Russell’s Two Legacies

             Russell’s Two Legacies

 

             Bertrand Russell has two legacies: his Paradox and his Principia. His Paradox is concisely stated, wittily illustrated with a quaint tale, and logically devastating. He asked: consider the set of all sets, and only those sets, that do not contain themselves. Does it contain itself, or not? The answer is: yes as much as no!

            Russell illustrated his Paradox with a quaint tale about a village’s  barber. The barber shaves all those, and only those, who do not shave themselves. Does the barber shave himself? Yes as much as no!

            You can tell similar tales. For instance, that village is watched by a watchman, who watched all those, and only those, who do not watch themselves. Who watches the watchman? The watchman watches himself as much as he does not.

            The village jester laughs at all those, and only those, who do not laugh at themselves. Does the jester laugh at the jester? The answer to this question is, yes as much as no.

            Related to these is Gödel’s Paradox: “ ‘is not provable when it quotes itself’ is not provable when it quotes itself.” That statement uses coding to call itself unprovable. This yields a paradox unless proof does not equal truth.

            Russell’s Principia is an attempt to suppress Russell’s Paradox, and win the day for the logicist program. It is long, dense, unreadable by most, and its mission was defeated by Gödel’s Paradox. Russell tried to ban self-reference, but self-reference is inherent in arithmetic, given coding.

             Russell’s Principia is long, dull, obscure, unreadable, specialized, and failed. Russell’s Paradox is short, sweet, clear, witty, adaptable, and effective. I think that Russell’s Paradox will long outlive his Principia, which will be remembered only for taking hundreds of pages to prove that 1+1=2.

I see in this a kind of Shakespearean family tragedy. Lord Russell had two brainchildren: Principia Mathematica, the legitimate heir, and Russell's Paradox, the by-blow conceived in youthful folly. The two waged war, and the bastard defeated the legitimate heir. 

            I also see in this an object lesson in pragmatic memetics:

Keep It Simple, Stupid.

            And why? Because all men are mortal. We don’t have time for windy nonsense; we only have time for witty nonsense.
 

 

Paradox-logic addendum:

            The Kleenean-logic solution to the paradox of the jester is that the jester only half laughs at the jester, with a forced and rueful chuckle. The Diamond-logic solution is that there are two jesters, who laugh loud and long at each other.

 

The Silence of the Students

The Silence of the Students

 

Gaza is not the only atrocious war now raging. Why is there no high-minded student protest against the ongoing genocide against the Rohingya? Or in Darfur? Estimates: 13,700 to 40,000 for the first; 98,000 to 500,000 for the second.

          The Rohingya are Muslims. Is Islamophobia involved in the silence of the students? Darfur is in Africa, hence its inhabitants are dark-skinned. So is racism involved in the silence of the students?

          My least inflammatory diagnosis is that humans tend to be indifferent to atrocities committed upon small distant groups without money. My critique is of the species.

Does Money Exist? 12 of 12

         Part 12. 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. By its own logic, professional economics must be corrupt. Therefore it 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!

 

 

 

         

 

 

Does Money Exist? 11 of 12

          Part 11. 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.  A necessary Pope is corrigible.

            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.

 

         

 

 

Does Money Exist? 10 of 12

         Part 10. Wider Implications of Jinx and Charm.

 

            According to Gödel, 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 Gödel’s Jinx and goes bankrupt! I theorize that this ironic pitfall explains the persistence of fiscal booms and busts.

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

             Gödel’s Jinx works because self-pride makes an infinite claim - namely, that there’s an infinite and consistent model of arithmetic - based upon finite data - namely, self-pride’s own small self. Löb’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 Löb, 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 Löbian 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.