The theoretical system developed by our research group demonstrably and verifiably opens up a new domain of human knowledge. As of this date, it amounts to approximately 50 person-years of innovative work. In the following four pages, let me tell you something about the background, the increasing rigor, and the further promise of this inquiry.
Since 1963, the work has gone through at least three distinct developmental stages:
- My earliest paper on this topic (1963) presents a theory of human behavior, stated in ordinary scientific English, but based on known premises which no one else had successfully used in this way. In a paper presented before the International Conference on General Semantics in 1965, I extended this theory of human behavior into the arena of large social institutions. Also, I made logical claims for the doctrine: self-consistency, and parsimony. When I gave the paper, I found myself applauded rather than shot down.
But while still at that conference, I came to an uncomfortable insight: I recognized that at that time, no one had yet specified the relations between logical assumptions and grammar for even one discursive language. That means that any discursive language remains in the role of "a language of unknown structure." Further, I recognized that one cannot know a doctrine better than one knows the language in which one states the doctrine.
Therefore, my theory lacked rigor—as long as I left it stated only in a discursive language such as English, I could not back up logical claims made for it.
I left that conference determined to perform a logical analysis of my doctrine, and to state it as an axiomatic system in a mathematical language of known structure. I intended to satisfy myself as to whether one could in fact back up the logical claims I had made for it.
- Working with John F. Randolph, then Fayerweather Professor of Mathematics at the University of Rochester, I succeeded in doing the required logical analysis. We wrote four long papers which utilized an algebraic set theory notation—the very paradigm of "a mathematical language of known structure"—to put the doctrine into the form of an axiomatic system.
At that point, we had something really new: a logically rigorous and empirically testable theory which comprehensively accounts for how a human deals with himself, with his non-living environment, with other humans and (in principle) with other species.
To call the theory comprehensive means that one can use it to study "happenings" on any level of interest, from that of molecular structure—e.g. the structure of heme molecules with various possible side chains, only a few of which have a shape that will allow the ring to combine with divalent iron so as to form the active center of a hemoglobin molecule—up to that of how the human species as a whole gains its living in the biosphere.
In 1969, the Journal of Theoretical Biology printed three of these four papers. That, too, created something of a stir—we received more than 1200 requests for reprints of one or more of these papers.
Meanwhile, I had what mathematicians refer to as a "new toy"—an empty form composed of empty set theory symbols, devised originally to account for the behaving-and-experiencing of individuals—and I set about finding out what else it could do. I successfully applied it to a number of topics: small group phenomena; large social systems; biological theory. I even made some trespassing ventures into the physical sciences. Eventually, I began using it to focus on the topic of the foundations of logic and mathematics. And at that point (fall 1971), I began developing another uncomfortable insight.
- The difficulty centered about a possible contradiction between the "content" of the theory and the notation in which I expressed this "content"—a collision between central premises. To express this difficulty, I will need to state the setting ("universe of discourse") for the developing theory, its central tenet, and the contrary of this central tenet.
- I can express the setting for this developing theory by means of a run-on phrase such as an-organism-as-a-whole-dealing-with-its-environment-at-a-date. When one defines a notational theory on a setting, one restricts discussion to the topics which fit onto that setting—thereby preventing oneself from unknowingly getting off the subject.
- I can express the central tenet of the developing theory in terms of the construct of an organism making a distinction or discrimination—expressible by a sentence such as "This IS NOT that!" In a world of ceaseless change ("-at-a-date"), this sentence appears valid in general.
- To express the contrary of this tenet requires the construct of our organism not-making a distinction, expressible by a sentence such as "This IS that!" In a world of change, this sentence appears never valid. Indeed, by the common definition of the term mistake (Old Norse, "to take wrongly"), whenever an organism non-verbally TAKES some non-verbal this as if it WERE some other non-verbal that, he makes a mistake.
- translated the findings of the set theory calculus of human behaving-and-experiencing into the new notation, obtaining a general theory of social systems;
- developed a "numbering theory," a "personal geometry", and a "notational physics with physicists in it";
- provided evidence suggesting that we humans can now encompass the physical, biological and human psycho-social sciences within a single frame of reference, based on a single set of postulates. This possibility seems to me to exceed the dreams of the seekers after a unified field theory in physics.
Let me paraphrase these simple-sounding phrases into more pretentious logical terminology: Where, in dealing with his environment, an organism non-verbally TREATS this as if it were that, in effect he posits the identity of this and that—he errs fundamentally; where he non-verbally distinguishes between them, he posits their non-identity—in that respect, he does not err.
Then the central postulate of the developing theory requires that, on this setting, we disallow the construct of identity (or the binary relation of identical with) in any guise or form, explicit or tacit. In the developing frame of reference, the construct of identical with has no usage except to designate situations in which somebody makes a mistake. In discrediting the construct of identity, I explicitly extend the designated realm of error to include the case in which our organism posits the identity of this with this (or of A with itself). The construct of self-identity conceals the claim that we KNOW what we have perceived and designated as A—knowledge we do not and cannot have.
To take the rejection of identity as one's central postulate does not lead to paralysis or aphasia. Instead, it strips away the pretense to delusional "knowledge," leaving us ready to act on our assumptions.
However, this central tenet MIGHT contradict the modern logical axiom of identity, which states, "For all x that belong to the delimited domain D, x is identical with x." Thus, in the mathematical theory of sets, one cannot dispense with the construct of identity: for, by postulate, every set qualifies as identical with itself.
Hence, I feared, there might exist or arise a contradiction between what my theory SAYS and the notation in which it says it. At this point, I can prove that such a contradiction does arise; then, however, I could only sense it as possible and feel sick to the stomach over it.
Eventually (Christmas 1971) I concluded that, so long as I continued using the mathematical theory of sets, I left myself no way of avoiding or otherwise handling that possible contradiction. So I resolved to abandon set theory, and all other formalized or discursive languages from the Western Indo-European (WIE) tradition, and to devise my own.
To shorten an already-lengthy story, in the spring of 1972, I made a fundamental discovery. It concerns the assumptions encoded, within WIE languages such as English or set theory, in the grammatical distinction between noun and verb. Briefly, we tell the nouns from the verbs by regarding any noun as identical with itself, and regarding no verb as identical with itself. By the same token, we regard that which we designate by a noun as also self-identical (really existing, persisting, static-and-unchanging), and that which we designate by a verb as also not-self-identical (somehow transient). In the WIE pattern, one obtains a "complete sentence" or a "well-formed formula" by placing at least one noun or noun-phrase next to at least one verb or verb-phrase. Thus, regardless of our intentions, regardless of whether we noticed or not, every time we form a complete sentence in a WIE discursive language or a well-formed formula from a notational language, we posit at least one static-and-unchanging "thing" which enters into more or less transient "relations." In other words, by utilizing the grammar of the WIE languages, we ACT as if, independent of any observer, that which exists independent of any observer has a structure identical with that of the grammar of the WIE languages.
This discovery opened the way toward the development of the desired non-WIE formalized language. I found a way to disallow the hidden assumption I had disclosed, and, by means of a small number of explicit logical steps, to derive a grammar from my chosen premises.
This too constituted a new development. Humans had never before had a DERIVED grammar to play with, only inherited, traditional ones; although the works of Edward Sapir and Benjamin Lee Whorf predict or foreshadow this development.
About then I started collaborating with the linguist Ronald V. Harrington of the University of Rochester. On this derived grammar we developed a "Let's keep track of what we say" language, analogous to set theory but fundamentally different in structure. As one way it differs from set theory and other traditional WIE notational languages, the developing notation systematically takes into account the observer. In this notation, one finds it impossible to make a statement except from the point of view of "an-observer-observing-the-observed."
Subsequently, we extended the notation, and
At the very least, the new frame of reference gives us an unfamiliar standpoint from which to view, and re-think, human concerns. That alone warrants studying it with care.