Thursday, October 20, 2011

Does Money Exist?

Does Money Exist?
Plutism Versus Goedel’s Jinx

This essay connects fiscal instability to a logic paradox which I call the “metamathematical jinx”. This is a treatise on Metamathematical Economics.

I start with a definition and critique of a new word: “aplutism”. Then I connect the social-constructivist defense of plutism to meta-mathematics. I briefly review metamathematics through Goedel’s Incompleteness Theorems and Loeb’s Theorem; using these results I define metamathematical “jinx” and “charm”. I then prove that money’s existence is jinxed and money’s accounting is charmed: that is, money exists only to the extent that you cannot prove that it exists; yet your books do in fact balance if they can prove it. I end this essay with some Metamathematical Reforms, a brief critique of an alleged science, and a vain self-validation.

Part 1. Aplutism defined and critiqued.

Aplutism (a - ploo - tizm)(adj.: Aplutic) n. (syn.: Amonetarism, Achrismatism. ant.: Plutism)(from Ancient Greek, ‘treasurelessness’, ‘moneylessness’) 1) Philosophical disbelief in the existence of money. 1a) Doubt or denial of money’s intrinsic value. 1b) The claim that money is always a fiction, sometimes a folly, and often a fraud. 1c) Any political-economic system designed to be separate from the money system.  2) Wealthlessness; poverty; personal lack of funds.

Aplutism is to the market as anarchism is to the state and atheism is to religion; it defies an established power by denying the existence of that power’s god. You can tell a culture’s true gods by noting which heresies are unthinkable. We have words for those who deny God, or the State, but here we must invent a word for those who deny this culture’s true divinity, the almighty Dollar.

The “aplutic question” is “does money exist?” It has two meanings, given the two definitions of aplutism; does money exist philosophically, and do I, myself, have any money. But the two questions are linked; for to anyone personally aplutic, it is as if no money exists anywhere in the world; and the fact that many people, much of the time, experience personal aplutism, suggests flaws within plutism. Certainly personal aplutism motivates individuals to devise “political-economic systems designed to be separate from the money system”; which by definition is public aplutism.

Aplutism in the public sense comes in soft and hard varieties. Soft aplutism is doubt in money’s existence; hard aplutism is outright denial of money’s existence. Soft aplutism can be called “agnostic aplutism” or “agnoplutism” if you don’t mind the neologism.

“Plutism” is another useful word; its meaning is inverse to aplutism’s: belief in the independent existence of money; belief in money’s inherent value; and also personally having money.

Part 2. Plutic Controversy

Please note that aplutism is not conventional anti-capitalism. An anti-capitalist denies the money system’s justice; an aplutist denies its presence. An anti-capitalist says that the money system is unfair; an aplutist says that it’s unreal. One denounces; the other refutes.

It seems absurd to ask if money exists; but the question improves upon acquaintance. It’s true that there are plenty of green pieces of paper claiming to be money, and people treat them as if they were money; but on the other hand, a church can exist, with preacher and flock, without its god existing.

Such a cult could intimidate everyone in town into worshipping the idol; but nonetheless prayers to the figment will go unanswered, and sacrifices to the image will not be rewarded. Nonexistence has consequences that will not be denied.

Aplutism claims that money is such an idol; specifically paper money. Is paper money an oxymoron? It’s created out of pure debt, basically by subtracting infinity from infinity. (Ask the Fed for details about the relevant sleight of hand.) Paper money is essentially a giant placebo; it works if people believe in it; but faith can vanish in a moment.

For instance, recently $1,000,000,000,000 in stock valuation disappeared. That trillion dollars wasn’t stolen, exactly (though some contrived to indirectly profit from this); nor was it money, exactly (though some got taxpayer money for this). The money ceased to exist, and indeed it announced that it never was. And strangest of all, right after being bailed out by a trillion taxpayer dollars, those responsible for the bubble carried on as if nothing unusual had happened!

Well, if ten hundred thousand million dollars can be fraud and illusion, then how much other money isn’t really there? Please note that this vanishing act has precedents; Wall Street history is full of booms and busts. In fact unstable money is the norm, unless there’s socialism and/or regulation.

I, myself, am only partly an aplutist. I distinguish between private goods, which I call “zero-sum” goods, and public goods, which I call “zero-difference” goods, or “common wealth”. Common wealth includes clean air, pure water, street lighting, rule of law, national defense, sewers, roads, bridges, mail and the Internet. Zero-difference goods are had by none or by all; and I say that they are naturally aplutic, for money is a system for managing zero-sum scarcity.

Money is a useful fiction for rationing private goods, less useful for public goods; but I don’t know where to draw the line between plutic private goods and aplutic public goods. I am in a state of doubt; and in this essay I argue that such doubt - a.k.a. soft aplutism, or ‘agnoplutism’ - is the wisest policy.

Part 3. Social Construction and Metamathematics

Does money exist? Certainly it’s a social construct, dependent on human  society. It’s a social game, so to be valid it has to be believeable. It needs consistency. When a sum flips unexpectedly between zero and a trillion, that tends to call doubt upon that sum’s utility or reality.

Money seems to exist as a measure of value; but if there were a single measure, agreed upon by all, then all trade would cease. Who would trade better for worse? But we do trade, because what’s best for me is not always what’s best for you; so exchange is rational. Trade happens because mutual profit is possible; but mutual profit is possible only if there is no single measure of value. Therefore money facilitates trade not by representing value, but by persistently failing to do so.

What does it mean to say that money exists? It means that money makes sense; that there’s a plausible referent for all the recorded transactions; the additions, the subtractions, the multiplications and divisions. Do the books balance? Could the books balance? That is the question. Money exists if its arithmetic lacks contradictions. The aplutic question reduces to: given the recorded transactions and contracts as axioms, is the resulting arithmetical account self-consistent?

But that is an undecidable proposition, as Goedel’s Second Incompleteness Theorem proves. In fact it is inwardly paradoxical; for any arithmetical proof system is consistent to the exact extent that it cannot prove that it is consistent!

I submit that money, like the consistency of arithmetic, bears a “metamathematical jinx”; that is, money exists to the exact extent that you do not believe that it exists. Money is skepticism-based; it’s as real as your doubt that it’s real.

Money scarcely exists, as befits a measure of scarcity. It exists as much as it’s scarce; that is, as much as it does not exist. Money is a paradox!

Part 4. Elementary Metamathematics

Money is based upon arithmetic; and the study of the logic of arithmetic is called metamathematics. The ‘meta’ is there because arithmetic can study itself; so paradox is possible.

In metamathematics, statements about numbers themselves bear numbers describing their syntactic form; so number statements can refer to each other’s formal properties, including provability, consistency, unprovability, and refutability. It’s also possible to construct statements that refer to their own properties; I call such statements “quanta”.

For instance, I call “this sentence is unprovable” the “quantum of self-doubt”. “This sentence is refutable” is the quantum of self-shame, “This sentence is irrefutable” is the quantum of self-pride, and “This sentence is provable” is the quantum of self-belief.

Call a property of statements “jinxed” if its quantum is false:
“Property P is jinxed”    if and only if
“This sentence has property P” is false; it does not have property P.
A jinxed property does not apply to its quantum.
For instance, “This sentence has six words” does not have six words; therefore “has six words” is jinxed.

Call a property of statements “charmed” if its quantum is true:
“Property P is charmed”    if and only if
“This sentence has property P” is true; it does have property P.
A charmed property applies to its quantum.
For instance, “This sentence has five words” has five words; therefore “has five words” is charmed.

According the Goedel’s First Incompleteness Theorem:
“This sentence is unprovable” is unprovable if your logic system is consistent, otherwise not;
“This sentence is refutable” is refutable if your logic is inconsistent, otherwise not.
So if your logic system is consistent then unprovability is charmed, and refutability is jinxed.

If your logic system is consistent, then self-doubt is true but unprovable, and self-shame is false but irrefutable. On the other hand, if you prove self-doubt or refute self-shame, then your logic system is inconsistent. Self-doubt and self-shame are inherently uncertain; attempts to resolve these paradoxes backfire.

According to Goedel’s Second Incompleteness Theorem:
“This sentence is irrefutable” is refutable.
That’s because the quantum of self-doubt sets a trap. If you assume that self-pride is true, then your logic system must be consistent; so self-doubt must be unprovable; hence self-doubt must be true; but that would be a proof of self-doubt; a contradiction. Assuming self-pride yields a contradiction; this refutes self-pride.

Self-irrefutability refutes itself. I call this Goedel’s Jinx.

According to Loeb’s Theorem:
“This sentence is proveable” is proveable.
This is because the quantum of self-belief is in fact the negation of the quantum of self-pride; true to the extent that the other is false. Since self-pride is refutable, self-belief is provable.

Self-validation validates itself. I call this Loeb’s Charm.

A statement is consistent if and only if there is a model of arithmetic, within which that statement is true; and it is provable if and only if it is true in every model of arithmetic. Therefore ‘true in some model of arithmetic’ is jinxed; and ‘true in every model of arithmetic’ is charmed. In metamathematical terms, existence is jinxed and universality is charmed!

Part 5. Metamathematical Aplutism

Does money exist? Either philosophically, or on a personal level? Money exists philosophically if and only if its alleged movements make sense; that is, if the money system, which is a self-referential arithmetical accounting system, is consistent. Can it prove itself to be consistent? According to Goedel’s Second Incompleteness Theorem, consistency is jinxed; any self-referential arithmetical system that can prove its own consistency is not in fact consistent.

Since the existence of money is equivalent to a jinxed property - namely, the consistency of one’s arithmetic - it follows that money’s existence inherits the jinx. That is, if a money system can prove that its money exists, then its money does not in fact exist.

Money exists on the personal level only if its alleged presence can be documented; any doubts in the matter must be taken seriously; and despite such systemic skepticism, money always comes short anyhow. Therefore it is folly to assume, let alone deduce, that you have any money. Account for it, directly, yourself, and then you can be sure, but not until. If you foolishly assume that your money exists, then you and it will soon be parted.

The same doubts apply on the public level. If you wisely doubt that the money game makes sense, then the books might balance anyhow; but if you foolishly believe that money has value in itself, then ten hundred thousand million dollars can softly and suddenly vanish away.

Therefore it is wise to doubt that money exists, either in the public or the personal sense. That’s soft aplutism, a.k.a. agnostic aplutism, or ‘agnoplutism’. (Suggestions for superior neologisms are welcome!) By Goedel’s Second Incompleteness Theorem, consistency is jinxed; therefore so is the existence of money; so if the money system is valid, then its validity must remain in doubt. Money ‘scarcely’ exists; its existence is uncertain - as befits a measure of scarcity.

But given all this self-doubt, in what can we have faith? Self-faith, of course, as Loeb’s Theorem implies. Provability is charmed; so if your accounting system can prove that your accounting system is valid, then it is indeed valid, at least within its own terms. If the books balance, then even if the money it’s counting is fictional, then it’s still a balanced fiction. It might sum to nothing, but that would be an honest nothing. Thus we return to credo, or faith, as the foundation of credit!

By Goedel’s Second Incompleteness Theorem, existence in general is jinxed, so in particular money’s existence is jinxed; it might not exist, and if the money system can prove that its money exists, then that money does not in fact exist. By Loeb’s Theorem, validation in general is charmed, so in particular validating one’s own accounts is charmed. Though money may not exist, still a balanced book is a balanced book, and it can prove it.

Money scarcely exists, as befits a measure of scarcity. Money might not exist, both yours and the banker’s; don’t take anyone’s word for it; yet honest book-keeping justifies itself. This is metamathematical economics, yet it is also plain common sense.

Part 6. Revelation of True Price.

Please note that my aplutism is motivated by self interest, like any other economic theory. I doubt the existence of money, mine or anyone’s, in the hope of keeping around what little there might be.

I invented aplutism as a satire, a conscious absurdity; and it works as a satire, for it reveals that its opposite – plutism – is an unconscious absurdity! For I put it to you that there is no such thing, intrinsically, as money, because there is no such thing as a free lunch, and intrinsically valuable money would be a free lunch.

That’s the plutic fallacy. If money existed in itself, then money would breed money; a free lunch.

Why did ten hundred thousand million dollars softly and suddenly vanish away? Because a gang of well-paid men thought that financial manipulation created value. They were plutists, in both senses; they had money, and they thought that their money was valuable in itself.

The brokers trusted the Magic of the Marketplace to create wealth from money alone; and as a sign of this mystery they moved their money in a circle. Lo and behold, the Magic of the Marketplace did indeed manifest; and it manifested in a price; and the price was given by a mystic symbol; and the mystic symbol was the circle they moved their money in; and what number does the mystic circle symbolize?


Part 7. Antiplutic Norms.

This essay’s skeptical critique of  the money system is mild, compared to some people’s raging contempt for the money system. Indeed there are entire sectors of society in which money not only does not exist, it must not exist. Morality demands that certain situations not involve any money at all.

A spouse who sells sexual favors is called unfaithful, and divorced; a judge who sells rulings is called corrupt, and disbarred; and a soldier who sells military secrets is called a traitor, and executed. I call these “antiplutic norms”, and they enforce the necessary incompleteness of the money system, in defense of competing systems.

For how much money, dear reader, would you accept in exchange for your citizenship? Or your human rights? Or your name?

Would you change your religion for a cash payment? If not, then why not? If so, then for how much? Can you pay a libertarian to become a communist? If not, then why not? If so, then for how much?

Part 8. Wider Implications of Jinx and Charm.

According to Goedel, existence is jinxed; to claim one’s own irrefutable presence ensures self-destruction. Therefore a money system, in the very act of proclaiming its own solvency, runs afoul of Goedel’s Jinx and goes bankrupt! I theorize that this ironic pitfall explains the persistence of fiscal booms and busts.

Goedel’s Jinx also applies, I think, to similar collapses in politics and religion. Invincible empires and infallible faiths have a way of going bust; Goedel’s Jinx explains why.

Goedel’s Jinx works because self-pride makes an infinite claim - namely, that there’s a infinite and consistent model of arithmetic - based upon finite data - namely, self-pride’s own small self. Loeb’s Charm works in reverse; self-proof makes a finite claim - that it has a proof - based upon sufficient data - its own vain self. Self-validation validates itself because it speaks only of itself, and so risks nothing.

According to Loeb, universality is charmed; to proclaim self-necessity is to repeat a truism. Self-proof is empty necessity. It says nothing, and it says it; it proves itself because bubbles rise. Correct self-accounting is an example of a Loebian self-validation bubble in finance. I leave it to the reader to find similar charmed quanta in politics and religion.

One would expect self-existence to be a humbler claim than self- necessity; after all self-pride merely calls itself true in some model of arithmetic, whereas self-belief calls itself true in every model of arithmetic. But what self-belief needs is merely a proof, which is finite; self-pride needs an entire infinite number system. The joke is that there might not be any models of arithmetic; it’s inherently uncertain; a mystery which self-pride tries to resolve, and fails.

Part 9. Metamathematical Reforms

Here are two Metamathematical Reforms based upon these principles:

To the Roman Catholic Church: Forget the mad heresy of Papal Infallibility; for infallibility is jinxed. Instead proclaim a doctrine of Papal Necessity, for necessity is charmed. Even a backwoods Protestant bear-hunter will rudely agree that the Pope is necessarily Catholic; and the flock will discover that a necessary Pope is much more adaptable than an infallible one. An infallible Pope must accumulate errors; but a necessary Pope can correct errors. Indeed, error-correction is what a necessary Pope is most needed for.

And to the State of Israel: Forget the mad demand for a Right to Exist. There is no such thing as a right to exist. Existence is jinxed; it’s an accomplishment, not a given; it cannot be guaranteed. Fortunately there’s a right to Self-Determination, and even a right to Self-Defense. These are universal, hence charmed. Self-determination and self-defense aren’t as soothing as self-existence would be, but self-existence doesn’t work, and they do, sort of, and they’ll just have to do.

Part 10. Critique of an alleged science, and a self-validation.

If money might not exist, then is there a science of money? Is economics truly a science? For science requires objectivity, and who can be objective about money? Certainly not those paid to study it; for they are paid by those who have money, rather than those who do not, and he who pays the piper calls the tune. Therefore all professional economics has a built-in plutic bias; it must ignore aplutic doubts, and attack antiplutic norms.

To be objective, an economist must not expect to reap personal gain from his or her findings. Therefore scientific economics, if it exists, must be done aplutically, moneyless, in the public domain. Otherwise it is not science, but is instead pseudo-science, propaganda, deceptions and delusions paid for by the rich.

Professional economics must hide its useful insights, if any. Amateur economics like this essay lacks plutic bias, but is incomplete, marginally competent, and under-marketed. Either way, truly scientific economics is scarce - as befits a science of scarcity.

Truly scientific economics is scarce; so this essay just might be the only scientific economics treatise that you have ever read. Therefore this essay declares that this essay is necessary!

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