More on 1 = 2
7 Oct. 2001/7 Oct. 2010
© Henry A. Flynt, Jr.
For right-handed people. Take a lightweight black rod 15 inches long and a quarter-inch in diameter. (Even better, 5/16 inch in diameter.) Hold the rod vertically, at its bottom, between the middle and ring finger of your right hand, at the near center of your visual field. The background may be a stark white wall. Gazing at the rod and choosing a focus (possibly by default), you determine whether you see one rod or two. It is a perception that has to be resolved in one of two mutually exclusive ways as long as you sustain it. The focus that yields two rods may be of more interest.
At the top of the rod, touch it with the tips of crossed ring and middle fingers of your left hand. Because of the rod’s length, you can get your left wrist and arm out of your line of sight.
With the left fingers, you feel two rods, a famous illusion. With your right fingers, you perceive one rod from two contacts. That is not considered an illusion. These are not choices; they are invariable.
What you see agrees with what you feel in one hand or what you feel in the other hand, but not both. Normally, two of the three avenues will report that there are two rods.
Husserl can try to discover something in the phenomenon that convicts it of illusion, e.g. my right fingers feel only one rod. But if such arguments convince Husserl, it means that he is pursuing the chain of indications as far as he has to go to reach the reality posited in advance by common sense in this civilization. In other words, he demands “long or longitudinal collations.” But that does not help. The collation of sense-data need not converge to the approved answer. “Illusory reports” can be in the majority. You cannot prove that your senses inform you wrongly by your senses.
This evidence shows 1 = 2 to be true to “things” (apparitions). The laws of arithmetic are not true because “that’s the way things behave.” Rather, common sense gerrymanders the apprehension of “things” to make the latter conform to the propositions of arithmetic. Or—there aren’t any things (rods). Things are psychotically deformed interpretations of the sensory stream.
After all, do not forget that whether there is one apparitional rod or two is a choice—and where does choice-making live? Can we tolerate a concept of things in which subjecthood is a component of the thing? All reality is posited dogmatically and transcendently. For amplification, see “Personness II,” etc.
Arithmetic is not about whether the “entities” simultaneously present and being tallied are physically real. If you see two herds of unicorns in a hallucination and add the tallies of the two herds, the result is supposed to obey the laws of arithmetic. You are performing the addition on placemarkers. Whether those placemarkers have things-in-themselves as their essences has nothing to do with arithmetical truth. That is what the mathematicians have been screaming about ever since Plato. The truth of 2 + 2 = 4 does not depend on substantive contingencies like whether soap bubbles burst while they are being added.
Actually, the passage of time may pose a problem for arithmetical truth. That is why mathematics is always done in the “standing now.”
Or to put it another way, even if you were adding two multitudes of soap bubbles and one of the bubbles burst, it would not disprove any arithmetical proposition. All arithmetical truths are relative to a designated “now.”
(Pragmatically, the fact that the counting itself occurs in that annoyance, passing time, has not been investigated.)
If we could not step out of our inconvenient personness and freely partake of “God’s time”—the standing now—timeless time!—there would be no arithmetic. If we did not play head-games worse than any inconsistent world-state in any dream, there would be no arithmetic.
Let me resume with the question of whether the placemarkers counted are evidences of substantial beings. Any demand for substantial beings unlocks a yawning trap door. Substantial beings endure, right? That means that they are emplaced in timeful time, that annoying dimension mathematics wanted to get rid of. A solid body becomes a “log” in four dimensions. (A worldline.) How finely can this log be cut along its length (duration)? Don’t even think about it. Does the log ever “step on itself”? Don’t even think about it.
“I do not guarantee that arithmetic will work unless you apply it to solid, permanent bodies like rocks. I’ll take my stand on solid rocks.” Excuse me, but you have not understood one word of Dr. Science. Do you really think that color exists anywhere but in human mentation? What you call “color” physics knows as the rate of vibration (in the old, pre-quantum optics). Color is an illusion for you because you aren’t fast enough to count the vibrations. And—the same for the rock. It is an illusion for you because you are so low-resolution and so insensitive. Did you really think there was anything like a rock out there, that the rock is anything but your cerebral processing? Dr. Science!
In the traditional language, mathematics presupposes that “now” and eternity are the same thing. Mathematical propositions have no tense. That’s what the mathematicians have been screaming about for 2500 years. That is why mathematicians have delusions of the extra-mundane. That’s why they are starry-eyed, at least some of the time. That’s why physics at the high end loses all pretense of being empirical. (“A universe exists corresponding to each consistent set of laws.”)
The bearing of all of this on my 1 = 2 demonstration is that: the fact that it is for apparitions that I falsify the laws of arithmetic in no way diminishes the falsification. I falsify the laws of arithmetic in the present instant and that is sufficient to falsify them, since the present instant and eternity are the same thing.
Arithmetic is not about whether mundane objects have separable things-in-themselves beneath their appearances. Mathematical propositions are not synthetic a posteriori. Do I really have to say this?
In sum. The lessons cannot be diminished by saying that they are lessons for illusions but not reality. The lessons do not pertain to whether <what is registered as occurring> is real in the external realm of things-in-themselves. The lessons pertain to obligatory relations among the meanings of labels and to the obligatory implications of possible situations and to perceived relations among placemarkers. (Or, to honor the import of the evidence, the obligatory implications of impossible situations.) It is perfectly permissible to use illusions as evidence on the latter points. Just as I can guarantee that: if you ever encounter a unicorn for real, it will be a one-horned beast with its legs positioned like legs in the horse family.