An Introduction to Hierarchical Introspective Logics
I have been recently revisiting an esoteric paper by Nash called “Hierarchical Introspective Logics” and because of some research and talks with others I feel I am slowly starting to draw insight from it. It talks about the nature of Godel incompleteness theorems and how it relates to Turing’s “extensional” work on parallel observations.
The writing is a consideration of the possibility (or certain possibility given the premises) of statements that are true but unprovable as such. Nash makes a remark about the nature of the proof of the existence of such statements:
It is notable that Godel’s construction of an unprovable, yet true, proposition in a generic sort of formal system is accompanied also by a proof, under reasonable hypotheses, of the truth of that “unprovable” proposition. How is this achieved? Well, of course, the proof does NOT occur WITHIN the formal system for which the Goedel proposition was constructed, rather it is given verbally in the normal style of argument for published mathematical papers.
The conclusion of the writing is something I want to speak (write) to:
It seems plausible or at least conceivable that knowledge actually gained from the study of Nature, plus cultural evolution, would in time lead to decisions, positive or negative, about the adoption of axioms relating to set theory that seem to us now as quite optional in merits.
On the Unscientific Nature of Ideal Money
One of the first people that could re-articulate the insight of Ideal Money (or at least a reasonably identifiable portion of it) back to me, to my satisfaction, recently pointed out a tweet by @nickszabo4:
This sentiment is furthered here:
The point my peer was making is that Ideal Money is not a scientific argument and although we touched on this in dialogue in the past I wasn’t properly receptive of the point and I took it as criticism (in a way it is but I should allow the point to stand).
On the Comparable Nature of Falsifiability
Ideal Money is not a falsifiable conjecture even if it could be brought down to a formulated conjecture of some sorts. It could be very true we will achieve Ideal Money but there is no way to replicate the experiment such that we can show there is a scientific nature to its advent (perhaps if there were multiple habited planets at a similar state of advancement this could be approached etc.).
So I see a comparability here with Nash’s observations on Godel and Turing’s work in that Ideal Money COULD be an inevitable outcome but since there is no falsifiable experiment seemingly possible to test it as a conjecture there may be no way to attract the attention and proper consideration of true scientists.
Interestingly Bitcoin as an experiment also seems to lack this scientific quality.
Re-Visiting the Nashian Observation of Keynes
I have previously made the contention with Saifedean Ammous’ books “A Bitcoin Standard” in that he launched an ad hominem attack on Keynes simply because if the truth of Keynes Bancor proposal was held up to Ammous writing it would expose him as a charlatan.
This blog I found highlights my point while also misrepresenting Nash’s definition (oddly enough because the author quotes the definition given).
This is part of Nash’s definition for a Keynesian (from the blog):
A Keynesian would continuously seek to achieve “economic welfare” objectives with little regard for the national currency.
The author “refutes” Nash with a quote of Keynes:
John Maynard Keynes wrote in the New York Times of 10 June 1934:
I see the problem of recovery, accordingly, in the following light: How soon will normal business enterprise come to the rescue? What measures can be taken to hasten the return of normal enterprise? On what scale, by which expedients and for how long is abnormal government expenditure advisable in the meantime?
… for how long is abnormal government expenditure advisable in the meantime?
And concludes:
In the meantime. Got it? Not “continuously”. Only at times when policy has done so much damage to the economy that a Great Depression ensues. Then, and then only, said Keynes.
Nash was wrong about Keynes. Nash was careless.
But what the author doesn’t realize is that Nash VERY explicitly separated his criticism of Keynesianism from Keynes:
The thinking of J. M. Keynes was actually multi-dimensional and consequently there are quite different varieties of persons at the present time who follow, in one way or another, some of the thinking of Keynes. And of course SOME of his thinking was scientifically accurate and thus not disputable. For example, an early book written by Keynes was the mathematical text “A Treatise on Probability”.
The label “Keynesian” is convenient, but to be safe we should have a defined meaning for this as a party that can be criticized and contrasted with other parties.
So let us define “Keynesian” to be descriptive of a “school of thought” that originated at the time of the devaluations of the pound and the dollar in the early 30’s of the 20th century. Then, more specifically, a “Keynesian” would favor the existence of a “manipulative” state establishment of central bank and treasury which would continuously seek to achieve “economic welfare” objectives with comparatively little regard for the long term reputation of the national currency and the associated effects of that on the reputation of financial enterprises domestic to the state.
I think it is clear Nash was cautious and that the author of the blog was not. But what is more to the point for this writing is that the author is pointing to the same line that I am in regard to the Keynes actual intention in creating the Bancor.
The Re-levance of Bretton Woods
The Bretton Woods conference was a very significant event in our history. It was called near the end of WWII as leaders in the world realized it was quite possible we could slip into a third world war if we didn’t make preparations for the ending of the second. There needed to be agreements made on how the global economy functioned and Keynes was involved in the considerations. Keynes was touting his Banor proposal which in effect was an international settlement unit that was to have an apolitical nature. But his proposal was not favored by the Americans that ultimately had the most influence as the greatest benefactors of the war. This and the nature of the Bancor proposal is explained well in this short lecture:
The outcome that was chosen was not Keynes desire and gave the United States control of the de facto world reserve currency which was in effect the USD convertible to gold at a fixed exchange rate.
On the Comparability Between A Bitcoin Standard and Bitcoin as a Globally Held Inflation Target
I recently corresponded with an Australian central banking researcher because of a paper I read by the same person. I asked them if they might consider Bitcoin as an inflation target for major centrally banked currencies rather than simply its qualities as a global money. They wrote back and asked (loose quote) “What would you peg it too, a basket of commodities? How could you change the supply when it’s fixed?”
Unfortunately I only ever get this response (I got a similar reply from @n_cachanosky) and I don’t get any chance to clarify the mistake they are making in understanding what I am suggesting. I tried to point it out and was abruptly told to submit a whitepaper and that no further correspondence would be necessary.
@derose also, immediately upon my suggestion that Bitcoin could serve as a proper basis for a globally held inflation target, suggested that Bitcoin wouldn’t be a very good fit. I recently dm’d him this (with no reply):
Consider this paper and specifically one aspect I will highlight: https://www.bankofcanada.ca/wp-content/uploads/2016/03/swp2016-14.pdf … It explains formulaically that on the gold standard, ie with an internationally held medium of exchange, there was a corridor in which central bank policies could affect the exchange value of their currencies. The paper goes on to explain that the corridor effectively only exists as a function of the cost to arbitrage. So as the cost limits towards zero the corridor shrinks. Given bitcoin as a relatively costless and instant internationally held medium of exchange, consider the similarity between having no corridor for exchange rate variance and a world in which all major centrally banked currencies are targeted for stability with the exchange price of bitcoin. And if you read this, try to convince me you are too dumb to understand what I just pointed out :) For the relevant quotes/citations see my summary (ie the formulas used to explain): https://medium.com/@rextar4444/a-central-bank-backed-perspective-of-a-bitcoin-standard-4472eb2ba3fb …
That is to say in regard to the division and conflict between those that tout bitcoin as the new gold standard and those that believe inflation targeting is important…They are actually both means to the same end and not at all mutually exclusive.
There is no difference but perspective in regard to the notions of Bitcoin as a neo-gold standard or Bitcoin as an inflation target. They approach the same result although it isn’t immediately obvious especially depending on your alignment otherwise.
A Note On Deflation and “Stable” Money
When I first put forward the significance of Ideal money and its relation to Bitcoin I made the mistake of touting it as a call for the value stabilization of money. I later learned that the argument could only be palatable if there was no such call and after a more careful read I realized that Nash did not imply the money would be stable. Rather, it is a call for the inter-relational stability of our major currencies. This is why Bitcoin, if it became a global used currency, would satisfy Nash’s argument-if everyone used the same currency then there would be no political influences that create differing value trends via interference in the supply.
But I have never fully abandoned the possibility that the ultimate outcome could be what is otherwise known as impossible even though you cannot peg Nash on explicitly proposing literal value stable money.
In a world of Hyperbitcoinization, the austrian view is evoked, which does away with the want for stable money and instead believes that people can simply adjust with the prices as they rise.
It was this concept that sparked Selgin’s challenge to the community and the ensuing debate:
On the Inferiority of Inflationary and Deflationary Contract Options
In Ideal Money Nash notes:
Consider a society where the money in use is subject to a rapid and unpredictable rate of inflation so that money worth 100 now might be worth from 50 to 10 by a year from now. Who would want to lend money for the term of a year? In this context we can see how the “quality” of a money standard
I think we can consider contract formation with either a deflationary medium or inflationary in this regard. It really matters whether you are the creditor or the debtor in this context depending on whether the medium for repayment is inflationary or deflationary.
It would be difficult to pay back a loan in which the value to be paid because is increasing dramatically over time and for the receiver of payments it would be unfavorable to receive such payments if they are inflationary in nature and less in value over time.
So it can be understood that for each party there are considerations that must be factored in and one obvious conclusion is that the unpredictable nature of the value trend of the medium in question perturbs contract formation.
But I think what isn’t so obvious is that there needs to be an alternative option from which an opportunity cost can be drawn for this to hold true and of course it is this alternative option for “saving” that becomes the comparable measurement for whether the contract medium is in fact deflationary or inflationary.
Nashification > Hyperbitcoinization?
In a world with only one currency there is not these problems of considering the inflationary effects because there could be no other option regardless. However, in a world where Bitcoin is the ubiquitous currency that pushed all other “fiat” currencies to their demise it cannot still be said that the problem of contract formation is solved.
The entire history of money shows that any superior medium could be used as a money, regardless of government control, provided the pressure for a better quality medium continues to increase. Value is not something that can be mandated by a government because a people might perfectly value a medium that allows them to escape the control of such a government.
So for these reasons I think it could be argued that a theoretically value stable (which is perhaps not possible) Bitcoin would be more ideal than an intensely deflationary Bitcoin.
Of course as central bankers and Bitcoiners alike will agree Bitcoin’s perfectly predetermined and finite supply rate seemingly preclude it from being value stable.
It is very much expected to be deflationary by all parties that make conjectures based on the assumption that it might be successful.
Nashification > Hyperbitcoinization
Here I am thinking about the Nashificaiton end which is where central banks enact monetary policies that cause their money supplies to be issued such that there is value stability between their respective currencies and Bitcoin. I explained in this writing how it is not particularly the make-up of the basket or target chosen for money issuance that creates a strong value trend for a currency but rather the trustworthiness of the issuance schedule. A more accurate basket would be more optimal but so would simply a more trustworthy promise.
Most people, Bitcoiners especially, cannot understand how an infinitely supplied money could be value stable versus Bitcoin which has a scare supply. But money has a utility that serves the population that uses it and historically we have seen that there can be EITHER too much money or too little.
If the population has too little Bitcoin, and it demands more, the only way it can be served is with an increase in the exchange price to get it. In a world of Nashification if the people needed more money and their central bank refused to inspire the issuance of it then that respective currency would be valued less for the utility that is money (and in fact they might then turn to alternatives such as Bitcoin).
On The Importance of Convenient Prices
There is tremendous value in simply having prices quoted conveniently.~Ideal Money
I did have a short lived dialogue with Francis Coppola on the subject of having an internationally held pricing system. Her sentiments were that having floating exchange values or our respective currencies is not sub-optimal since you can always make the conversion regardless.
Not sure I can find the exchange but quickly after she backed away from this assertion and I wasn’t able to make a perfect counter as I wasn’t expecting to be disagreed with in this manner.
I would change my assertion now to include a “change over time view”. That is to say, in an instant we can make an easy price calculation regardless of differing exchange rate trends. But of course if we can’t predict the trends over time then these differing trends will decrease the accuracy of even short term contracts. For long term contracts this is obviously incredibly detrimental.
Here Szabo works are supportive of the convenience of having a single price for commodities in a market:
A world of pure barter has O(N²) prices for N commodities, and the mental transaction costs in such a world are correspondingly much higher than a world with a single currency and O(N) prices.
On The Introduction of Axioms
We begin to return to Nash’s paper on HIL but also with a relevant quote from Ideal Money:
I think there is a good analogy to mathematical theories like, for example, “class field theory”. In mathematics a set of axioms can be taken as a foundation and then an area for theoretical study is brought into being. For example, if one set of axioms is specified and accepted we have the theory of rings while if another set of axioms is the foundation we have the theory of Moufang loops.
So, from a critical point of view, the theory of macro-economics of the Keynesians is like the theory of plane geometry without the axiom of Euclid that was classically called the “parallel postulate”. (It is an interesting fact in the history of science that there was a time, before the nineteenth century, when mathematicians were speculating that this axiom or postulate was not necessary, that it should be derivable from the others.)
So I feel that the macroeconomics of the Keynesians is comparable to a scientific study of a mathematical area which is carried out with an insufficient set of axioms. And the result is analogous to the situation in plane geometry, the plane does not need to be really flat and the area within a circle can expand hyperbolically as a function of the radius rather than merely with the square of the radius. (This picture suggests the pattern of inflation that can result in a country, over extended time periods, when there is continually a certain amount of gradual inflation.)
The missing axiom is simply an accepted axiom that the money being put into circulation by the central authorities should be so handled as to maintain, over long terms of time, a stable value.
In HIL Nash’s eventually gets to the comparability of what seems to be the evolution of the base language used to express logic and the introduction of adding axioms that imply completeness with an ability to “prove” what is not provable within the base logic system.
This reminds of me of this quote from Ideal Money:
It is so desirable in game theory to have transferable utility that that those using game theoretic analyses go ahead and use the transferable utility concept although it might not be entirely fitting except for individual games of comparatively small weight played by large insurance companies.
And what seems also relevant is Nash’s Bargaining Problem paper which shows the value of money in trade. The paper seems to observe the comparison between two scenarios and two parties facing a barter situation. Nash observers the two situations in regard to one not utilizing a medium of exchange and another that does. He shows that more trades can happen with the introduction of a transfereable utility.
But there is an obvious assumption not really stated that the TU being considered is stable in value (or in other words there are no alternative option or there is no time consideration).
I thinking then that we have already made many observations based on the concept of Ideal Money and that Nash highlights this as an already “accepted axiom”.
On Social Order
So there could be scientific minded people that cannot discern the value from an unfalsifiable conjecture but then I think we might be able to make quantitative (I’m not sure this is the right word please correct me otherwise) arguments that are decidable but based on axioms with which we cannot prove to be “true”. And that eventually as enough of these argument rest on the unprovable axiom then it will be socially acceptable to then turn around and argue that one must show that by not evoking such an axiom there can be higher payoffs achieve than the ones that are put forth based on the unprovable axiom.
One such example is Ideal Poker as a generalization of Nash’s Ideal Money proposal and specification towards the online poker industry which makes use of this game theoretical observation from Ideal Money and might eventually be used to counter the “shit-coin” narrative that so many seemingly insecure bitcoin maximalists tout:
(1): Games with transferable utility. (and) (2): Games without transferable utility (or “NTU” games). In the world of practical realities it is money which typically causes the existence of a game of type (1) rather than of type (2); money is the “lubrication” which enables the efficient “transfer of utility”. And generally if games can be transformed from type (2) to type (1) there is a gain, on average, to all the players in terms of whatever might be expected to be the outcome.
