Spring Cleaning For The Mind: On `Proof,’ Part I

by Jonathan Tennenbaum

 “You have to prove your case…” “Demonstrate to me on my own terms, that what you say is right…” “Where are your facts? Give me the hard facts!” “I agree with you, but my wife…” “That sounds exaggerated. How can you be so sure?…” “Why should I believe you? I heard something different from my friends and high-level contacts!”

Most arguments tend to be a waste of time, because they avoid the really sensitive issue, underlying everything else: What does it mean to KNOW something, as opposed to merely having an opinion, belief or strong impression? And how is actual knowledge communicated? By what sort of deliberative processes might human beings arrive at shared, valid judgements of reality? What is the authority, by which a scientist (for example) might uphold a truth, otherwise regarded as obviously wrong or absurd by the overwhelming majority — or even every single one — of his colleagues?

At first glance, the mathematical notion of “proof”, as historically associated with Euclid’s elements of geometry, would seem to provide an {ideal} model of rational argumentation on any subject. According to this method, one first seeks to identify, as a “common denominator” and foundation for argument, those most elementary propositions and facts, as are acknowledged to be self-evident and true by all thinking persons. Then one seeks to reduce all other truths to those elementary ones, by means of logical deduction.

Unfortunately, most people nowadays lack even a rudimentary acquaintance with the old-fashioned treatment of Euclidean geometry as a lattice-work of theorems deduced from a set of definitions, axioms and postulates. They are thereby deprived of a most useful means, with which both to conceptualize the devastating fallacy of deductive notions of knowledge, and to grasp the LaRouche-Riemann correction of that fallacy.

Accordingly, I propose to approach the problem, this time not through geometry per se, but with reference to the practice of political organizing, whereby the issues of “knowledge” and “proof” are posed again and again, on a daily basis.

The trouble starts, typically, when the organizer asks himself or herself: “How do I CONVINCE this person to do [what they should do]?

This almost instinctively leads to the question: “How do I acquire the necessary AUTHORITY to move the mind of this person?” Having difficulty locating his or her INTERNAL authority — and Lyn’s authority — in a rigorous process of discovery of universal principles, the organizer tends to fall back on a dangerous ruse: To appeal to the purported authority of certain, strongly-held beliefs and opinions in the minds of the people one is attempting to organize, as the basis for eliciting agreement with the proposed proposition

In other words: the organizer wittingly or unwittingly adopts, as the standard of “proof”, that which public opinion accepts as “convincing arguments” — RATHER than those processes, by which reality can actually be made known to the cognitive processes of the individual, sovereign human mind. This inevitably leads, in the form of argument too commonly practiced nowadays, to the following parody of formal deductive method:

1. Select a set of basic, commonly-accepted concepts and a set of basic propositions, which appear so self-evident, that they are generally regarded as true beyond any doubt (or at least taken to be so by the person you are trying to convince!). This selection of concepts and “self-evident truths” plays a role analogous to the set of definitions, axioms and postulates in Euclidean geometry.

2. Now formulate the proposition you wish to “prove,” in terms of the adopted system of basic concepts, fulfilling the demand of your interlocutor: “to express your point in terms I can understand.”

3. Supplement, as required, the array of “basic, self-evident truths,” with a complementary array of “facts” — perceptions of events, as expressed and interpreted in terms of the given basic concepts, axioms and postulates, and having a comparable, self-evident quality of “hardness” and authority. “Facts” of the form, typically: “I heard him say it myself,” “I saw it with my own eyes, on television,” and so forth.

4. Now construct a (more or less rigorous) chain of deductions, showing that the proposition you are putting forward is a logical consequence of the given array of “basic truths” and “hard facts.”

5. Now tell the person: “You see! My proposition is a theorem of the postulates and facts, whose authority you accept. Therefore you must accept what I am saying.”

A bit of honest reflection, will show that the mode of argument, used by most people most of the time, does indeed converge on a parody of the mathematical-deductive method, along the lines just sketched. And, when this method fails to achieve the desired result — as it most often does fail, and in a deeper sense ALWAYS fails –, then we tend put the blame on the “irrationality” of the person we are arguing with, or on a purported lack of a sufficient arsenal of “hard facts” to back up our argument. Yet, the essential folly was on the organizer’s own side.

In the spirit of “spring cleaning,” let us look more carefully at this purported solution to the dilemma of “proof.” A very simple observation reveals a devastating fallacy — a fallacy of such incredible virulence, that it can bring down entire civilizations!

The very nature of a DEDUCTIVE argument (by definition!) is that it systematically EXCLUDES from consideration, everything except the original array of definitions or concepts, axioms, postulates and purported “facts” — the latter being framed on the basis of those same, generally-accepted concepts and axioms. Our argument was confined entirely to the “virtual world” of our interlocutor’s concepts and assumptions. At no point did we ever address reality itself! At no point did we oblige, or even encourage our interlocutor to actually DISCOVER anything about the real world!

We were arguing as if at a blackboard, in a room without windows. The very form of our argument was such, that no universal physical principle could EVER be discovered or otherwise known by such means. To the extent we “succeeded” in convincing our interlocutor, we actually perpetrated a fraud. Because, the “agreement,” thus elicited, is purely accidental and has occurred in the absence of any real process of cognition.

All this brings us to an agonizing paradox: If we cannot base ourselves in the authority of generally-accepted, “self-evident” truths, then what can we start with? What do we do, when, in the now-typical case, our interlocutor’s basic axioms are incompatible with every essential principle of reality, as these have become known to us, above all through the work of Lyn?

Archimedes reportedly once said: “If you give me a lever and a place to stand, I can move the Earth.” Our task, indeed, is to move the Earth. Where, then, shall we stand?


“Science is a manifestation of action in human society…. One cannot know a scientific truth by logic, but only by life. ACTION is characteristic of scientific thought.” –Vladimir Vernadsky

In the first installment of this discussion, I set forth an elementary paradox, arising constantly in political organizing, and which might be restated in brief as follows:

In the course of arguing any point with a person, most of us have a nearly instinctive tendency, to seek for some commonly-shared, fundamental beliefs, values or opinions — plus commonly-accepted “hard facts” — as a basis for an essentially deductive “proof” of the point we are arguing for. But, what if the person, we are arguing with, seems to have a completely opposite set of basic assumptions?

Sometimes, in this situation, organizers resort to a clever, but ultimately disastrous form of cheating. They think to themselves: “This guy here has some beliefs and opinions which are totally opposed to our axioms. He will freak out if I show him what LaRouche really stands for.

“So let me find some a couple of specific issues where he will agree with us.” In other words: avoid a confrontation on the axiomatic level, by carefully selecting a small {subset} of theorems derived from “LaRouche’s axioms,” which happen at the same time to be theorems in the other guy’s axiom-system, or at least to be {consistent} with the latter — even though the two sets of axioms are themselves mutually inconsistent!

Of course, the “common ground” secured this manner, is entirely spurious, and can fall apart at any moment. But exactly for this reason, it becomes a trap for the organizer foolish enough to have cheated in the first place! For, the unfortunate organizer now has a stake in maintaining the illusory “agreement,” and attempts to constantly “screen” the contact from any direct confrontation with what we really stand for. The result is profoundly demoralizing for everyone involved.

Only {apparently} opposite to the indicated tendency, is the “super hardline” tactic, typified by: “No compromises! If the guy doesn’t agree with then hang up on him immediately!” Either way, we are avoiding the real issue, which is how to confront and {change} the fundamental axioms of thinking in another person.

Before returning to our organizing situation and a proposed solution to the paradox, let’s stop to clarify in our minds the crucial distinction between a fundamental axiom, and a mere isolated opinion or theorem.

The characteristic of a fundamental axiom or principle of thinking (they signify essentially the same thing, in this context) is, that each such axiom or principle implicitly shapes the {entirety} of our thinking. A change in any axiom implicitly changes how we think about each and every other object of thought. To put it another way: such principles, imbedded in our mind as singularities in the form of fundamental ontological assumptions, shape the entire {geometry} of our mental processes. All other ideas, opinions, judgments etc. are determined by that geometry, but do not determine it.

What determines the outcome of a person’s action upon the Universe, is not the apparent, literal content of his or her individual judgments and opinions per se, not positions on this or that issue, but the geometry of their mental processes as a whole. And that geometry is what we are acting upon, with greater or lesser success, when we organize.

But is it really possible, in a fundamental sense, to change people’s minds in such a profound way? When we attack our own and others’ nagging doubts on this account, an epistemological monster invariably pops up in front of us: the Kantian paradox, in one or the other of its countless reincarnations. For example: If “the way a person thinks,” the form of conciousness, is given {a priori} — as “pure reason,” inborn and prior to all experience — then it would seem to be unassailable and impervious to any fundamental change. For, all a posteriori evidence, including our attempts to argue with the person, will simply be interpreted within the given geometry of the mind, without having any effect upon that geometry. (“I am as I am, so you can’t change me.”)

But if, on the other hand, there is no “pure reason,” but the fundamental axioms of thinking are a more or less arbitrary product of our upbringing, education, environment, etc. then where is the standard of truth? How could we ever know anything for sure? (“All judgments are relative. My opinion is as good as yours.”)

Now, as a matter of fact, the history of religious beliefs and cultures generally, as well as the historical development of physical science, demonstrates beyond any doubt, that sweeping changes in the pervasive “geometry” of human mental processes {do} in fact occur — both in individual persons, and in entire societies. They occur all the time in periods of rapid, generalized scientific progress, as typified by the Golden Renaissance.

On the other hand, we have direct experience, in recent decades, of a process of rapid cultural degeneration, which is not a consequence of this or that wrong opinion, but rather the result of negative changes in the sets of fundamental axioms underlying practically all cultures of the world.

Not only do such positive and negative changes occur, but (as LaRouche has demonstrated in most devastating fashion) they are, in every known case, ultimately the result of conscious intentions.

But changes in the prevailing axioms of society, have {physical} effects, effects that are manifested in gross terms on the historical scale of the rise and collapse of cultures and civilizations. These same effects are {measurable}, on even much shorter time-scales and more precisely, by the methods of physical economy. The possibility of judging, measuring, and forecasting in advance, the net impact of alternative choices of fundamental axioms of thinking, on the power of entire societies to maintain and improve their physical existence per capita, is inseparable from {cognition}. By correlating the measurable physical effects produced by successive such choices, with the quality of the human mental processes — implicitly reproducible in our own mind — which generate either positive or negative series of choices of axioms, we can judge the relative truthfulness of those mental processes, their degree of agreement with the laws of the Universe.

The Kantian paradoxes pop up, automatically, when the implications of cognition are ignored.

Now reflect on the quoted statement by Vernadsky. Take the case of a creative scientist, discovering a new universal physical principle. What is the subject of the discovery? Not a so-called “objective physical Universe,” not an object “out there,” supposed to exist as if independently of human activity! No! The creative scientist is deliberating on his or her own {thinking processes}, and those of his colleagues and society generally, with a view toward correcting or improving upon those fundamental principles that govern our thinking about how we act upon the Universe.

The judgment validating the discovery takes the form of an {inequality}: the demonstration, that the discovery of a superior principle, and the accompanying modification of the aggregate array of pre-existing principles, implies a {higher} potential rate of increase in Man’s per-capita powers to command the Universe, than was previously achievable. In the simplest case, the inequality is satisfied by detecting and correcting a systematic falllacy in our way of thinking about the world.

This is our model of a non-deductive “proof”: proof by {discovery}, proof by {improvement}. The ultimate criterion is not {logical} in nature, but {moral}: advancing the common good of Mankind.

To the extent we can account for the geometry of our mental processes, as the accumulated effect of an ordered series of such discoveries of improvement of geometry — each of which can be qualified as a discovery of universal principle relative to our own action in the world — then our knowledge and practice becomes fully intelligible in the form of a self-subsisting Riemannian manifold. Only then do we really know what we are talking about. Then we can {prove} what we know to any person, who is willing and capable of reenacting, in his or her mind, the process by which we came to know what we know.

Now turn back to our organizing situation. The preceeding train of thought points to a radically different approach, than the failed, pseudo-deductive procedure we examined in the first installment of this series.

First: don’t waste time on theorems, but get at the axiomatic issues immediately, by the least-time path. Use theorems only as vehicles to address the axioms. Second: “prove” by bringing people to discover how their own mental processes become more powerful, the world more intelligible and their ability to change it, stronger, when they adopt a superior axiomatic standpoint to the demonstrably flawed one, they held up to that point.

Somebody might retort: “Surely you don’t mean we have to go through all that epistemological stuff with our contacts! We have no time for that.”

But someone might think we had a lot of time to waste, considering the woefully low efficiency of much of our organizing, and the sheer man-hours expended! The most decisive thing to be conveyed, can be conveyed as if in an instant, by little more than a happy shift in attitude or mood on the part of the organizer. This is nothing unknown to an experienced organizer: we do succeed, part of the time. The problem is, to do what succeeds, {all} the time.

So, instead of getting tied up arguing the truth or falsity of proposition

, consider something like the following:

“Look, the reason you get taken in by the kind of nonsense you are telling me now, is, that you never studied what LaRouche has to say about the difference between human beings and animals.”

“What do you mean?”

“You voted for Bush (or Gore), didn’t you?”

(A moment of embarrassment.)

“Well, in view of what has happened to us all, as a result of that kind of mistake, wouldn’t you agree, that the difference between Man and beast should be the key issue in all politics?”

“Fantastic! I never thought of that.”

Contrary to Kant, the form of conciousness is not a God-given, fixed entity. It is subject to deliberate improvement, by our God-given powers to organize!