© Avi Sion, 1990.

This essay was written in 1990. It does not necessarily reflect the author’s current viewpoints. (It was not included in the 1996 revised edition ofFuture Logic.)

Story ofFuture Logic.

My purposehereis to trace the story of the book,Future Logic, for the record. Since I believe the book to be a major renovation of the science of logic, which hopefully, G-d willing, will become very influential, it seems important to specify for historians how it actually developed. I hope that my doing this is not taken as evidence of conceited self-display; my spirit is more one of ‘getting the facts straight’. Additionally, the topic is interesting for logicians, because it presents a case-study of the development of logic in an individual.

1.Early Influences.

2.5 Years = 20 Kilos.


4.Getting It Together.


1.Early Influences.

Education in logic may well date from early childhood. Even if the parents, and surrounding society, make no effort to instill intellectual processes in the child, it seems bound to absorb from them attitudes and ways of thinking, which may be characterized as ‘logical’. From the example of my parentsz”l, I learned the nobility of honesty, to avoid anger (a lesson I did not always find easy) and be reasonable and cheerful, and cleanliness and orderliness (to be methodical). School, of course, inculcates logical reasoning, though it unfortunately rarely does so in explicit terms. I was good in mathematics and science, but also enjoyed art and subjects like English, geography and history; I was maybe above average, but nothing special. However, apart from such general influences, I do not detect in my own childhood any predilection to logic.

My interest in a conscious, rational approach, was only sparked at the age of sixteen, upon reading an novel by Ayn Rand calledAtlas Shrugged. This Jewish-American woman’s writings were for the next five years of my life very important to me. I read all she and her associates wrote, and many of the books she recommended. My father, while not discouraging those youthful interests, often counseled me to avoid naive and dogmatic positions, not based on personal experience of life; my mother expressed concern with the hardening effect these doctrines had on my character.

I have not read any of Ayn Rand’s writings in over twenty years, having soon enough become disenchanted with many of her positions on various subjects. Also, looking back I see that her influence on my thought and life has not always been beneficial. Nevertheless, I must also recognize retrospectively that some of her attitudes and ideas were positive influences, and be grateful. These include such values and virtues as: search and respect for facts, rationality, thinking things out, thinking for oneself, awareness of goals and means, relating thought and action. On the negative side, I gradually realized, was a certain self-destructive narrowness and rigidity; positions sometimes overly defensive and extreme. But nobody is perfect, and one must still acknowledge the good points.

Ayn Rand complained that most modern philosophers, academics and educators, and indeed a large segment of her society and culture (she passed away in the mid-70’s, if I am not mistaken), had virtually abandoned Reason as a value (936-993). It may be that this complaint stuck a chord in me as a Jew, because I was at that time studying the Holocaust, in such books as Leon Uris’Exodus, William Shirer’sThe Rise and Fall of the Third Reich, and even Jean-Paul Sartre’sReflexions sur la question juive.Scary stuff, needing explanation and corrective measures, which she seemed able to provide.

This impelled me to study logic, reading the books on the subject recommended by her. I read H.W.B. Joseph’sIntroduction to Logic; I can still recall the pleasure it gave me. I read most of the works of Aristotle, with great admiration. I read W. Windelband’s histories of philosophy. Later, books (whose names I have forgotten) by Albert Einstein and others, popularizing the ideas of Relativity and Quantum Mechanics, taught me more about the methodology of modern science. Those few authors were my main sources of information concerning work done in philosophy and logic as such, though I have doubtless over time gleaned material from other sources.

2.5 Years = 20 Kilos.

I was preparing to study mathematics and physics at university, but gave up the plan when I saw that I was already developing my own ideas in writing. Over a period of some five years, from 1969 to 1974, I accumulated some twenty kilos of manuscript. I was a young immigrant in Canada, in my early twenties. During the day, I worked on various odd jobs (white-collar, service, hard-hat), and at nights or on weekends or in-between jobs, by myself at home, I would think and write. I read relatively little and had virtually no contacts with intellectuals or academics.

My starting point was logic, but this gradually, inevitably, led me into epistemological and ontological issues, and attempts to formalize ethics. At the end, only about 10% of my work was in formal logic. These notes and essays are the backbone of the present work. This was independent research, not a restatement of the work of other authors. I knew I was doing well whenever, to my consternation as you can imagine, I found out that something I had discovered by myself had already been dealt with by some modern logician or philosopher.

My treatment of Aristotelean logic and elementary hypothetical logic was based on Joseph’s presentation, though I preferred a more bare-bones approach. My definitions of the categories and types of modality (which I called modalities and modes, at the time), were based on Aristotle’s philosophical analyses; but much of the formal work on modal categoricals was new. The discovery of categories and types of conditioning (other than the well-known ‘if-then’ form), and the concept of basis (in contrast to connection), as well as the ensuing development of the logics of these various forms, were entirely original. I also at that time sketched a novel theory of generalization and particularization (which however turned out to be too simplistic), on which my more recent efforts are built.

As my knowledge of logic and philosophy progressed, I looked on Ayn Rand’s work more and more critically. I found it to be deficient in both form and content. Perhaps because of my training in mathematics and physics, all too often her definitions seemed imprecise and her proofs not so rigorous. She was not herself a formal logician, although her ‘Stolen Concept Fallacy’ is an important contribution, which certainly motivated my inquiry into the formal logic of paradoxical propositions (I was not aware until later that modern logicians had done some work in this area).

Nevertheless, her absolute faith in the cognitive powers of the human mind, and in our ability to know reality, still puts her high in my esteem. Her heart, in this respect, was certainly in the right place, as far as I am concerned. Were it not for that strong message, and her romanticization of the independent thinker, it is doubtful that I would have gone into logic research. She set for me the general goals; but with regard to the details of epistemology and ontology, I very soon branched out on a separate path.

Gradually, thanks mainly to Windelband’s presentations, my respect increased for all philosophers (and for the university establishment, for that matter); I could no longer view them according to her negative stereotypes. They were not irrationalists or anti-rationalists, but people like myself doing their best in the pursuit of truth. Though I did not agree with everything they all said, I could well see that there was some truth and value in everything each of them said. Each new perspective, each new insight, is an earnest offering to the whole enterprise — and in my view, they could all be reconciled, and shown to complement each other.

Perhaps best summarizing my position at that time is the statement I read recently, by Hintikka, that ‘to understand everything is to pardon everything’. In addition to this generous and constructive viewpoint, I came to see the truth of the saying that ‘the wise man is he who knows that he knows nothing’. Indeed, it is this perception of the infinity of Truth that finally blocked me, and caused me to stop writing. There was no end to it. I could sit down anytime and think new and seemingly important thoughts on the subject. Improvements were always possible. I could not publish my work, I was too much of a perfectionist, too immature to control my creativity.


In the last year or two of that early period of writing, I had become interested in religion, which stresses action over thought. Influenced by the youth around me, I first looked into Buddhism, Hinduism, and Taoism, and was highly impressed by the profundity of their understanding of the indefinable aspects of the world and of consciousness, in comparison to Western philosophy. Oriental philosophy offers a very sophisticated world-view; and it succeeds in giving a credibility to mysticism, which transcends the fixed parameters of Western philosophy. Although the latter seems on the surface like a freer and more rational enterprise, it imposes certain bounds on itself. Also, contrary to what one might expect from mystics, they produce very consistent systems of thought.

Still, in the last analysis, the impersonal atheism (not to mention elements of idolatry) in these religions put me off. I later read the Christian Bible and the Moslem Koran, but as a Jew was not personally very enchanted by them. My interest in Ayn Rand had by that time of course completely disappeared, because of her naive view of spiritual life, as ‘mysticism’ and antithetical to reason. In my view, these could be harmonized, and indeed were complementary. Nevertheless, Ayn Rand’s strong influence on my work remains undeniable; my faith in the efficacy of reason and the ultimate objectivity of human knowledge comes from her.

Thereafter, I got seriously involved in Judaism, which seemed to me even more profound, because of (among, needless to say, many other reasons) the complexity of its logic, its greater willingness to accept loose ends and apparent contradictions. This may seem like a paradoxical statement, coming from a practised logician, but I had learned the creative value of problems and the naivety of pat solutions. Judaism, because of its complex merging of the intellectual and spiritual aspects, required a degree of openness and humility, of self-suppression, which to me was the hallmark of truth and wisdom; existence is ineffably deep and complex.

Anyway, I stopped all philosophical writing at that point, telling myself that I would resume in later years, when I got some further experience of life. I remember thinking that Aristotle had managed to write his works quite late in life (in his sixties, if I recall rightly).

In the course of the next 10 years, I worked as a statistical researcher, for the World Health Organization in Geneva and Copenhagen, and the American Jewish Joint Distribution Committee in Jerusalem. I learned epidemiological study methods, mainly through research relating to oral health, onchocerciasis control, gerontology, early childhood, and social work. I also traveled a lot — in some thirty countries, in Europe, North America, Africa and Asia.

This naturally aroused my interest in global problems like hunger, and caused me to think about political-economy issues and search for a consistent social philosophy. I traveled from Randianlaissez-fairegradually through to Marxist ideas; but I soon enough returned to more balanced views. I was also influenced by the back-to-the-land ideas of some of my generation; this motivated me to resume my formal education about five years ago, and to study agriculture till I got a B.Sc. My thesis proposed certain statistical indices of agricultural productivity, with a view to rationalization of land-use patterns.

My interests are now much more abstract. My thought is: G-d is in charge of things, and economics and politics are subsidiary to the moral law — so there is no need to get so worked-up. Also, a few years of marriage ending in divorce, somehow taught me that time flies very quickly and one is well advised to use it wisely. I therefore set precise self-improvement goals for myself, and pursued them relentlessly.

4.Getting It Together.

Experiencing the pleasure of goal-directed learning as an adult, encouraged me to return to philosophy, and write this long-discarded book on logic to begin with, as a Ph.D. dissertation for Pacific Western University, of Los Angeles, California. My advisor was a certain Dr. Simeon Wade, Professor of Humanities (Ph.D. Intellectual History, Harvard University).


In January of 1989, I rented a small cabin on quiet and natural Denman Island, B.C., Canada (the Extreme West, as I like to call it), and got to work with sustained discipline, writing full-time for the next year-and-a-half, living off my savings. The existence today of personal computers, and excellent word-processing programs, was also a big encouragement. Without these technological advances, I may never have been able to take up such an (for me) enormous task.

I had only to go back to my old notes, and type them out. That is true of most of the deductive parts — modal and conditional logic. The parts on class logic and inductive logic, and on the history and philosophy of logic, are new, though I had long ago very briefly considered a theory of factorial analysis. Note that the latter is to some extent influenced by Jewish logic. I have to admit that I did not work as hard as I should have; I should for instance have taken the time to read Aristotle’s works all over again, in order to be able to trace his influences on my past work more precisely: but it just seemed like too much to take up at once.

Incidentally, on a personal note, all this writing and reading, particularly the computer, considerably weakened my eyesight. Also, I smoked a lot, though occasional walks by the sea and Tai Chi exercise seem to have kept me healthy. My social life was reduced to a minimum, but solitude can be very reposing. I worked, ate and slept in one room, with windows on all four sides, surrounded by Nature — trees and mountains, birds and deer. The days seemed like mere hours, the weeks like mere days.

My broadest motive in writing this book was, simply, that I was given a gift of knowledge as a youth — I thank G-d for this kindness — and a good thing should be shared. I was also motivated by, to be frank, a very human ambition for respect; I felt that, to be at all heard by people, it was necessary for me to demonstrate my credentials in a big way. On a higher level, I think it important to combat atheism, and in particular its current expressions as anti-Semitism and anti-Zionism; I strongly believe that these phenomena are, at least partly, products of illogical thinking.

In any case, 15 years of life experience, out in the world, away from my ivory tower, made me realize that logic is indeed a virtually abandoned subject. Some claim that ‘today logic is taught at almost every university, and for many courses it is a compulsory subject’ (New Enc. Brit., 23:250), but my own impression from interviews with people is that universities give their students only token grounding in it, if any. It seems to be effectively considered a specialized field, of little interest and value to other sciences or the humanities. It is significant that, to my knowledge, no university grants the title of Doctor of Logic; expertise in the field is not seemingly recognized as a distinct profession.

In any case, the daily spectacle of muddled thinking by the media, politicians, and the general public, is evidence of shortcomings in the educational process. In short, I perceive a need for logic at this time. I suspect that the loss of general respect for logic today may in large part be due to the symbolization of logic, pushed to an extreme during this century. The science which was precisely supposed to guide everyone into clear thinking has become double-Dutch to most people, myself (I admit shamefacedly) included. I mean, who nowadays has the spirit of patience needed to decipher that stuff? An effort is of course required of the reader, but the material should be presented in recognizable form.

I have told the story of this book in so much detail to make a point. Most of the work presented in the preceding pages consists of independent discoveries by a young man, with little academic training and a limited knowledge of what other logicians have contributed to the field since the beginning of this century. These facts could be viewed negatively, as terrible methodology — one should know the state of a science before venturing to improve it. But I prefer to see the positive side: ignoring a segment of history may be likened to traveling in a time-machine.

Modern logic took off at the beginning of this century on a certain course, and its achievements have been undoubtedly enormous. But another tack might have been taken, and it is interesting to compare the results. They might overlap partially, but there are sure to be valuable differences. Every change of perspective brings in its wake its own special effects. For this reason, before typing out my notes, I made it a point to avoid any external influence. I decided: first develop my own theories, and only thereafter compare them to other people’s. That is why you will find few scholarly references in the course of this book; only in the last few chapters do I consider the historical context.

In fairness to myself, I could not have proceeded otherwise. I find it very difficult to read other people’s theories, without almost immediately being sent off on tangents of my own. It is not a fear of ‘infection’ or that I am overly critical; rather, my mind is too quickly stimulated by very little. Had I been more fully acquainted with modern developments, I would probably have been convinced that the subject was exhausted, and not have bothered doing my own research, and not made certain novel discoveries. Adding a detail here or there does not give me much satisfaction; I need to believe that what I do is somehow important to be sufficiently motivated.

After reading theNew Encyclopaedia Britannicaarticle on logic, I went back through my previous work, and rewrote or edited much of it, increasing it by about 50%. Having more information on the mainstream views about logic, made it possible for me to comprehend the concerns of my colleagues, and address them in their own language, as it were. I learned a lot from their work, and it stimulated in me new ideas. The theory of class-logic was one of the results of this additional research. Also, my definitions of logical modality and understanding of the role of the laws of thought, had to be much improved to satisfy the rigorous standards of contemporary logicians.

Note that my ideas concerning space-time, phenomena, universals, the nature of consciousness and the structure of the mind, sense-perception and recognition — these date mostly from way back, although I did not refer to my old notes in writing them. However, they were also influenced by my later spiritual studies. A further layer, the last quarter of the book, the historical and critical perspectives, was based on additional readings. I was obliged to focus on more academic issues to defend my thesis, but I did not always enjoy that work; still, in retrospect, it taught me a lot.

The reader will judge for him or her self whether my attitudes and approach paid off. I see the results as felicitous. Of course, no man knows it all, and perfection is always beyond our grasp; what is important is to try and improve things somewhat. The beauty of logic is its relevance to every other field of human endeavor, and I look forward to seeing what (hopefully positive) effects this attempt to invigorate the subject will have on other disciplines and on society in general, over time.

I want to finally mention the role played by my religious convictions in this whole effort. Writing this book was a job that had to be done sooner or later, and it has been for me a‘tikkun’, a rectification, a repair.

Stopping my logical and philosophical researches some years ago had thankfully liberated me from the fatiguing tyranny of words and endless reasoning, and let me get on with my life. However, in time, my Judaic studies seem to have brought me back full circle; Judaism has a high regard for words and logic, while at the same time it arms one against their excesses. Especially, it keeps one more humble, and more flexible. Also, I have found that Jewish tradition is rich in ideas unknown elsewhere, so that it always gives a Jew additional perspectives on things. One always stands a bit outside, even while being well inside.

And of course, my practise of the religion has given me more peace of mind, optimism, strength, and understanding, and thus enabled me to pursue my life’s goals more effectively. Daily prayers and Torah-study gave me patience and courage; and the rest and beauty of the weekly Shabbat revived my exhausted energies and inspiration. The Jewish holy days, which I celebrated with the Vancouver and Toronto communities, were also very regenerative.

Thank You, Dear G-d, for Your Kindness to me.


**Pacific Western University in Californiawas at the time a reasonably well-respected distance learning establishment, which though not accredited was authorized by the California Education Dept. to grant degrees based on its study program. I enrolled in it on the basis of the recommendationgiven to it by John Bear, an expert on higher education, in one of his books, and in view of the fact that my advisor was going to be a Harvard Ph.D. (Dr. S. Wade). Moreover, I personally visited the PWU campus on Sepulveda Blvd. in Los Angeles, and met with the aforementioned professor, to assure myself of the validity and value of this educational institution. I followed the study program and received the coveted degree after about two years, based on my doctoral dissertation “Future Logic”.

PWU in California, is not to be confused with the universities with the same namein Hawaii and in Louisiana. It “operated from 1976 until 1990 as a [California] State Authorized Degree granting institution. In 1990 California law regulating private colleges and universities began to change. These laws required that all private colleges and universities in California become California State Approved under the newly formed State of California Bureau for Private-Postsecondary and Vocational Education (BPPVE). Schools were given several years to make this transition. Pacific Western University in California was granted Candidate status as a California State Approved Institution in January 1991 and maintained this Candidate Status until it became California State Approved in 1996. From 1996 through 2005 Pacific Western University in California maintained this State Approved status. In that year the University’s assets were sold. The new ownership formed California Miramar University (“CMU’).”

For more on the history of PWU in California, see:http://educationservices.us/faq.html.