Appendix - Zeno & Humpty Dumpty

Zeno seems to be the first philosopher/mathematician to formally address the inherent dichotomy involved in viewing a continuum in terms of elements composing it. The explanations and the "resolutions" of Zeno's paradoxes that I have seen miss the point. As soon as Zeno's paradoxes are seen to be particularizations of the postulate that the "whole" is somehow greater than the sum of its "parts", it then becomes apparent that he was right. There is a dichotomy between the "pure thoughts" and the "real world" they attempt to represent. There is an implied "limit" on all rational thought, which leads to an unequivocal conclusion that all rational theories are "incomplete".

I have attempted to get at this dichotomy in essentially two ways: first, by establishing a point of demarcation between rational and mystical thought, and second, by "defining" that point of separation as the result of the necessary requirement of conscious thought to have a focus of attention. While doing that, I took care to point out that even though not emphasized in rational thought, mystical elements cannot be entirely removed; they are retained, if only in the form of "meaning" and "intuition". I also tried another way to ameliorate the "incompleteness" of any rational theory by suggesting that a different focus of attention would yield different limits and different insights, which could then be combined to form a more complete, "unified" theory of knowledge. I even went so far as to suggest some methodology to accomplish that objective.

I have already admitted that I still learn in childish ways. Fairy tales and nursery rhymes are frequently intended to teach some important lessons. Children do learn from them even though the insights they learn are not always those intended. In that spirit, I will propose that the "Humpty Dumpty hypothesis" is equilavent to the one proposed by Zeno. Humpty Dumpty, a personified egg, just fell; all his parts were still there, yet he was no longer the same. The sum of all his parts was not equal to the "whole" Humpty Dumpty. Was he no more? Could he ever be again?

All the king's horses and all the king's men couldn't put Humpty Dumpty together again! Why not? Is it because they just didn't know enough? After all, years ago, if a "part" like a finger or a limb were separated from the other parts of the the body the parts could not be put together again either, but today, with increased medical knowledge and surgery, they can be. Perhaps, in the future, Humpty Dumpty could be again, if someone were willing to try hard enough - to learn enough - to put the parts together.

What is the lesson to be learned? Is it that the haphazard disruption of the integrity of a "whole" into its parts leads to a chaotic "mess" that makes it difficult or impossible to reconstruct the integrity of the "whole"? Or is it that once the integrity of the "whole" is disrupted by a separation into "parts" - no matter how haphazardly or carefully that might occur - the "whole" no longer exists and can never be put back together again?

It is hard for me to believe that anyone can seriously accept the second "lesson" or conclusion. Sure it's true that the "whole" no longer exists as a "whole", but all its parts are still there. It is just ignorance or a lack of knowledge or ability that could prevent a reconstruction of the "whole". Perhaps with a more careful separation into its parts with care being taken to observe how the parts are connected to form the "whole", enough knowledge and ability could be attained to reconstruct it.

What is harder to believe is that there are many examples in literature and philosophy that take that second conclusion a step further. Not only is Humpty Dumpty no more, not only can he never be again, but also it is now questionable that he ever really was, except perhaps as a figment of the imagination. Certainly his past existence can no longer be used as evidence for anything that can be today or in the future.

Isn't that silly? Or is it just me?

What is even worse than that and even harder to believe is that someone could propose such a "lesson" as "philosophy" and actually be considered to be a "philosopher" by succeeding generations.

Hume and Descartes

Let me give just one example. I am going to "pick on" David Hume (1711-76) for several reasons, some of them personal. Perhaps, for the sake of intellectual honesty alone, I should give a brief explanation of why I consider Hume's position to be an insult to the integrity of philosophy, as are some of the mathematical "proofs" of impossibility.

I had mentioned previously that I had quit college to write a book when I realized that I was a philosopher rather than a student of philosophy or psychology. Of course, that book began as a philosophy of psychology. It was never published, and I am probably the only one in the world who thinks that it was important. I returned to college to get a B.A. in philosophy primarily because I thought it would be the easy way to get that piece of paper that everyone seems to think is so important. After all, I already was a philosopher; I should have no difficulty understanding other philosophers.

Well, it didn't work that way. I am pretty confident that I understood the philosophers I read, and could easily define the limits of their positions, point out some of their errors, et cetera. The problem, it seemed to me, was that the teachers I had did not understand what philosophy was really about and misconstrued much of what the philosophers had to say. To be able to pass the courses and get my degree, I had to avoid doing any of the required readings so that I would have only one layer of misconceptions to deal with = that of the teachers.

In my first course in philosophy, the first two philosophers studied were George Berkeley (1685-1753) and David Hume, in that order. I was impressed with Berkeley, and despite the limitations of his position, which he himself carefully established, I would certainly classify him as a philosopher. Then I read Hume. My first reaction was that Hume was short for Humor. His work must have been included in the textbook as comic relief. Perhaps his work was included to show - as I intend to do here - how an otherwise intelligent man could fool himself to believe utter nonsense. To my amazement, his work was considered serious, valid philosophy. He is actually considered to be a philosopher. I am still amazed.

I realize that it is not really reasonable to hold a grudge against someone who died long before I was born. Perhaps he led a sheltered childhood and never heard of such things as Humpty Dumpty or of points that could see beyond what they could see.

I have more practical reasons to "pick on" Hume, because his arguments undermine some of the foundations of rational thought. Basically, Hume analyzed the "causal relation" (the "whole") by separating it into its parts of "cause" and "effect". He then severed the causal relation by replacing it with one he called "constant conjunction" by showing that knowledge of what was called "causes" and "effects" was dependent on the experiences of the "constant conjunction" of one followed by the other. His analysis is beautiful. He was a very keen observer. Then he went too far.

Because mistakes could be made - because an "effect" could be ascribed to a wrong "cause" (whether by faulty observation, poor judgment, or coincidence) - he concluded that the causal relation was untenable. It could not be believed. It could not be used to explain observed phenomena. It did not exist. Conclusions based on a "necessary" relationship of "cause" and "effect" could not be believed because all that was left was the ("unnecessary") relationship of the constant conjunction of "A" followed by "B".

Since "logical reason" is based on "necessary" relations that are abstract analogs of "causal relations", truth (the "whole") could never be known with certainty; all that could be known with certainty were the experiences themselves (the parts). His position is called skepticism.

Lest I be accused of misconstruing his position, I shall include a definition of Humism found in the second edition of Webster's New Twentieth Century Dictionary, unabridged:
"Humism, n., the system of ideas or teachings of David Hume, Scottish philosopher whose skepticism restricted knowledge to experiences and impressions and denied the possibility of ultimately verifying their truth."

Can someone who is skeptical even of the thinking processes that lead him to such a conclusion really be believed?

If the causal relation (Humpty Dumpty) is separated into its parts of "cause" and "effect" (yolk, white, shell) and if those parts cannot be reconstructed (neither Hume nor all the king's horses and all the king's men could do it), then the causal relation is no longer the same (Humpty Dumpty is no more), and the causal relation can never be used again (Humpty Dumpty will never be again), and the causal relation never really was (Humpty Dumpty was only a figment of the imagination), but the parts can be used to establish a new "whole" of "constant conjunction" (an omelet with shells?).

If there are no causal relations, then why should scientists search for the "laws" of nature? If laws could cause no effect on a society, why bother to pass them? If hunger is not a cause of eating, why do I feel so upset when I try not to be bothered by such a petty detail?

If there is no faith in the ability to find truth with rational thought, then what's left is mystical contemplation, which might be a tenable philosophical position, but to be consistent it would have to exclude the use of reason in the process. All that Hume might have proven is that human nature allows men to have doubts that could stand in their way of knowing the truth. After all, Hume does show, in his analysis, the power of reason to ferret out the mistakes of ascribing wrong cause to the wrong effect. He shows the causes of doing so, then denies the power of reason to be able to do what he has already done.

His (Hume's) position on moral philosophy is an analog. He analyzes the moral imperative implied in the term ought and concludes that the moral philosophers ought not use the terms ought and ought not.

It may not be reasonable, but I guess that I do still hold a grudge against him and his followers. Hume should have known better. He was an educated man. Rene Descartes (1596-1650) had already established the most natural basis of the certainty of knowledge that is, and must be, the product of reason. Hume, being an educated man, should have been aware of that work, which had already been around for over a century. Yet instead of using his obvious talents, his keen mind, powers of observation, and analytic ability in order to build on what was already known, he ripped out the foundation, then - rightly concluded that no edifice of truth could be built by reason without such a foundation. I feel sorry for all those otherwise intelligent people he duped. Maybe I should feel sorry for him, too, since he confused and confounded himself as well.

Descartes' postulate is so simple it is truly beautiful. It has been so badly misinterpreted by using it out of context, especially by some of the "existential philosophers", that I will simply state it and then drop it like a "hot potato". I shall merely include a parenthetic comment in its restatement to re-establish the proper context so that the undistorted, intended meaning is clear.
"I think; therefore (I know with certainty that) I am.

It would not be so bad if the distortions and perversions of the pseudo-philosophers were restricted to disputes in ivory towers. Unfortunately, such distortions and perversions have a way of filtering down into everyday life.

One way they do that is by the contamination of the language that is used in the course of human affairs. The sociological effects, though subtle, can be profound. Such distinctly human "effects" can best be seen in terms of "values" that are "caused" to "shift" in relation to the various purposes of human activity.

Purposes, goals, or "ends" of either an individual or a society are derived from "moral imperatives", i.e., what each believes "ought" to be.

The "moral imperatives" are derived from the "logical imperatives", i.e., what is necessary to maintain consistency and order.

The "logical imperatives", in turn, are derived from the "natural imperatives", i.e., the "laws" of nature that "govern" the universe, e.g., "cause" and "effect".

Or is it the other way around?

It seems that the "processes" indicated here are two way relations with "feedback". Thus today's purposes are both effects and causes at the same time; they are the effects of yesterday's experiences and actions and the causes of today's actions and experiences. Today's actions and experiences are in turn causes of tomorrow's goals, actions, and experiences.

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