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I heard once of a miracle the like nowhere else could be found.
It happened, I'm told, in France, where the ridiculous consorts with the profound.
Out of nowhere appeared Rene Descartes, a philosopher of some renown.
As hungry as you might expect, he went to the restaurant of Ronald the clown.
Lo, he contemplated the menu for to find a suitable repast.
"I think I shall have a hamburger," said he, "to break my centuries-long fast."
"Would you like fries with that?" the clerk said. He merely asked and did not insist.
After musing for a moment, Descartes proclaimed, "I think not." and promptly ceased to exist.
If we want to create a Rationalist physics, then we have an obligation to use the minimum of axioms in addition to those that underlie our mathematics. But how can we choose those axioms? What criterion can we apply to produce all of the axioms that we need and only the axioms that we need? I believe that we can do no better than to follow the example set by Rene Descartes.
In 1637 Rene Descartes (1596-1650) published his famous "Discours de la Methode", in which he laid out, step by step, his method of reasoning out problems in philosophy, in natural philosophy (as science was called then) in particular. He intended to transform philosophy from the analysis of ancient texts into the application of reason to the solution of problems. He no longer accepted "The Ancients knew everything" as his basic assumption, but rather, as we Americans like to say, "There's a reason for everything."
Descartes' made the application of doubt, of refusing to accept statements about Reality purely on trust, the first part of his method. Through the use of doubt he hoped to remove from consideration those propositions that he could not support logically, for which he had insufficient evidence. Descartes applied doubt so radically that he doubted not only other people's reports of what's real, but he also doubted the evidence of his own senses (he was, of course, engaging in a purely philosophical exercise; Descartes did not allow his method of doubt to interfere with his daily life). At the end of that exercise Descartes reached the conclusion that the only fact about Reality that he could not doubt was his own existence; after all, he reasoned, he must exist in order to doubt his existence. We usually express that conclusion in the Latin statement, "Cogito; ergo, sum." (I think; therefore, I exist), though Descartes wrote the original in French.
Using that conclusion as a self-evident axiom, Descartes attempted to deduce the laws of Nature. Unfortunately, he was not as strict with the rules of reason as he should have been (in some ways he was still reasoning as the Schoolmen had done, giving words more power than they actually have), so his results came out wrong. In fact, Isaac Newton (1642-1727) showed that they were wrong. In his Philosophiae Naturalis Principia Mathematica, in which he laid out his three laws of motion and then worked out the law of gravity, Newton showed that Descartes' vortex theory of planetary motion contradicted Johannes Kepler's third law of planetary motion. But Kepler had inferred his third law (as he had inferred his first and second laws) by induction from actual observations of the planets' motions interpreted through Copernicus' new model of the solar system. Because, as Francis Bacon required, observation trumps speculation every time, scientists discarded Descartes' theory.
In part Descartes failed because he didn't know what the product of his deductions was supposed to look like. Galileo had only begun the mathematization of the most basic physics and the only natural laws known in anything like the modern mathematical form were the laws of planetary motion that Johannes Kepler had only recently worked out. The law of gravity had not been discovered yet; there were no mathematical laws of electricity and magnetism; the nature of light and the nature of matter were matters of the purest speculation heavily constrained by theological considerations. However, over three centuries have elapsed since that time and scientists have learned a great deal more about the nature of Reality. We know what the result is supposed to look like, so, like the fellow who works jigsaw puzzles while looking at the picture on the box (that would be me), we can cheat. Thus, I believe, the time has come to create a Rationalist physics of the kind that Descartes sought.
Let's begin with Descartes' cogito. I know that I exist because I know that I think. But what do I think? What passes through me that I call thought?
My thinking comprises a continuous (so far as I can tell) series of images, most of which appear to give me information about a world that exists outside me. Can I say for certain that such a world, called Reality, truly exists? How can I know the answer to that question?
My thinking has an aspect that may help us. As each thought passes through me I pass a judgement upon it. I decide whether the thought feels good or bad to me. Hearing Bedrich Smetana's "Vltava" (The Moldau) gives me great pleasure and makes me feel good. Seeing pictures of Nazi concentration camps makes me feel bad. To the greatest extent possible to me I listen to Vltava far more than I look at pictures of Nazi death camps and I make such an effort in order to satisfy what I call my desires.
In order to satisfy my desires I seek to maximize the good thoughts that pass through me and to minimize the bad thoughts that pass through me. But if I exist alone, if I comprise all that exists, then I must create all of my thoughts. And if I create all of my thoughts, then all of those thoughts must conform to my desires. Thus, I can infer that if I comprise all that exists, then I will have only good thoughts.
But I do have bad thoughts. I have thoughts that conflict with my desires. Because they do not conform to my desires, these thoughts do not come from me; therefore, they must have come from something not-me. But in order to provide me with thoughts that something not-me must exist, so I infer the existence of a thing or things other than me.
To sum up that proof by contraposition we have the following syllogism: P implies Q. We have not-Q; therefore, we must have not-P. If I am all that exists, then I create everything. I do not create everything; therefore, I am not all that exists.
I now assert that I cannot be separate from that something not-me. If I were separate from it, then it could not affect me. Thus I must be part of that something that gives me thoughts (percepts). I call that something Reality. And I call the thing reflected in the thoughts that Reality gives me the Universe. Now I want to know what I can say about that Universe, what I can assert about it, put to a proof, and verify as true to Reality.
I can assert that the Universe comprises more than one object. As proof I offer my knowledge that the Universe comprises at least two objects - me (who has thoughts) and not-me (which gives me thoughts).
If more than one thing exists, something must exist to distinguish those things; otherwise, they would exist as the same object. What can I say about that distinguishing something?
1. It must clearly distinguish not-me from me.
2. It must allow not-me to give thoughts to me.
3. It must not give me thoughts itself. It must exist purely as a medium for the conveyance of thoughts as percepts.
4. It must accommodate all objects and all changes in distinction that actually exist.
We must thus have a void continuum with one simple property - extent. Thus we must have space, in which all things exist.
My analysis of my thoughts tells me one more thing about the nature of Reality. I know that I have a thought and another thought and another thought and so on. I can call having a thought an event, something that happens. But I can distinguish thoughts, one from another, and I can thus distinguish events, one from another. We can call what distinguishes events from each other time. As one wag put it, time prevents everything from happening all at once.
We thus infer that we exist in a Universe that comprises objects that exist in space and act out events in time. Further, we can infer that an object can occupy one position in space at one instant of time and then occupy a different position in space at another instant of time. If Reality did not allow that statement to come true, then events would not occur. So Existence has so structured Reality that objects can have motion.
I must admit that the reasoning in this essay seems weak in places. But I believe that as the Map of Physics evolves we will find ways to remove the weaknesses and to strengthen the logic to create a solid axiomatic foundation on which the Map of Physics can rest. I believe that we will eventually prove clearly and verify firmly that the mere fact of existence necessitates the Map of Physics.
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