On the use of logic and mathematics in economics
from Lars Syll
Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion – thus:
Major Premise: Sixty men can do a piece of work sixty times as quickly as one man.
Minor Premise: One man can dig a post-hole in sixty seconds; Therefore-
Conclusion: Sixty men can dig a post-hole in one second.This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.
Ambrose Bierce The Unabridged Devil’s Dictionary
In mainstream economics, both logic and mathematics are used extensively. And most mainstream economists sure look upon themselves as “twice blessed.”
Is there any scientific ground for that blessedness? None whatsoever!
If scientific progress in economics lies in our ability to tell ‘better and better stories’ one would, of course, expect economics journals being filled with articles supporting the stories with empirical evidence confirming the predictions. However, the journals still show a striking and embarrassing paucity of empirical studies that (try to) substantiate these predictive claims. Equally amazing is how little one has to say about the relationship between the model and real-world target systems. It is as though explicit discussion, argumentation and justification on the subject aren’t considered to be required.
In mathematics, the deductive-axiomatic method has worked just fine. But science is not mathematics. Conflating those two domains of knowledge has been one of the most fundamental mistakes made in modern economics. Applying it to real-world open systems immediately proves it to be excessively narrow and hopelessly irrelevant. Both the confirmatory and explanatory ilk of hypothetico-deductive reasoning fails since there is no way you can relevantly analyze confirmation or explanation as a purely logical relation between hypothesis and evidence or between law-like rules and explananda. In science, we argue and try to substantiate our beliefs and hypotheses with reliable evidence. Propositional and predicate deductive logic, on the other hand, is not about reliability, but the validity of the conclusions given that the premises are true.
Deduction — and the inferences that go with it — is an example of ‘explicative reasoning,’ where the conclusions we make are already included in the premises. Deductive inferences are purely analytical and it is this truth-preserving nature of deduction that makes it different from all other kinds of reasoning. But it is also its limitation since truth in the deductive context does not refer to a real-world ontology (only relating propositions as true or false within a formal-logic system) and as an argument scheme is totally non-ampliative — the output of the analysis is nothing else than the input.
If the ultimate criterion of success of a model is to what extent it predicts and coheres with (parts of) reality, modern mainstream economics seems to be a hopeless misallocation of scientific resources. To focus scientific endeavours on proving things in mathematical models, is a gross misapprehension of what an economic theory ought to be about. Deductivist models and methods disconnected from reality are not relevant to predict, explain or understand real-world economies.
Leave a comment
—– look inside —– $5.94 / $20.00
—– look inside —– $4.90 / $8.00
—– look inside —– $15.99
—– look inside —– $5.99 / 12.99
—– look inside —– $5.93 / $12.99
—– look inside —– $4.97 / $9.90
—— Ugarteche, Puyana and Madi ——
Gerson Lima / Maria Alejandra Madi
Edward Fullbrook and Jamie Morgan
————— Michael Hudson ————–
Maria Alejandra Madi / Jack Reardon
————- Edward Fullbrook ————-
—————— Steve Keen —————–
————— Richard Smith —————
————– Gustavo Marques————
– Victor Beker and Beniamino Moro –
————– Lars Pålsson Syll ————-
—————– Stuart Birks —————-
Edward Fullbrook and Jamie Morgan
———— Armando Ochangco ———-
Shimshon Bichler / Jonathan Nitzan
————— Mauro Gallegati ————–
————— Herman Daly —————-
————— Asad Zaman —————
—————– C. T. Kurien —————
————— Robert Locke —————-
Real-World Economics Review Blog 
Economics (mostly) is as scientifically predictive as the famous advert suggesting that 8 out of 9 cats prefer a certain kind of food. What a shame that cats were not allowed to chase mice freely, and have ended up being obese!
The cat and mouse story with economics continues unabated. Perhaps on May Day, some might join a worker’s march and sweat a little for the sake of the profession.
Apart from specific errors the mathematics used is not mathematically wrong. It is simply that a critical category error is present in economic analysis. The category error is that fitted equations unfettered by the quantity calculus are treated as theoretically valid. Only equations with quantities with small integer indices can be theoretically valid.
Therefore while the mathematics might be valid mathematical manipulations, they do NOT apply in our universe. It must be considered nonsensical that most quantitative analysis applies only in some alternate universe.
We must cease the pretense that mainstream economics is anything except a normative discipline. Hence, we must return to moral philosophy and ask ourselves what is right for people, living things in general and ecosystems. Economics should then be fully conformed to our ethical and democratic decisions. Instead, we make a fetish of a set of axiomatically derived algorithms and formulae (from a century-old mechanistic theory) which direct production and distribution in an autopilot fashion that drives people into unemployment, poverty and homelessness, causes mass extinctions of species and wrecks the climate and biosphere.
One of the characteristics of machine and automated production is that you can make a lot of mistakes very quickly. * To then run this machine and automated production system by the essentially automatic and inflexible algorithms and formulae of mainstream economics, is to compound this into the most terrible error.
*Note: For example, in the current context of climate change and species extinctions every automobile manufactured for personal transport is a mistake. In this very literal sense, we are now making a lot of mistakes very quickly.
The above statement on May Day was mine, but got lost in robotic engineering somehow.
The Geometric possibilities of anything new coming out of such formulations are next zero, and if, by any remote chance, it’s slightly more, it will be dependent on which dictator is selling more arms to his favourite fellow.
“Deductivist models and methods disconnected from reality are not relevant to predict, explain or understand real-world economies.”
A case of the pot calling the Kettle black? Inductivist models and methods disconnected from reality are not relevant to predict, explain or understand real-world economies either. In the real world “I” isn’t worth anything if no return is in the offing. Yet in the inductively obtained primal Keynesian identity Y=C+I, all factors are real and determinate ex ante. Instead, to understand the ontology of a _dynamic_ real-world economy: C determines I through Y over time. So either the determinant of I is indeed a static portion of Y, i.e. a dynamic economy can yet be made sense of statically, or you are simply wrong. Neither deduction nor truth finding is the enemy, stubbornly holding on to a inductive reasoning “ueber alles”, regardless of its inherent shortcomings, is.
Shimshon Bichler and Jonathan Nitzan in their conclusion to “Capital accumulation: fiction and reality” manage to sum up and refute modern economics in one masterful sentence:
“You cannot build an entire social cosmology on the assumptions of individual rationality, equilibrium and perfect markets – and then blame the failures of this cosmology on irrationality, disequilibrium and imperfections.”
They continue:
“In science, these excuses and blame-shifting are tantamount to self-refutation. What we need now are not better tools, more accurate modelling and improved data, but a different way of thinking altogether, a totally new cosmology for the post-capitalist age.”
Bichler and Nitzan clearly mean that we do not need better tools in the current paradigm as the paradigm itself is based on false premises. They propose the need for a new paradigm, “a totally new (social) cosmology”. To explore the cosmology analogy, the physical cosmos is a single connected system and cosmological science deals with it via a relational theory framework. In such a systems framework, the positions and other properties of existents are only meaningful relative to the positions and other properties of other existents in the system. In a social cosmology, this immediately suggests that individual “rationality” is not discretely atomistic and fixed. Rather, individual rationality is socially conditioned and thus fluid or at least malleable. Collective, as well as individual, rational and irrational behaviors also do exist, or rather arise, as emergent properties. The essential problems to be dealt with here are ontological problems. What really exists in a socioeconomic system and how do these existents relate each to each?
Bichler and Nitzan refer to “the duality of real and nominal”. They expand on this to refer to the splits of “subject and object, idea and thing, nomos and physis”. As I see it, the problem of the duality of the real and the nominal is what modern economics fundamentally and comprehensively fails to deal with. This constitutes the foundational ontological and scientific failure of modern economics. When the premises are wrong, all the deductions which follow the premises are wrong.
When we are dealing with physical phenomena, the fundamental laws of the cosmos are independent of human understanding or modelling of them. No matter what you or I or any human thinks of the Laws of Thermodynamics or even whether we are ignorant of them, the fundamental phenomena follow a course which can be well modeled by those laws when those laws are mathematicized to permit accurate descriptions and empirically verifiable predictions. However, when it comes to socioeconomic phenomena, what we think and believe enter into the constructions and emergent outcomes of socioeconomic phenomena themselves (along with fundamental law effects also entering into the constructions and outcomes). At this level, any theory of the system enters into the system as a compounding or complicating element. Thence meta-theory (theory of the impact of theories on the system) will also enter into the system. These theories enter into the system by changing the behaviors of human subjects, not by changing any fundamental laws of course.
It is not possible to mathematicize the above process into fundamental economic laws for the simple reason that most socioeconomic rules are arbitrary and may be changed at any time. Here we must distinguish between rules and laws. Rules are social decisions on how to conduct matters. Hence rules in this sense are any and all of customs, legal laws, accounting rules, finance rules and so on. Rules instituted into systems become algorithms or recipes; lists of ingredients, methods and time orders for doing things. Any of these rules may be made one way or made any other way with the major proviso that rules which contradict fundamental laws are not actionable. Rules which self-contradict are also not actionable unless one rule takes precedence over another rule.
It is not possible to fully mathematicize the changing ground of socioeconomics precisely because the bounds of the problem can be changed by changing the rules of the game (meaning the cooperative-competitive game) of socioeconomic behaviors in praxis. The socioeconomic system which we seek to model continually mutates as we change its rules. Changing the rules happens by any and all of fiat or consensus up to and including gaming, loophole finding, criminality and so on. Also, theories of the system enter into the system as outlined above. Changing the rules sets up new constellations of bodies and interactions (as processes) and annuls other constellations. This statement refers again to the relational system cosmology analogy. This is not just an n-body problem where n is a huge number. It is also an “n-rule” problem where the rules continually mutate in designed and un-designed ways.
The totally new social cosmology Bichler and Nitzan very rightly call for is not predictable nor even envision-able in many ways. Being a new and emergent complex system it will demonstrate radical novelty. Radical novelty in systems emergence theory is not predictable because an explanatory gap, or an epistemological gap, unavoidably exists between the precursor or substrate system and the next radically different system.
Calls to theoretically elucidate (and worse, calls to mathematically delineate) the new system are totally inoperable calls. We cannot predefine it by positive or prescriptive statements. We do not know the right way to go as it is an open-ended problem with an infinite or near-infinite move tree. The problem is as if it were a hyper-complex chess game played on an near infinite board. The analogy of search tree “look ahead” logic is appropriate. In a massively complex open-ended problem, the series of perfect moves leading to perfect or “won” game is incalculable. What are calculable are very bad and indeed dreadful moves which lead to checkmate (human civilizational or species extinction) in a “few moves” meaning in a relatively short time frame.
Thus the problem is not to find the “perfect moves” or the theoretically “perfect system” for calculating perfect moves. (Modern economics pretends to be this idealized perfect system.) Instead, the problem is to avoid the really bad moves. Our practice of late stage capitalist economics (neoliberal economics) has revealed and is revealing a wide panoply of really bad moves. In summary, the really bad moves clearly revolve around;
(a) treating the free goods of nature (of the biosphere) as infinite;
(b) running an endless growth economy on a finite planet;
(c) allowing algorithmic (and “autocatalytic sprawl”) processes to run unimpeded according to the current prescriptive theories of capitalism without regard for real system impacts.
(d) allowing algorithmic (and “autocatalytic sprawl”) processes to run unimpeded according to the current prescriptive theories of capitalism without regard for real system impacts.
Points (b) to (d) are really elaborations on point (a) rather than truly separate points. However, the elaborations are important. They indicate the areas where we should start changing things to avoid the obviously bad moves. It is the use of our science, logic and humane ethics to avoid the obviously bad moves which will in effect instantiate a move away from the blind implementation of the ideological or faith logic and algorithms of orthodox economics. It is the method of avoiding obviously bad moves (obviously correct to a high degree of certainty to science and to human consequential ethics) which can likely shift the system to “a totally new social cosmology” even though we cannot envisage or predict the emergent form of that system.
As you point out “No matter what you or I or any human thinks of the Laws of Thermodynamics or even whether we are ignorant of them, the fundamental phenomena follow a course which can be well modeled by those laws when those laws are mathematicized to permit accurate descriptions and empirically verifiable predictions”.
So the physical realisation of decisions already made in setting up a production plant are predictable as they record the output of a physical plant.
.
Frank Salter cherry picks–i.e., uses as a straw man argument so he can intellectually parrot of the same old canard he parrots ad nauseum on this blog) from Ikonoclast’s lucid post thereby grossly misrepresenting and distorting its real meaning.
The irony is that Salter’s claim is proven false by empirical evidence in that prior to the Global Financial Crisis “decisions already made in setting up … production plant[s]” unpredictably were changed due to unpredictable human behavior that brought the global financial system to a near death experience.
.
It is the height of hubris to claim that “decisions already made in setting up a production plant are predictable as they record the output of a physical plant” in the face of real world evidence to the contrary proven by what really happened–fall in production output– in the wake of the 2007-2008 GFC.
.
To reveal how truly irrelevant and useless Frank Salter’s parroting of his ludicrous claims are one only needs to observe the following exchange between Frank Salter [FS] and Dave Marsay [DM]:
.
Of course Lars has better things to do then engage with the deaf, dumb, and blind who refuse to see the logical fallacies in their own intellectual parroting of, what is in Frank’s own words, “essentially irrelevant” claim that ignores the reality that we live in an uncertain world and when the world’s global financial system collapses and credit dries up production plans change radically (think radical uncertainty), and literally minded folk like Frank lack the meta-ability to understand, let alone grasp, the true underlying causes of such radical uncertainty, per his own admission: I am not well versed in financial crises. I therefore need to pass on that. Irony, it seems, is that Frank thinks once plans are made they never change because, after all, he has correctly used the quantity calculus!
If you did due diligence and look up the references you would might make at least one apposite contribution. But to skip to the chase. You have repeatedly failed, however often you have been politely asked to demonstrate the validity of your claims — How does my transient analysis fail to do exactly what is claimed? I do NOT expect you to be answer that question. That would require academic effort rather than simply trolling.
Your ridiculous comments prove you have never studied my analysis. You have clearly no idea what the quantity calculus is and its significance in theoretical understanding.
To pick up your final misconceived point. The mathematics I presented describe all possible outcomes of production. It you had looked at the graphs, you would have seen that they show all levels of output from zero to the maximum possible.
I find inconceivable that any competent academic would fail to justify their reasoning. But as I said, I do NOT expect you to to do anything other than shout louder.
I have read your papers references Frank. That cgsnges nothing. In fact the flatly refute your utterly ridiculous modeless modeling claim.
Frank “the graphs of my quantity calculus prove that supply creates its own demand, even at zero output” the troll Sa[y]lter.
Rob, if you read any of the 1.8 million scientific papers from first principles, which you describe as modelling without models, you would understand how ridiculous your comment is. I am not sure how to describe what you think you are saying. You insist that you are right despite overwhelming evidence to the contrary.
John, why do you continue to share your delusions of what I have said? You never deal with the reality. The quality calculus is completely accepted by scientists and clearly not understood by economists. I present a mathematical analysis which accords with reality and which you appear be incapable of understanding. That I am able to comprehend, but to claim that I have said things that I have not is totally dishonest. As I said in my earlier reply to you, I do not actually expect you to deal with the reality I presented. As usual you fail to disappoint. If you wish to discuss my analysis, deal with what it says and not with your fantasies.
No delusions Frank… Salter’s reality “My paper is on manufacturing development not on economies.” [New comment] Utopia and epistemology 3/27/2018 8:42 AM
Salter, the troll, can’t help himself to yet incessantly push his “reality” onto a forum that tries to come to grips with the determinants of supply and demand in economies. I’ll stop feeding the troll now.
The first step in understanding, managing, defining or predicting any system is an accurate measurement system for quantification purposes. The field of economics specifically and actively avoids an accurate understanding of money to hide it’s pitiful and pathetic performance to date. This duck and cover is probably the smartest thing that economists do.
The classical labour-time of production is the natural abstract measure of output.
Despite being put off by John Vertegaal ‘s kettle calling Frank Salter’s pot black, I have thoughts probably worth adding to the valuable contributions of Lars, Ikonoclast and RRDulin.
Lars’ story of digging holes in 60 seconds reminded me of how, when studying development of parallel processing in computers, a fellow scientist showed me how this was being achieved in ordinary linear logic by pipe-lining – in effect time-sharing – as in a production line. (That of course is the basis of multi-programmed computers and multiplexed communication). On a hole-digging production line, it is quite reasonable that sixty men might churn out holes at a rate (on average) of one per second. As criticisms of the conventional syllogism as presented by Lars, I might point out that the words in its premises merely point to aspects of reality, and a context – ultimately the whole of reality – amounts to an unarticulated and therefore missing premise. Articulating this, “In the context of a production line, sixty men may well produce holes in an average time of 1 second”.
Carrying this forward to Ikonoclast’s lucid exposition of Bichler and Nitzan’s arguments, for sure “You cannot build an entire social cosmology on the assumptions of individual rationality, equilibrium and perfect markets – and then blame the failures of this cosmology on irrationality, disequilibrium and imperfections.” But can we not blame it on the failure to set rationality in the context of language, and the creation of irrationality by failure to define terms, hold fast to them and not change the context they are pointing to?
Ikonoclast goes on: “when it comes to socioeconomic phenomena, what we think and believe enter into the constructions and emergent outcomes of socioeconomic phenomena themselves (along with fundamental law effects also entering into the constructions and outcomes). … Thence meta-theory … enter[s] into the system by changing the behaviours of human subjects, not by changing any fundamental laws. … Here we must distinguish between rules and laws. … rules may be made one way or made any other way with the major proviso that rules which contradict fundamental laws are not actionable.”
I’m not interested here in the rule of exponential growth contradicting the laws of living on a finite planet. My interest here is in which came first, laws or rules: the chicken or the egg? Insofar as the laws are human articulations of what we have perceived, mustn’t the rules of articulation have come first? Cannot the language we take for granted as pointing to the physical laws be misdirected (as they were with Ptolemaic cosmology and arguably – in the context of electromagnetic energy as against that of Newtonian masses – the denial of perpetual motion machines)?
This leads us to RDDulin’s comment on the need for “an accurate measurement system for quantification purposes”. In the context of the use of money in the economy I entirely agree with him, but again, let us expand the context a little further. The concepts defined by words are also a type of measure (of what type of object as against how many of them). In the language of geometry, concepts define set boundaries and we count (quantify) the points (representing objects) within them. However, it is not necessary to have “an accurate measuring system”. All that is necessary is for the objects and concepts to be absolutely distinct. Fuzzy logic does not produce fuzzy answers. It can be absolutely true that a length, say, is more rather than less than a metre, even if one cannot say by how much. Digital communication depends on this, restoring signal forms (not meaning) to a more accurate shape while they are still recognisable as one thing rather than another. What in everyday life is generally much more important than precise quantities is doing things in the right order, and correcting wrongs and side effects before they spread.
Like all human processes logic is historical and cultural. The form and uses of a logic reflect these. Formal logics developed in ancient India, China, and Greece. Greek logics, such as Aristotelian logic (or term logic) as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic. Christian and Islamic philosophers such as Boethius (died 524), Ibn Sina (Avicenna, died 1037), and William of Ockham (died 1347) further developed Aristotle’s logic in the Middle Ages, reaching a high point in the mid-14th century, with Jean Buridan. Between the 14th century and the beginning of the 19th century use of formal logic declined. Empirical methods ruled the day, as evidenced for example by Sir Francis Bacon’s Novum Organon of 1620. Formal logic returned only when combined with mathematics during the 19th century. Here formal logic was transformed into a rigorous and formal discipline that took as its exemplar the exact method of proof used in mathematics, a return to the Greek tradition. During this period modern “symbolic” or “mathematical” logic was created by the likes of Boole, Frege, Russell, and Peano. Development of mathematical logic continues, based on the work of Gödel and Tarski, along with the fields of analytic philosophy and philosophical logic, in such focuses as modal logic, temporal logic, deontic logic, and relevance logic.
More than you wanted to know about logic? Sorry. Everything has a history, including formal logic. Citing Ambrose Bierce’s story about logic from “The Unabridged Devil’s Dictionary” is appropriate. Logicians and mathematicians, now blending into one field are not empiricists. They are rule followers. If one follows the rules of logic, whichever logic is preferred, or the rules of mathematics, whichever math is preferred creates logically or mathematically acceptable results. There are multiple problems with this conclusion. The most important being that in order to use rules humans must interpret their meaning. Often interpretations differ. Thus, results differ. This is clearly the case with the Aristotle-based “syllogism arithmetical” from Ambrose Bierce. Sometimes mathematics, logic, and science can benefit one another. For such to occur, however, the emphasis must be scientific, not mathematical or logical. When searching for empirical facts (patterns/outlines) mathematics and logic must help scientists reveal these, not hide them behind rules of logic or mathematics. In simple terms, scientific work emphasizes catch-as-catch-can rather than rule following. The rules of logic and mathematics differ around the world and over history, but the commonality is there are rules that must be followed. Also, in common is that the rules determine the results of the use of logic or mathematics. Science, on the other hand has no hard and fast rules. It is the process of figuring out how things, any things are created, change, and effect humans and nonhumans. Scientists will try just about any approach to this work. Which brings up the question of ethics. Which approaches fit with cultural ethics and which do not?
I thought a little historical text might be interesting. This topic has been discussed before. I don’t have the entire text (yet, will get it) but here is bits and pieces taken from another source.
I first read a rework of this author in another source, but that is another story.