How should I respond to people who invoke Gödel’s name when dismissing my work?

Oct 2015
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Arizona
In 1999 I published a book, Axiomatic Theory of Economics.

Since then I have found that economists who have not read even the simplified exposition will invoke the name Kurt Gödel when dismissing my theory.

I know who Gödel is, but I do not see what the foundations of mathematics have to do with me. I rely only on widely accepted calculus and real analysis results that should be familiar to any practicing engineer. The antipathy I get from economists has nothing to do with number theory – most of them would be hard pressed to even define a prime – it is all about me stating my assumptions clearly before proving my theorems.

So my question is:

How should I respond to people who invoke Gödel’s name when dismissing my work?

I am reminded of Van Helsing holding up a cross to Dracula, except for economists it is Gödel’s Incompleteness Theorems that ward off the evil logician.

Have other people at My Math Forum faced similar criticism? How did you respond?

FYI I am NOT a follower of Gerard Debreu. I have my own theory. Something else that I have noticed about economists is that they are incapable of recognizing that it is possible to have more than one axiomatic theory that purports to describe the same phenomena. I have found it impossible to disabuse economists of the belief that Debreu (who was parroting Bourbaki) fully defines the axiomatic method.

Economists claim that the practice of deductive logic rises or falls with the fortunes of this one man, regardless of what axioms the practitioner is using. I reply that, since Debreu lost all of his followers in 1974 when his theory went down in flames, accusing me (who was eight years old at the time) of having ever been a follower is actually a straw man attack.
 
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Well, you should reply that it is absurd and lock them in a asylum. Gödel's Theorems are something very specific, only if your axioms formalize a system where we can translate all true sentences in terms of Peano Arithmetic, and some other conditions, it simply makes no sense their claim, but then you should lay down your axioms here for us to take a look.

An argument against you could be this:

On the one hand, if we can translate your axiomatic in terms of PA, your axioms would be perhaps not so economical, but purely mathematical, so one wonders whether they capture important notions in economy like rational and irrational choices (you would be a sort of Leibniz if you came out with such thing!!). On the other hand, if that's not possible, your axioms would be perhaps too psychological to be an interesting formal system, hence an interesting and powerful axiomatic, meaning: if some sentences are not clearly true or clearly false, forget it.

Consider Spinoza. He laid down a sort of axiomatic for Ethics. Do Gödel's Theorems prove that Spinoza's axiomatic is incomplete and that it cannot prove its own consistency? No, absurd. But can we say that by that Spinoza's work has no value? No, but it is certainly not rigorous as mathematicians would expect them to be because notions employed in his axioms are stuff like God is Good, God makes the Better Choices, etc. So what we extract from the theorems if they rely upon some entity no one knows whether it exists or not? Or if we don't know what is Good and what is Bad? Is this defined? Is killing 1 to save 10 good or bad? etc.

It is difficult to proper axiomatize Physics, let alone other sciences of the "human" branch.

As a last comment: even if was the case that Gödel's Theorems apply to your system, what this means is that the notion of provability has not the same extension of the notion of true sentences in all models, it does not mean that you cannot make a good use of your axiomatic, it means precisely that assuming it is consistent there will be some true sentences not provable in a finite number of syntactic steps departing from the axioms: which ones? Mathematicians do not know the complete answer of this, they know only some examples, like Goodstein Theorem and the Gödel sentences themselves.

If you are interested in this check the book of Torkel Franzén: Gödel's Theorem: An Incomplete Guide to Its Use and Abuse, where he dismisses a lot of drivel people write about it. It is a fantastic book.
 
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Now I noticed the link in your post above to your paper. I cannot say I understand that because I'm ignorant in your area, but looks like your Theorems are the expression of your Axioms, but your axiomatic is not clearly listed anywhere. Correct me if I'm mistaken.

The paper looks interesting, at least for a neophyte like me.

For instance, your final blow

"But, 14 years after Gopikrishnan, they must admit that statistics do
not create theory. Only the axiomatic method can create new theory."

is somewhat vague but I got your point. I agree in principle, but here I'm using my own notion of Theory derived from mathematical logic. Your opponents would disagree with you and they have some basis: the notion of a Theory is not the same given several branches of science.

For instance, one says "I have a theory that wormholes connect us to another galaxy or universe region". This is not the notion of Theory I have in mind, but I cannot say it is wrong since people can use terms consistently with different meanings, so you would need to define it if not defined somewhere.

Your references are kind of meager for the purpose you have in mind, maybe you should address more literature to make sharp the differences between your approach to the vast majority out there. Example:

on page 4 you say

"The method of mainstream economics really has a third variable which
is never mentioned and that is the time unit for supply and demand. It is well
known that elasticity is a function of this time unit and, if this is true, one
calculates a different price depending on whether one speaks of weekly or
monthly supply and demand. "

and I wonder where is the literature with the formal presentation of what you are attacking.

On page 15 you write:

"Stock and price, however, are inversely related, so increasing one or
the other does not necessarily increase aggregate utility. "

Question: isn't it in conflict with your claim on page 4 that

"It is a mistake to inquire whether I support Say's assertion that
"supply creates its own demand" or Keynes' assertion that "demand creates its
own supply"; Axiomatic Theory of Economics is detached from that debate."

Sorry if I'm missing something, but looks like the first claim uses implicitly the fact that too high prices shy away stock buyers because they have a limited supply of money (or other inter-exchangeable resources), and too much stock will drop prices precisely because now money (or other inter-exchangeable resources) is abundant so the stocks are cheap to acquire, so further increasing of stocks won't bring more consumers precisely because they have enough stock. In few words: looks like a supply and demand mechanism.

So, Aguilar, I found your paper interesting, so correct me if I'm wrong in any comment I made.
 

CRGreathouse

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Nov 2006
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How should I respond to people who invoke Gödel’s name when dismissing my work?
I need more information before giving a useful answer. Could you explain more of what those people write or say? (Quotes would be useful.)
 
Oct 2015
57
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Arizona
Thank you for your well-thought-out comments and questions, Al-Mahed. I will reply later as I am short on time now and will just fill in some background and supply some quotes for CR Greathouse.

I published my book in Sept 1999. In June 2000 an organization calling itself the Post-Autistic Economics Network was founded that denounced me and anyone who employs deductive logic of mental illness – autism. The founders were supposedly some anonymous undergraduate students in France, which I question, as I believe that it was founded by these four men (the latter now a woman):

Edward Fullbrook (English)
Steve Keen (Australian, English)
James Gailbraith (American)
Donald/Deirdre McCloskey (American)

But the fact that these Englishmen and Americans fabricated a founding in France ties them closely to the attack on the committee of French mathematicians Nikolas Bourbaki and the French economist Gerard Debreu, who relied heavily on Bourbaki when he published Theory of Value in 1959. It is possible that the Bourbakis were still influential in their homeland as late as 1959 and it is possible that Debreu’s theory survived past 1974 in his homeland, though his influence outside France ended in 1974 when a series of paper were published pulling his theory apart at the seams. But it seems unlikely that either Bourbaki or Debreu had any influence even in France in 2000 when the Post-Autistic Economics Network was founded.

The Post-Autistic Economics Network uses the word “mainstream” a lot, by which they mean Bourbaki in mathematics and Debreu in economics. At this late date, use of the word “mainstream” is absurd. It is obvious to everybody that no post-war mathematician gives Bourbaki any credence and the anti-Debreu has been the mainstream of economics for forty years. Yet today, it is a rite of passage for young economists to dig up the moldering corpses of these men and ritualistically stick another knife in their skeletal ribs, “killing” them again and again.

Regarding quotes, here are some:

James Devine said:
The original statements by the rebellious French economics students define autistic economics in terms of its one-sided and exclusionary interest in “imaginary worlds,” “uncontrolled use of mathematics” and the absence of pluralism of approaches in economics. The hard-core autistic walling off from the societal environment can be seen most strongly in the specific, highly abstract, axiomatic school that the students protested against.
Devine’s son is autistic and so, while he is not a psychiatrist, he knows the lingo well enough to “diagnose” me in medical terminology. Note that we have never met in person – his diagnosis was based entirely on the title of my book as I am sure he never read it.

The Swede Lars Syll is one of my most vociferous critics (e.g. Axiomatic Economics - Total Horseshit) and as late as 28 December 2014 is still accusing me of autism, while his comrades by then had mostly switched over to their new strategy of citing Gödel, which I will discuss below.

Syll is a blogger. The Real World Economics Review (previously the Post-Autistic Economics Review) is their official publication and this quote is from their mission statement:

Real World Economics Review said:
It is accepted fact that the economics profession through its teachings, pronouncements and policy recommendations facilitated the Global Financial Collapse (GFC). To date, however, the world’s major economics associations have declined to censure the major facilitators of the GFC or even to publicly identify them. This silence, this indifference to causing human suffering, constitutes grave moral failure. It also gives license to economists to continue to indulge in axiom-happy behaviour.
Their editor writes:

Asad Zaman said:
It is a completely mistaken idea that scientific theory is based on deductions from a series of postulates – that is the description of the methodology of mathematics… There is no science which uses axioms and logical deductions to derive scientific theory.
Asad Zaman said:
Mathematics is not a “science” since it is not based in any direct way on observational evidence. Unlike scientific laws, mathematical laws are not affirmed observational evidence. Recognition of the possibility that there are bodies of knowledge which are not science would lead to greater tolerance and pluralism which is currently desperately needed.
Source: http://www3.unifr.ch/econophysics/sites/default/files/Deification_Science_Zamen.pdf

There are many economists who cite Gödel when attacking me, but most are quoting Zaman because he is a powerful editor and because he has a B.S. in mathematics and wrote two papers about Gödel. I will focus here on Zaman’s work because he is one of only a few extant economists with any background in math and because his papers are recent and represent a change in strategy, away from the autism accusation and towards a reliance on Gödel. (The Post-Autistic Economics Network changed its name to the World Economics Association in May 2011)

Gödel’s Theorems & the Limits of Reason

Asad Zaman said:
The axiomatic-deductive methodology of mathematics leads to logical certainty without requiring empirical confirmation – we do not asses the validity of the Pythagorean Theorem by drawing triangles and measuring their sides.
This is not true. I quote (p. 406) my college textbook:

Edwin Moise said:
This theorem tells us that it may be very hard to tell the difference between a hyperbolic plane and a Euclidean plane, if you are allowed to inspect only a small portion of it. One of the possibilities for physical space is that planes are hyperbolic, but that the portions of them that we can examine from the earth are ‘small,’ so that the deviation from the Euclidean angle-sum formula A + B + C = 180° is too small to be detected, for every triangle small enough for us to examine. C. F. Gauss made a test of this sort, using the peaks of three neighboring mountains as the vertices of his triangle. He was unable to observe a deviation from the Euclidean formula, but obviously it is possible that his mountains were too neighboring.
Asad Zaman wrote Gödel’s Theorems & the Limits of Reason on 12 April 2015, which makes his ignorance of Gauss’ experiment particularly surprising since he mentions it (but gets it wrong) in this paper, published four months earlier on 26 December 2014

Is Scientific Methodology Axiomatic?

Asad Zaman said:
Measuring triangles from mountaintops is an attempt to establish a synthetic truth that Euclidean geometry holds on the surface of the planet – under certain mappings, this would prove false since the surface is curved.
Zaman is conflating Riemann with Lobachevski. The reason Gauss went to the mountains was to test Lobachevski’s theory; for this he needed line of sight between vertices. Contra Zaman, the surface Gauss was on is not curved because it is defined as the plane that intersects the three mountaintops, suspended above the curved valleys below. We do not go to the mountains to test Riemann’s theory; we go to the oceans where any sea captain can tell us that the Pythagorean Theorem does not work for him.

REFERENCES

Debreu, Gerard. 1959. Theory of Value: An Axiomatic Analysis of Economic Equilibrium. New York, NY: John Wiley & Sons, Inc.

Devine, James. http://www.axiomaticeconomics.com/JD-2002-AutisticEcon.pdf

Moise, Edwin E. 1990. Elementary Geometry from an Advanced Standpoint. New York, NY: Addison-Wesley Publishing Company

Real-World Economics Review. http://www.axiomaticeconomics.com/example_of_censoring_axiomatic_method.pdf
 

CRGreathouse

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I must be missing something, since none of those quotes mention Gödel and the one link mentioning Gödel doesn't seem to talk about you or your book anywhere.
 
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I skimmed the Dr. Asad Zaman's entry, I didn't like it that much. Looks like a bit of post-modern philosophy.

My comment is: euclidian geometry IS decidable and there is no uncertainty on this. The fact that the 5th postulate cannot be proved from the other 4 is finally shown by the equiconsistency proof of Beltrami-?Klein that the 3 geometries are mutually consistent. And incompleteness is not surrounding Geometry in this sense, we can indeed put forward a formal system deciding the truth-value of geometric propositions as shown by Tarski if I'm not mistaken.

Alas, that hardly means that the 5th postulate being true or false is a matter of choice as I can choose if I eat bananas or mangos.

My interpretation here is: if I catch a flight to China, 5th postulate is enough, if I travel through the galaxy in some spaceship fast enough to get closer to light speed, then 5th postulate is a bad tool to describe my travel. Period.

But here a heavy opponent exists, search for Conventionalism and Poincaré.

On the other hand, I don't know what is your reason to debunk ad hominen those people. Maybe it would be a good idea to link to your formal presentation.

I'd take a look in that book I mentioned.
 
Oct 2015
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Arizona
I must be missing something, since none of those quotes mention Gödel and the one link mentioning Gödel doesn't seem to talk about you or your book anywhere.
Interesting… my name no longer appears in Zaman’s paper about Gödel. Also, the publication date has changed, though the URL remains the same.

I cannot now prove that Zaman was citing Gödel as a rebuttal of my work, but I can show you where Zaman links to this paper a month before it was supposedly written. Let’s start at the beginning in chronological order:

31 December 2014. I observe that economics bloggers were rallying around a man named Asad Zaman and, in particular, citing his paper, Deification of Science & Its Disastrous Consequences as proof that axiomatic economics is not science.

I post Mr. Zaman’s paper at the Econophysics Forum and quote this whopper:

Asad Zaman said:
It is a completely mistaken idea that scientific theory is based on deductions from a series of postulates – that is the description of the methodology of mathematics… There is no science which uses axioms and logical deductions to derive scientific theory.
Deification of Science & Its Disastrous Consequences | Econophysics Forum

I point out that Euler’s founding of ballistics is a counter-example. Admittedly, calling Mr. Zaman a fool was probably a tad provocative, though I was a bit peeved that his sycophant, Lars Syll, had attacked me three days earlier. Syll calls me autistic, a charge I had not heard since the Post-Autistic Economics Network changed their name to the World Economics Association in May 2011 and one I am rather sensitive to. (FYI I am not autistic.)

27 February 2015. Asad Zaman responds, linking to this paper:

Gödel’s Theorems & the Limits of Reason

In this paper Zaman refers to me by name, calling me a “science worshipper” and compares me to Pope Urban VIII. (FYI The Pakistani Zaman is an Islamic extremist – he doesn’t like the Catholics.) He states that Gödel’s Incompleteness Theorems refute all that I have written.

I do not respond to the charge that Gödel refutes my work, largely because I do not know very much about number theory. I do not think Zaman does either – I took note of the fact that he conflates Riemann with Lobachevski – but I did not at the time want to get into an argument on a subject that I had little expertise.

27 March 2015. I post a critique of Yanis Varoufakis, who is a close friend of James Galbraith, one of the founders of the Post-Autistic Economics Network. At the time that I wrote this, I was unaware that Mr. Varoufakis was the finance minister of Greece.

http://www3.unifr.ch/econophysics/sites/default/files/Review_Varoufakis_Arnsperger.pdf

3 April 2015 The Econophysics Forum goes down and stays down. E-mails to the Université de Fribourg go unanswered.

15 April 2015. The Econophysics Forum comes back online, thanks to the valiant efforts of its administrator, Matus Medo.

Recovered from a security problem | Econophysics Forum

27 April 2015 I belatedly become aware of Fribourg’s recovery, as I had stopped checking in every day, thinking they were gone for good. I comment that, in the meantime, I had observed bloggers associated with the World Economics Association (where Mr. Zaman is an editor) saying that the Université de Fribourg had it coming for promoting the axiomatic method, though none of them personally took credit for the cyber attack.

27 May 2015 My critique of Varoufakis’ academic paper has created a firestorm among all the Marxists pulling for him in his conflict with Greece’s creditors. I wasn’t trying to do this – I didn’t even know he was finance minister (I thought he was an academic) and I made no mention of politics – my paper just happened to come out at a time when Varoufakis was a controversial figure.

I had previously assumed that Zaman was behind the cyber attack, largely because it was bloggers on his website gloating about it. But, with all the death threats and similar remarks coming from the Marxists, it occurred to me that Varoufakis is the more likely culprit. The Université de Fribourg went down only days after I posted my critique of Varoufakis but over a month after my spat with Zaman; also, a finance minister has more resources for carrying out such actions than an editor.

I comment at the Econophysics Forum that Varoufakis is an official representative of the Greek government and so carrying out such an attack would amount to state-sponsored terrorism if it could be proven true. (FYI Russia shut down the Estonian government’s site in 2007, so cyber attack as state policy is not unheard of.)

Two months later, my suspicions are partially corroborated when Varoufakis is indicted for treason on charges of hacking into the Greek government’s tax records to obtain confidential financial information about every Greek citizen.

Yanis Varoufakis may face criminal charges over Greek currency plan | World news | The Guardian

If Varoufakis and Galbraith, who was in on it with him, can hack a government tax collection website, they can certainly hack a university website. Sites with confidential financial records have far higher security than academic sites.

22 November 2015 I post at My Math Forum the question left unanswered after my spat with Asad Zaman in February 2014: How to respond to the claim that Gödel refutes me? I find the link to Zaman’s paper about Gödel at the Econophysics Forum and look at the header to get the publication date, 12 April 2015.

I do not re-read the paper and so do not notice that the part about me being a “science worshipper” who was refuted by Gödel is missing, nor do I notice that the 12 April 2015 date flies in the face of Asad Zaman linking to his own paper on 27 February 2015.

Take note that Mr. Zaman edited his paper to remove my name and change the publication date DURING the time that the Econophysics Forum was down, actually three days before Matus Medo brought it back to life. Also, take note that my paper was then (and still is) only found at the Université de Fribourg and at my own website.

I’m guessing that Asad Zaman thought – on 12 April 2015 – that the Université de Fribourg was gone for good and so I effectively no longer existed, allowing him to re-write his history with me having never existed. But, when I popped back into existence on 15 April 2015, Zaman did not reinsert the text about me being a science worshipper refuted by Gödel. Maybe he didn’t save a copy.
 
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CRGreathouse

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Well, I suppose that moots the issue then!
 
Oct 2015
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Arizona
On page 15 you write:

"Stock and price, however, are inversely related, so increasing one or
the other does not necessarily increase aggregate utility. "

Question: isn't it in conflict with your claim on page 4 that

"It is a mistake to inquire whether I support Say's assertion that
"supply creates its own demand" or Keynes' assertion that "demand creates its
own supply"; Axiomatic Theory of Economics is detached from that debate."

Sorry if I'm missing something, but looks like the first claim uses implicitly the fact that too high prices shy away stock buyers because they have a limited supply of money (or other inter-exchangeable resources), and too much stock will drop prices precisely because now money (or other inter-exchangeable resources) is abundant so the stocks are cheap to acquire, so further increasing of stocks won't bring more consumers precisely because they have enough stock. In few words: looks like a supply and demand mechanism.
No, because stock and supply are different things. Stock is the quantity that exists at a particular moment in time and supply is its first derivative, the change in stock over some time period; that is, how much is produced every week or every month minus what is consumed or lost during that time period. I quote from p. 23 of my Simplified Exposition of Axiomatic Economics:

I assert that the stock of phenomena is more important than the supply because all of the decisions made regarding a phenomenon are based on its stock (how much of it is in existence), and not on how much of it happened to be produced in some arbitrary time period. Phenomena are the same whether they are produced in one time period or another. Most people do not know and none care what the supply of phenomena is, they are concerned with the stock; this week's or month's supply is only a small part of the available stock.
But you cannot be blamed for conflating stock and its first derivative, supply, because many economists use the words interchangeably, sometimes in the same sentence.

I quote now at length from my Critique of Austrian Economics, pp. 3-5, though this is not just an Austrian problem; all economists are like this.

Skousen asserts, “Let A be defined as the area of the APS [Aggregate Production Structure]. Thus, A represents the gross output of an economy during the year [GNO]” (1990, p. 195). Clearly, his APS graph describes a flow of goods.

What did Hayek, the originator of the structure of production, intend it to represent: a yearly flow of goods or a distribution of wealth? These are, after all, very different things. Hayek (1967, p. 40, italics added) writes:

Friedrich Hayek said:
The area of the triangle shows the totality of the successive stages through which the several units of original means of production pass before they become ripe for consumption. It also shows the total amount of intermediate products which must exist at any moment of time in order to secure a continuous output of consumers’ goods.
Also? In the first sentence, the word “pass” implies a flow of goods passing by during a certain amount of time. The second sentence refers to the total amount of goods that exist at a moment in time. It is highly irregular for a graph to mean one thing and also something else.

This confusion persists throughout Prices and Production. Hayek writes, “When I use the expression producers’ goods, I shall be designating all goods existing at any moment which are not consumers’ goods” (1967, p. 37). But then, when moving from triangles to histograms, he writes that he will “make cross sections through our first figure [the triangle] at intervals corresponding to the periods chosen, and to imagine observers being posted at each of these cross cuts who watch and note down the amount of goods flowing by” (1967, p. 43). “All goods existing at any moment” is not the same thing as “the amount of goods flowing by.”

Later, Hayek repeatedly refers to the “stock of capital” (1967, p. 137 et passim) and writes, “any given demand for consumers’ goods can lead to methods of production involving very different demands for producers’ goods, and the particular method of production chosen will depend on the proportion of the total wealth not required for immediate consumption” (p. 143). His use of the word “wealth” here clearly refers to a stock of capital.

By 1935 this confusion had been brought to Hayek’s attention, but he failed to act decisively. His four-year-old lectures, destined to become his best-known work, had much room for improvement, both in style, to reflect his mastery of the English language, and in substance, to reflect the firestorm of criticism they had provoked. Instead, in the preface to the revised edition of Prices and Production (1967, pp. x-xi), he wrote:

Friedrich Hayek said:
‘[D]emand’ for capital goods... does not consist exclusively or even primarily in a demand exercised on any market, but to a perhaps even greater degree in a demand or willingness to continue to hold capital goods for a further period of time. [i.e. stock is more important than supply] On the relationship between this total demand and the monetary demand for capital goods which manifests itself on the markets during any period of time, no general statements can be made.... [i.e. stock and supply are different things, measured in different units, and not directly related] The simplest assumption of this kind that I could make was to assume a fixed relationship between the monetary and the total demand for capital goods so as to make the amount of money spent on capital goods during a unit period of time equal to the value of the stock of capital goods in existence.
Retaining this “simplest assumption” was a big mistake. He should have abandoned consideration of the money spent on capital goods during a unit period of time and focused only on the stock of capital goods in existence.

This confusion persists even today. Garrison writes, “The time dimension that makes an explicit appearance on the horizontal leg of the Hayekian triangle has a double interpretation. First, it can depict goods in process moving through time from the inception to the completion of the production process. Second, it can represent the separate stages of production, all of which exist in the present, each of which aims at consumption at different points in the future” (2001, p. 47). Then, incredibly, he “resolves” this issue by putting two labels on the horizontal axis of his graph.

The problem is that most economists, not just the Hayekians, seem incapable of distinguishing between a supply, or flow, of goods and a stock of goods. It is easy to find examples in almost any economist’s writings where the words “supply” and “stock” are used interchangeably, often in the same sentence. Rothbard has written a long book about economics (1970), yet it is unclear whether his aggregate production structure depicts a supply or stock of goods. Maybe, like Hayek, he means one and also the other.

Skousen is at least consistent but, unfortunately, he is consistently wrong. He definitely means the amount of goods flowing by every year. My work is about stock, not supply.
Note that when I say "by 1935 this confusion had been brought to Hayek’s attention" I mean this:

Joan Robinson said:
"[Hayek] expounded his theory and covered the blackboard with his triangles. The whole argument, as we could see later, consisted in confusing the current rate of investment with the total stock of capital goods, but we could not make it out at the time.

REFERENCES

Garrison, Roger. 2001. Time and Money: The Macroeconomics of Capital Structure. New York, NY: Routledge

Hayek, Friedrich A. [1935] 1967. Prices and Production. New York, NY: Augustus M. Kelly, Publishers

Rothbard, Murray N. [1962] 1970. Man, Economy and State. Los Angeles, CA: Nash Publishing

Skousen, Mark. 1990. Structure of Production. New York. NY: New York University Press
 
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