that once occurred. This is the error theoreticians like Lanza make. Because the past no longer exists, the human conceptual idea of past can be altered as often as necessary, but we cannot relate this concept to actual events rationally, since those events no longer exist in the sense we have defined and our knowledge of how those events really occurred is questionable. If we were not present when it happened, we have no certain knowledge of the event (and, indeed, even if we were present during the fact, our observation might still be questionable). The observer can alter his/her conceptual version of the past as often as s/he wants. Then go ahead and say this observer is the “first cause” of it—sure. But this cannot relate in any way to the events (which no longer exist).
There is a fundamental rational gap between our theoretical or conceptual interpretation of the past and those events in themselves, precisely because they no longer exist. Is this any reason to deny the autonomy of external reality? I can’t imagine why.
Even with a historical record we could never have certain knowledge of past events in the way we can with present events. And so ideas about past events seem up for grabs. But the solipsistic attitude of Dr. Lanza and those like him that the actual past events are determined by the observer is a ridiculous grant of too much authority to the human animal, simply because we are conscious. Whether we were conscious now or not, the events that have occurred will have still occurred, just as events occurring at this moment would proceed with or without our conscious awareness of them. When you stop paying attention to your breathing, your heart does not cease. When you’re not aware of bees in the spring, they’re still flying around pollinating flowers. Do you need to be there? No. Yesterday, a man somewhere in the world murdered his wife. Were there an infinite amount of possibilities that were “collapsed” by someone’s observation?
There is no need to deny an observer–independent reality when we realize the rational mistakes that lead us in the opposite direction. It is much more prudent to assume the autonomous existence of external reality. I think that this will allow scientists not only to simplify their theories, but to remove the metaphysical excess that has grown on them like a fungus. In real science, the simpler theory is the preferred. But how can we even know the simpler theory if we’re not first aware of the choice?
A number of potential realities are claimed to “exist,” yet theoreticians like Dr. Lanza are using the word as incoherently, incorrectly, and inconsistently as other Quantum theoreticians. It is because of this line of thinking that these theoreticians have departed from real science. If it exists, then we say that it is. If it does not exist, then it is not. It is irrational to say that an object both exists and doesn’t exist at any given time. This is not science. If we aren’t speaking in mythological terms, and I assume that is not the intention of scientists to do so, we can’t be allowed to speak like this. Errors like these in Quantum theory are due to a simple overlook of the very basics of rationality. If these are corrected, I would hope that Quantum theory (or something similar) could open up new scientific vistas into the realm of subatomic particles without nonsensical metaphysics as a byproduct. First, however, physicists must be made aware that they are making these fatal errors.
I hope to see less of this thinking in the future, but I know I’ll only be disappointed. Metaphysical, pseudoscientific thought (sometimes blended with New Age spiritualism) is a growing trend and, to me, unlikely to fade out any time soon. Whether a true science of the universe can be salvaged from this wreckage of bad science remains to be seen.
Thanks for reading.