Chapter 10.  Proofs of Theorems

Table of Contents


Proof of Fundamental Theorem


Fundamental Theorem

Immediate Corollaries

Operational Morality



Proof of Fundamental Theorem


Social theorems are never proved as rigorously as theorems in number theory, for example; but my proofs of social theorems are as rigorous as some proofs that satisfy many applied mathematicians.  After all, the idea of a proof is to convince someone that something is true – often oneself.  These proofs are as good as any I have seen in social science. 

Fundamental Theorem

The hypothetical worlds W′ and W″ are described in Chapter 1 and in Chapter 4.

Theorem 1 (Fundamental Theorem).  In W′, a necessary condition for sustainable happiness and, in W″, a sufficient condition for sustainable happiness is the abandonment of materialism.

Note.  Sustainable happiness for all of humanity and the associated conditions necessary and sufficient to attain it were defined in Chapter 1.  The term sustainable happiness has been used throughout this essay.  Unfortunately, the investigation of the sufficiency conditions involves a rather extensive research project to answer four important questions:

1.         Will the population of the earth stabilize?

2.         At what level?

3.         Will the equilibrium population density of the earth be sustainable at an adequate level?  In other words, can we achieve a strong quasi-steady-state economy with adequate abundance for all?

4.         Can this be achieved without coercion?

One of the most important points that I hope to make in this essay is that this research is absolutely necessary.  Someone must carry it out.  Humanity cannot afford to wait until nature determines the answer for us.  By then we may be too far along the path toward extinction to turn back.  It is a proverbial fault of human beings that we wait until the last minute.  We must resist giving in to this tendency in this crucial (perhaps final) case.

Necessity Proof.  The difficult part of the proof is to show that materialism is occurrence equivalent with tyranny, geophagy, and falsity.  This was done in the previous chapter.  But, we must not forget the easy part, namely, to show that sustainable happiness is inconsistent with tyranny, geophagy, or falsity.

In W′, autonomy is a necessary condition for happiness; thus, by definition, tyranny is inconsistent with happiness.  But, tyranny makes relatedness difficult as well.  In W′, to be effective we require intrinsic motivation; i.e., effectiveness depends on intrinsic motivation.  Materialism introduces extrinsic motivation; therefore, effectiveness, which is a prerequisite for happiness, is poisoned.  This is clear nowadays as most people hate their jobs and society suffers from widespread alienation.

Relatedness is necessary for happiness; however, our relationships with persons in authority will be poisoned eventually by the need to prevent them from obtaining information that might facilitate their exercise of tyranny.  Normally, this entails justifiable falsity.  Even seemingly satisfactory relationships between ourselves and people who have or might have authority over ourselves or others are invalid, as they depend upon a misunderstanding or a pretense on the part of one or the other or both.  Thus tyranny implies falsity, which is inconsistent with the relatedness necessary for happiness.  Although the Truth Axiom is not violated, the Freedom Axiom is.  This situation would obtain so long as authority persists, that is, until the last vestiges of authority, in the form of leadership in the modern sense or plain old despotism as it is commonly practiced in employment, in religion, and throughout the world, disappear.  (Of course, we are not obliged to execute a direct frontal assault upon a superior force if we wish to fight another day under more favorable circumstances.)

We have agreed that one of the prerequisites of happiness is safety, i.e., assurance that the other prerequisites for  happiness will not be lost.  Actually, the term sustainable happiness is redundant.  Sustainability is a prerequisite for happiness and as long as geophagy persists we will not have the assurance of sustainability that we require.  This is most crucial.  Also, in W′, it is clear that materialism per se will undermine sustainable happiness directly.  We must consider two economic scenarios:

Case 1 (Scarcity):  In the scarcity scenario, upon which all modern economic theory is based, the losers in the improper “game of life” will be unable to satisfy their own tissue deficits and the tissue deficits of those who depend upon them.  At the present time, we have widespread hunger and malnutrition, which is guaranteed to get worse so long as materialism flourishes.  But, in addition, materialism endangers sustainability not just because of overconsumption but because of under-consumption (deprivation) too.  Desperation, envy, and righteous indignation characterize the normal psychological states of many people.  As fewer and fewer people are needed by the economy we can expect a growing class of people who threaten political stability whether they are in jail or not.  Crimes grow more bizarre and pathological daily, but these are the expected fruits of an absurd economic system that cannot perform adequately for a growing portion of the population that will soon include all but the super-rich.  Among the deeply dissatisfied are college professors, physicians, engineers, scientists, skilled labor, as well as the hard-core unemployed!

Case 2 (Abundance):  Even in the unlikely abundance scenario, materialism (life being an improper game) violates the Truth Axiom because, in our indoctrination in the schools, life is presented as more nearly fair than it actually is, i.e., essentially as a proper game, although the term was not used.  Suppose life were a proper game.  Even in this subcase, the Freedom Axiom would be violated because no one may be forced to play a game when he wishes to do otherwise.  Moreover, how could life remain a proper game when one has to cheat to win?  (The part about cheating is easy to prove by examples and induction.  The proof is in Chapter 8.)

Most arrows in Fig. 9-1, other than those noted below, are for aesthetic or metaphysical purposes only.  The necessity part entails the following steps: (i) showing M  G, (ii) in the energy scarcity case, proving tissue deficits will arise (the plentiful energy case is even worse).  Both cases are covered in Chapter 2, (iii) proving M  T & F  the impossibility of being effective in most cases (as evidenced by the fact that most people would not work at the job they hold if they didn’t need the money).  T & F also account for the bad relationships that make folks callous toward the tissue deficits of others.  All of the above prove that happiness cannot coexist with materialism.  Remember M is (stands for) materialism, T is tyranny, F is falsity, and G is geophagy.

Sufficiency Proof.  Most of the sufficiency part can be managed easily, however we have assumed that tissue deficits can be satisfied despite severe shortages of primary energy supplies and a large population.  To remove the premise about W″ requires that (i) we show population stabilizing at 10 billion or decreasing to the optimum and (ii) we establish the ability to meet the energy requirements of the entire population by sustainable harvesting of biomass (or some other renewable primary energy source).  Calculating our ability to do this is a major research project but cheap compared to any of the Big Science boondoggles.  However, in this version of the proof, we assume that we are in W″; therefore, tissue deficits can be satisfied for all of humanity provided only that we share our resources approximately equally.  This will be done if we abandon materialism.  For the rest of it, the three requirements of Deci and Ryan for happiness are (i) autonomy, which, without M, is assured, (ii) effectiveness, which is within the grasp of every undiminished person through an educational system (free of falsity) that emphasizes what is interesting to do on an individual basis, and (iii) (wholesome) relatedness, which should be easily accessible in a world where people are no longer in head-to-head adversary relations of the most ruthless type – even in high-school.  Finally, in a world without tyranny no one can take anything away from us, so the “safety” requirement will be met.  Additional scientific research on human motivation might permit the removal of the assumption about , in which case the Theorem would be restored to the simple form:

Theorem 1* (Ideal Fundamental Theorem).  A necessary and sufficient condition for the sustainable happiness of all of humanity (including its posterity) is the abandonment of materialism.

Virtually universal happiness is contingent upon our ability to stabilize the size of our population and to harvest sufficient renewable primary energy.  Many prognosticators feel that it is reasonable to hope for population stabilization by the middle of the next century.  (I believe this is a reasonable expectation because of heightened awareness of the dangers we face, a concomitant rejection of the population policies of some religionists, and a liberalized attitude toward women and children, who may no longer be regarded as assets to be disposed of by men.  I hold these optimistic beliefs despite a resurgence of reactionary ideas, which should be put to flight as soon as enough people grasp their true implications.  What I’m hoping is that the rejection of conservative ideology is imminent and a new progressive liberalism is waiting in the wings.)  The energy problem is a major research area to which I am attracted as are many other scientists and engineers, therefore we have reason to be guardedly optimistic.  Thus, assuming W = W′ and provided W = W″, we have proved Theorem 1*.  The proof that W = W″ remains to be completed by scientists and engineers who have their priorities straight.

Immediate Corollaries

Given the Fundamental Premise, proved in Chapter 3, and the Fundamental Theorem, proved above, we may write:

Corollary 1.  The abandonment of materialism by nearly all of society (under the assumptions of the Fundamental Theorem, enumerated above) is a necessary and sufficient condition for any reasonable person to be happy.

Corollary 2.  The Fundamental Theorem implies communism (but not socialism in its manifestation as state capitalism).  [Note in proof (10-1-96):  Recently, I heard Noam Chomsky define socialism in a manner that would make it consistent with my philosophy, namely, as worker ownership of the means of production.]  Communism requires at least some economic planning (to account for far-flung or future needs), which requires the restraint of natural leaders, which nearly implies anarchy.  Probably, a system of anarchy moderated by a rational social contract is the most reasonable solution to the problem of restraining “natural” leaders.

Note.  Many people believe that recent events in Eastern Europe and in the Former Soviet Union have proved something about communism.  I can prove that  is not rational.  [Assume, on the contrary, that √2 can be written as p over q with p and q integers, as required for all rational numbers.  Thus, √2 = p/q.  Square both sides and multiply by q2 = q∙q to get 2∙q∙q = p∙p.  The right-hand side (RHS) has an even number of factors of 2 (twice the number of times that p is divisible by 2 since p appears twice), but the LHS has an odd number of factors of 2 (twice the number that q has plus the one in plain sight).  Contradiction!]  No such thing has happened to communism.  Recent events have proved nothing about communism.

Anyone who thinks otherwise should take a few hours off, skim through Proofs and Refutations by Lakatos [1], and, then, look at some good examples of proofs, perhaps in a mathematics for the layman type of book like What Is Mathematics? by Courant and Robbins [2] or The Mathematical Experience by Davis and Hersh [3].  (I began this note with a pretty good proof using reductio ad absurdum, with which we are all familiar, if for no other reason, because I stated it in Property 4 of external truth in Chapter 3.)

Theorem 2.  W =  W′.  Remember, W is the world as it actually is.

Proof.  This is the essence of the theory of Deci and Ryan [4].  Theorem 2 can survive a few errors in the theory of Deci and Ryan.  The reader who studies the literature on human motivation will be able to judge for himself.  [Note in proof (11-27-96):  Also, see the special bibliography at the end of Appendix III.  These papers constitute the proof of Theorem 2.]

Theorem 3.  W evolves into Wif and only if we abandon materialism.

Proof.  In the world W*, we have very general agreement upon the assumptions listed in Chapter 4.  W* is a world that depends primarily upon what people believe – about what people believe is allowed as well as what people believe is so.  Very few of the assumptions depend upon what is so, e.g., Item 5:  We assume that the ability to reason can be developed in the normal undiminished human being.  If this assumption turned out to be false, the world W* could not exist.  In W*, we have our minimal proper religion, which constitutes a social contract, which, in turn, constitutes a moral basis for a community living in peace and harmony essentially without laws and government.  Materialism, however, creates certain impediments, e.g., a vast universal propaganda machine that achieves nearly total thought control.  We must devise a scheme to eliminate these conditions – or get around them.  Perhaps, the global information highway is the answer.  That’s why the government wants to make certain it can read whatever is said on this electronic media.  We assume that without serious impediments we can convey the merit of this philosophy on a widespread basis.   Remember the six degrees of separation!

Conjecture.  W can evolve into W*.

Note.  This is a matter, at least partly, of faith in humanity.

Doomsday Theorem.  In W′ or in W″ (even), a sufficient condition for the extinction of the human race is the failure to abandon materialism.

Proof.  The proof that materialism implies geophagy and our description of geophagy and the damage that can result if it is not eliminated to the extent made possible only by abandoning materialism and artificial economic contingency essentially proves the Doomsday Theorem, which, frankly, is not very enlightening.  The reader should be convinced by now that materialism will motivate certain people (perhaps all people) to continue the destruction of the environment, if only to avoid failure in the global market.  Further, the current concentration of power precludes sufficient remediation or the enlightenment of the public by means of the mass media, which is controlled by geophagists.  Moreover, no policy will be in place to limit or reduce population, which alone will have sufficiently catastrophic effects that the world will end for the vast majority due to famine, war, and epidemic disease.  Fortunately, the much more useful Fundamental Theorem, just discussed, shows that we can be extremely hopeful provided mankind wakes up in time to effect the necessary changes in our institutions.  It all depends on us!

Operational Morality

We could derive operational morals, e.g., “Love thy neighbor”, from our moral axioms, theorems, corollaries, lemmas, and whatever else has been proved or assumed to construct a minimal proper religion.  Nevertheless, there are no specific operational morals mentioned in this essay concerning, for example, how people are to treat each other, except for the requirements of equality that ensure reasonable treatment independent of sentiment.  For example, I do not derive Statement 1 as a moral, even though I think it’s true.  I simply don’t need it.  Notice, too, that I don’t talk about love all the time.  Actually, people who are always talking about love make me nervous.  Can you blame me?  [In the next chapter, I mention in passing that we are all brothers and sisters, but I don’t mention any attendant moral requirements.]

Statement 1.  Generosity is preferable to greed.

Note.  Certainly generosity is one of the noblest virtues.  One might insist that Statement 1 be an axiom.  But, generosity comes from within.  A person could be incapable of a generous thought or deed and still behave acceptably.  It is hoped that the Freedom Axiom will promote generosity and, perhaps, one could make the case that Statement 1 can be derived from Corollaries 8 and 9.

October 13, 1995

Revised May 21, 1996

Revised July 2, 1997

Revised December 21, 2004


1.         Lakatos, Imre, Proofs and Refutations, Cambridge University Press, New York (1976).

2.         Courant, R,. and H. Robbins, What Is Mathematics?, Oxford University Press, New York (1948).

3.         Davis, Philip J., and Reuben Hersh, The Mathematical Experience, Houghton Mifflin, Boston (1981).

4.         Deci,. Edward L. and Richard M. Ryan, Intrinsic Motivation and Self-Determination in Human Behavior, Plenum Press, New York (1985).