By Philip Pilkington, a writer and journalist based in Dublin, Ireland. You can follow him on Twitter at @pilkingtonphil
The influence that mathematics has had on neoclassical economics is obviously quite profound. However, when looked at in detail it appears that a certain type of modern mathematics was in fact highly suited to the direction many in the economics profession took after the work of Leon Walras – the Frenchman who founded modern neoclassical economics – appeared on the scene. So, it should not be thought that it was simply the formal tools of mathematics that transformed neoclassical economics into the obscurantist doctrine it is today. Instead it should be understood that its obscurantist skeleton was ready and waiting for its mathematical flesh.
It has been said before – and not just by the present writer – that neoclassical economics amounts to a sort of theological system that bears no resemblance to reality for the simple reason that it does not aim at reality. But the relationship between the doctrine and its formal presentation is less often talked about. In a very interesting paper entitled ‘Kaldor on Debreu: The Critique of General Equilibrium Reconsidered’ philosophers of economics Thomas Boylan and Paschal O’ Gorman deal with precisely this. We will try to highlight and expand upon their fascinating observations.
A Mathematical Crystal
The authors begin by engaging with the British Post-Keynesian economist Nicholas Kaldor’s critique of neoclassical methodology. Kaldor insisted that in order for economics to progress as a modern science the neoclassical research program had to be completely demolished. The reason for such insistence was because Kaldor was an extremely practical man. He was deeply involved in debates of British economic policy in the post-war years and in his later years, from his perch in the British House of Lords he commented on the economic policy of his day.
Yet at the same time Kaldor was a theoretical economist. Thus, it is not surprising that Kaldor should think that good economic theory should reflect the real world as much as possible. Kaldor thought that neoclassical theory did not do this at all. In one particularly stark passage he wrote that neoclassical economics was “barren and irrelevant as an apparatus of thought to deal with the manner of operation of economic forces.”
Kaldor was particularly concerned that neoclassical economic theory was, for the most part, engaged in trying to construct what he called a “mathematical crystal” that was absolutely perfect and self-contained and had no relation to the real world. Kaldor believed that science, as opposed to a sort of mathematical aesthetics, proceeded in the other direction. Yes, theory should be logically consistent, but first and foremost it should deal with the facts at hand. If it did not do this in any meaningful way then any logical consistency was only so much decoration on an otherwise inedible cake.
Before moving on it is perhaps allowing Kaldor himself to get an extended word in on the neoclassical approach that has come to dominate the economics departments.
One of the ideas I wished to convey in my first lecture was that the type of economic theory which is the core of the subject as taught in western universities — and that covers North America, Western Europe, Australia, and so on – is pretty useless and indeed harmful for developing an understanding of the laws of motion of capitalist market economies. It is expressed with a phoney kind of precision or “scientism” of a most pretentious kind, using highly sophisticated, mathematical techniques for proving propositions which have no interpretative value of real-world phenomena, for the simple reason that they are based on a priori axioms which have no relation to the conditions which can be empirically observed. All this is aggravated, not helped, by the use of mathematics.
While Kaldor did have some very specific critiques of certain aspects of neoclassical economics, we will not consider them here (the interested reader can download the above cited paper for details). Instead, we will pursue the fertile line of thought taken up by Boylan and O’ Gorman.
Debreu as Platonist
The authors focus on the work of the French economist Gerard Debreu who was the first to lay out a complete articulation of a general equilibrium theory grounded in modern mathematics. They claim, however, that it is the type of mathematics Debreu used which gives us insight into the type of theorising he was actually doing.
Debreu’s method derived from a strain of mathematical theory that was, in a strong sense, ruthlessly unpragmatic. Such a tradition reaches right back to the ancients and to the work of the ancient geometer Euclid. In his ‘History of Western Philosophy’ Bertrand Russell links this to a whole tradition of philosophy which is concerned not with reality, but instead by idealistic abstractions. This tradition – which is strongly theological and metaphysical – is generally referred to as idealism and is usually traced back to Plato. Russell explains the connection as such:
There is in Euclid the contempt for practical utility which had been inculcated by Plato. It is said that a pupil, after listening to a demonstration, asked what he would gain by learning geometry, whereupon Euclid called a slave and said ‘Give the young man threepence, since he must needs make a gain from what he learns.’
This led to a manner of viewing the world in which passive contemplation of purely logical forms was thought to be the ultimate end of all thinking. Reality was then chastised by the idealist for not living up to the Ideals of geometry and the great Ideas generated in the mind of the philosopher or the theorist. Such thinking was, of course, immensely popular with the medieval theologians and those that came after them who often applied them as a means to meditate on the infinite perfection of the Christian God. We will come back to this latter observation in a moment.
Such a tradition lives on in mathematics right to this day. It is today generally associated with what have come to be called the Bourbakian School – after a group of (again) French mathematicians who wrote together under the pseudonym ‘Nicholas Bourbaki’. This tradition was passed down to Debreu and the neoclassicals through his use of Cantorian set theory – a powerful form of mathematics developed in the late 19th century. This led the higher, more theoretically-oriented neoclassicals to ultimately assert that pure theory should have absolutely no relation to reality. Indeed, in an extreme form the mathematical terms used in neoclassical economics are to be thought of as meaningless symbols – a rather strange approach when one considers that these symbols are supposed to represent real world phenomena.
Intellectual Hierarchy and Our Political Dark Age
This is, of course, not a scientific approach. It eschews empirical reality in favour of logical perfection. It thus becomes far more similar to the meditations undertaken by theologians of the Middle Ages rather than the applied logic of the scientists of the post-Cartesian era. What Debreu and his followers thus practice is a sort of Divine Mathematics. In doing what they refer to as economics they are not engaged in scientific discovery, but instead are working through logical problems in a sort of meditative pose. Their version of the old Christian idea of God they refer to as ‘the market’ or ‘general equilibrium’. This is then asserted to be the manner in which the real economy operates in the long-run. And this strange ritual is all undertaken prior to their looking at any empirical evidence at all!
The rather comical thing about this is that most higher-level theorists are well aware that what they are doing is not really any sort of theoretical economics when we understand that term in a scientific sense (modern science assuming both empirical correctness and logical rigour). It is instead a set of “what if” logical constructions that are worked through until they are thought to be perfectly consistent and harmonious. However, as Kaldor said, the higher-level theorists have not “managed to pass this message down the line to the textbook writer and to the classroom.”
Thus what we have is a strange hierarchy system in which higher-level theorists are well aware that they are engaging in mere logical games, while the lower-level theorists think that, for some unstated reason, neoclassical theory has some sort of empirical validity. The end result is that economists tend to be extremely foggy about real world problems.
This is not surprising given that their theoretical framework of choice aims at hiding reality from them rather than allowing them to approach it with a set of useful tools. Such a situation is not far away from the hierarchy of the Christian church in the Middle Ages where advanced theological scholars worked out logical deductions about God’s perfection and existence while lower-level priests disseminated this message as if it contained empirical truths. The higher-level were generally aware that they were engaged in a meditation of sorts, while the lower level thought that the higher-level had actually proved something about reality. Another term for this period is, of course, ‘the Dark Ages’. And many have concluded that the reason these ages were so dark was because the Church, which maintained authority on all intellectual activity, was engaged in idealistic reasoning constructed out of mere tautologies; just the same, of course, with neoclassical economics in our current political Dark Age.
Idealism as Formal Structure: The Mathematics of Infinity
Boylan and O’ Gorman make an extremely interesting case that we can observe this shift away from empirical reality and toward metaphysics or theology in the Cantorian set theory applied by Debreu and passed down to the neoclassicals. The authors point out that a major difference between Cantor and Bourbakian School on the one hand and their more practically-minded colleagues on the other is that while the former believe in ‘actual infinity’, the latter believe in ‘potential infinity’.
That may sound complex, but it is not very. As we all know numbers could be potentially counted to infinite – there is no “end” to the numerical chain and it could, in theory, stretch on forever. Now, more pragmatic mathematicians claim that while numbers are ‘potentially infinite’ we can never, as it were, draw ourselves back to view this infinity. Cantor, on the other hand, claimed that we could – hence why his method is referred to as ‘actual infinity’. Infinity is treated as if it actually existed as an observable or conceivable entity.
However, the idea that we – or some entity – could “zoom out” and look upon the infinite amount of numbers in existence is tantamount to positing an omnipresent God through whom we can grasp at the ungraspable. This objection was thrown at Cantor and his followers by his more pragmatically-minded colleague Henri Poincare who rejected the Cantorian system because he refused to “argue on the hypothesis of some infinitely talkative divinity capable of thinking an infinite number of words in a finite length of time.”
Some of Debreu’s proofs, according to Boylan and O’ Gorman, relied heavily on such a “theological mathematics”. That is, they could not be carried out in a finite number of steps and instead took on a timeless or Divine quality. This, of course, reflected perfectly the neoclassical obsession with an economy automatically moving toward perfection through a “Hidden Hand” mechanism. So, we can conclude that even in their formal presentation the higher-level neoclassicals are engaged in a sort of religious meditation rather than an attempt to fashion a theory which fits the real world. And that is how the idea of market perfection is squared with what Kaldor called the “mathematical crystal”.
It would be nice to think that escape from our present Dark Age would be possible by simply pointing this out to the lower-order neoclassicals, so that they could consider if such a methodology is appropriate for textbooks and students. Alas, this is not so. If the Dark Ages taught us anything it is that Heresy is considered an abominable crime. And while the neoclassicals do not today possess the methods of torture and execution held by the Church of that Middle Ages, they do possess almost total hegemony over both the university departments and the debates. And they have an extremely strong investment in the tautologies of the higher-order neoclassicals – indeed, they rely on such meditations for their Divine Authority.
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Philip Sir,
Andrew Haldane of the Bank of England is quite forthright in his view that neoclassical economics failed risibly in regards to the 2007/08 GFC.
As an economist himself, that just about sums up what’s wrong with economics presently, i.e., it is absolutely divorced from any kind of reality – it is, as you suggest, a religion rather than a science, and social science at that.
Whilst we have Prof. Steve Keen and the heterodox economists telling us to divest ourselves of most economics taught since the early 50’s, its telling that the London School of Economics ‘LSE’ is still erroneously referred too as the LSE, rather than its correct title, this being the London School of Economics and Political Science.
Until we can all start agin agreeing that economics is not a science, rather its a social science, we’ll be stuck in our current lapsed mental state and economy moving towards ‘beyond repair.’
Once more, you should be thanked for emphasising yet again that many of the foundations of neoclassical economics are false at best, and egregious in the extreme – that people and government agencies take this crud seriously is beyond me – Perhaps its time for an apology.
At least Haldane gets it, and for this I dream he may one day become Governor of the Bank of England – for which, he actually has been tipped by a few authorities I personally know.
A friend and I were talking about Haldane’s colleague, Adair Turner a short while ago. They strike me as somewhat tragic figures. Being practical and sensible people, they are aware that neoclassical economics is bunk. Yet, lacking an alternative their language remains punctuated with neoclassical phrases and ideas.
Of course, this is better than nothing and I’d prefer they were in charge than the likes of Bernanke with his monetarist QE nonsense. But their scepticism can only go so far, unfortunately.
Kinda agree with you, its like rabbits caught in car headlights.
The good news is that hopefully heterodox economics may finally gain a toehold in academia – remember, many of our leading lights, be they central bankers, economists of all strips and indeed politicians – particularly in the UK, were educated at a time when the Chicago School of Thought was hot in many a university department.
All I can say is I’m glad I only studied key economic tracts from their political perspective, rather than supposed scientific perspective, particularly given when even I in the late 80’s as an undergraduate was aware economics certainly was not science, or not science in the way I understood it.
indeed, having been a helpless victim of Thatcher’s two year experiment with monetarism, I can assure you the economics of Marx was more compelling than that of Friedman et.al.
Still, at least we are finally being made aware of another train of thought with regards economics and sociology in the form of Veblen, so hopefully, after nearly 50 years of having nonsense taught to our next leaders, Universities may finally rediscover what they are supposed to be about, rather than just business engines to churn out uncritical minds.
It is going to be a long time before a new economics theory reaches the students. Take Frederic Mishkin who was a total failure as an economist while at the Federal Reserve. He wrote a paper that extolled the virtues of Iceland’s economy just before the banks collapsed. He resigned from the Fed to write a book and teach his students at Columbia. Do you think he has learned anything? How many more classes will he teach the crap that he practised? Yes, it will be long time before reality takes hold in the real world.
Phil, All Economics is BASELESS Theory. Simply, he who has the Gold, rules. When one discovers the ‘rules’…aka The Business Methods and tools used to process the Economy, one will find the Gold, the Rulers, and the RUSE to make the finite…infinite.
Reminds me of Ludwig von Mises’ praxeology, which amounted to a rejection of empirical observation in favor of deductive logic from axioms.
Neoclassical economics continues to exist and its exponents continue to prosper only because it’s conclusions are convenient to those owning and controlling about 90% of everything worth owning and controlling. You don’t need mathematics to smell horseshit. The best way to deal with neoclassical economists is to pelt them with rotten eggs. Had we done that with Milton Friedman thirty years ago our contemporary disaster might have been avoided.
I agree that Uncle Miltie is way up on the list of people responsible for the mess we’re in.
But what you say, overall, is actually a vindication of economics. Economists claim that “incentives matter.” Now, if we apply that to economists themselves, we would conjecture that they’d shill themselves out to the rich and powerful.
Unfortunately it appears that the empirical data do bear this out…
I remember a colleague of mine (this is back when I was still working) coming back from a meeting with an economics professor whom he had been consulting on some obscure point and telling us all that when he objected to some things the prof. said because they were unrealistic, the prof just said “Oh, well, if you want to take the real world as a special case…”
The Real World As A Special Case recurs to my mind whenever reality buries some pundit under awkward facts. As Prof. Krugman keeps reminding us, however, that doesn’t stop them.
In his comment above, jake chase notes that an impractical theory can have a very practical use. But neoclassical theory shouldn’t be regarded as the only instance of convenient theory being invented for some very practical purpose. Racial superiority used to be regularly trotted out to justify colonialism and slavery. And before they got the vote, women were regularly patronised as inherently unstable, illogical and over-emotional – especially where money was concerned!
Good post–however, I think it is unfair to class Plato in this camp of unreality. While his dialogues are examples of logical reasoning they are, clearly, not particularly rigorous. What is great about Plato is that he presents us with a method which is dialogue. Two people agreeing to examine a subject throught give and take. The conclusions are interesting but the approach is as important. What is missing from economics and many other academic disciplines is a respect for dialectics and an openness to discussion and creative argument.
Much of the problem we face in looking at “economics” is that there is no such thing as “economics” apart from political economy. What we call economics is 100% political. Once this is understood we can do away with the insane notion of a “free” market. There is no and cannot be any such thing and it is easily proven. Since many economists use this free-market notion as something real all thinking that follows is erroneous. For those who do not get it, no market can exist without a political structure otherwise marauders would just make off with all the goods–very simple proof.
I think the shot at Plato is more over his Platonic Forms than his rhetoric. Platonic Forms says that reality tends towards conceptual absolutes. I.e., there is an absolute “goodness” that we exhibit (or don’t). This was partially aimed at moral relativism. If we convince everyone that absolutes exist, then that bolsters the case of moral absolutism.
One of Plato’s critics observed that he could see individual horses, but not “horseness” — to which Plato replied that that was because he was a buffoon. In my opinion, Plato lost that argument.
The connection to Euclid is interesting, as it’s always bothered me that we can conceive of a perfect circle, but can never actually create one in reality. Geometry is, as PhilPil points out, a Platonic Form with cosines.
“One of Plato’s critics observed that he could see individual horses, but not “horseness” –”
Plato might have countered — “But can you hear it?”
Philip,
A very interesting article, as usual, but I wonder if the egg and the chicken haven’t gotten switched around. “Bourbaki” sought to replace the existing theoretical basis for mathematics with what they argued was a more sound foundation that rested on the sort of set-theoretical constructions you described. (BTW, this has been challenged recently.) So, it’s likely that anyone looking to develop a mathematical model using the latest mathematical ideas of the time would have found their way to Bourbaki; that’s certainly true in all branches of science today, even physics, where the failures of economics don’t exist. And Bourbakian mathematicians were no more or less “etherial” than any other mathematicians—all mathematicians work to some degree in the world of theory. The Bourbakians were special in their insistence that they had found a more pure foundation for mathematics; the debate with Poincare over Cantor’s arguments (which, I believe most mathematicians today would say Poincare lost) had little to do with practicality in the sense of the physical world. In short then, Bourbaki may be a red herring. (No pun intended.)
Typically, all scientists, physical as well as social, start with a model of interactions based to some degree on observation. The interactions are then described in mathematical terms in the hopes that some predictable pattern will be described by the mathematical model (and proved by subsequent observations based on predictions made using the model). As Keen describes very well, the real problem is how Walras, Marshall, Debreu, et al. conceived of the market and the interactions among its participants. Mathematics is agnostic; to borrow from the NRA: Mathematics doesn’t make bad models; people make bad models using mathematics. Starting from notions of utility and price setting that are naive to the point of childish, the founders of what we call neoclassical economics built a model that simply doesn’t work and will never work no matter what mathematics you use. Keen’s point is that the model drive the choice of mathematics—If you want to describe mathematically the sort of magical supply and demand curves and ever-increasing “utility” from consumption, then you have to use certain mathematical concepts. But it’s a two-way street: in order to solve the resulting mathematical equations, you have to make certain simplifying assumptions in the model. As both Keen and Yves describe so well, the absurdity of the assumptions needed to make the basic model work mathematically should have been glaring to anyone in the field. And yet we have such luminaries as Paul Samuelson building the foundations of modern economics using ideas like ergodic theory that have no place in modeling economic activity other than to make the mathematics soluble.
I think that the real question is why we use the neoclassical model today in the face of the evidence of its failures; and how did the model return after being recognized as a failure. In short, I think the issue is far more political than mathematical. The ideas of the physiocrats and Adam Smith reflected the idea that society could be built without reference to some higher source of morality, i.e., religion and its attendant monarchy. In order to do this, they had to conceive of a self-regulating system for enforcing socially productive behavior, a sort of moral physics; that system was the market: People buying and selling would have to learn to get along or else starve; we all would have to be productive—and would reap greater material wealth—if we organized our production “scientifically” by specialization, etc. Of course these ideas also had to explain the great inequalities in the distribution of wealth, or anarchy would result without a sort of “physical” justification; they had the answer too—Those who had wealth were more “productive” than those who were poor; to anticipate Spencer, nature, ultimately perhaps the clockwork expression of the divine watchmaker, favored the more productive.
When the industrial revolution came, these ideas were even more attractive to the ruling elites in the face of growing unrest. Thinkers like Bentham and Mill wanted to explain human activity as the derived from a basic set of animalistic behaviors that were subject to a Darwinian selection of the “fittest”; the superiority of the so-called Protestant work ethic and American Exceptionalism (“Manifest Destiny”) were thus explained scientifically by Spencer and Sumner, who then justified all sorts of abuses of workers, farmers, and indigenous peoples, who were ruthlessly exploited by the masters of industry and capital. In the 20th Century these silly ideas were finally challenged and nearly laid to rest by the First World War and the Great Depression; but they were revivified by the need for the West to pull itself from Reagan’s “ash heap of history” in the Cold War, which saw the purge of critics from academia and public commentary in the 1950s. The great financialization of the West’s economies starting in the late 1960s, and the huge amounts of money spent on trumpeting the ideas of the likes of Milton Friedman and the Austrians who resurrected neoclasscial ideas, strangled the more sane and scientific economics that thinkers like Keynes and Kaldor started.
So, ironically, as you point out Philip, economics fills the role that Marx ascribed to religion—an opiate of the masses, albeit in the sort of scientific-mathematical costume that Kaldor and Hayek described as “scientism”. The highest of the priests probably understand the inanity of these models, but those, like Paul Krugman (or Dr. Zaius), who are not completely cynical justify their work as a “useful model if not taken too seriously” while the true believers chug the kool aid. But it’s the models and the motivations, not the mathematics, at work.
I don’t think the causation was unidirectional. The Walrasian system was already in place prior to Debreu. As I said in the article:
“… it should not be thought that it was simply the formal tools of mathematics that transformed neoclassical economics into the obscurantist doctrine it is today. Instead it should be understood that its obscurantist skeleton was ready and waiting for its mathematical flesh.”
However, the point about Cantor and mathematics was very specific. Cantor deploys the notion of “actual infinity”. Debreu takes this over and this ensures that some of his proofs cannot be undertaken in a finite number of steps. This, the authors of the cited paper argue, means that they literally cannot be applied to empirical reality. This, to my mind, makes them 100% Idealism.
Take a stupidly simple example: 2 + 2 = 4. That is, as you say all math/theory is, an abstraction. However, it can be carried out in a finite number of steps. Thus, it can be applied in the real world/empirically. If there are two apples on the desk and two apples on the floor, they can be added up.
BUT, if we’re dealing with “actual infinity” we cannot use it when applied to concrete empirical material. If we hypothesise an “actual infinty” of apples, this is just an Idea in the purely Platonic sense.
I’d encourage you to read the paper linked to at the start of the piece, it’s very good. As for my angle on this, I’m no mathematican. The paper interested me because of a certain contemporary French philosopher who is currently using Cantorian set theory to ressurect a very unusual form of Platonic Idealism which he is using, in turn, to justify revolutionary Communism. There is, to my mid, a definite link to what he’s doing and what Debreu was doing. And they were both engaged in Idealism in the purest sense.
Philip,
I read the paper, but I don’t think it changes my view. The problem with Debreu and Walras starts with a bad model of reality. The fact that he “proves” the model as a purely mathematical exercise using Cantorian set theory doesn’t change that fact that it’s a bod model of reality. So, the fact that the authors want to show that the mathematics behind the proof of a bad model of reality have no correspondence to reality doesn’t mean so much, in my view. As the authors quote Debreu himself, and other commentators point out, much of neoclassical economics rests on the absurd notion that arguments that meet the rigors of pure mathematics, which they happily tout has no relation to reality by the very definition of “pure”, still must (somehow) have meaning for reality through economics. But Euclid and Hilbert weren’t interested in the use of mathematics to describe reality: they cared about making the subject as purely intellectual as possible.
Your comments about “actual infinity”, Platonic apples, and finite steps don’t really hold water. Physicists and chemists appeal to infinity in their models all the time, and the mathematics that underlie their theories can be proven in a variety of ways, including using Cantorian set theory. The models are still accepted if they are shown to explain observed phenomina robustly. The debate between Cantor and Poincare is red herring in this case, reflecting an argument in the philosophy of mathematics that, I argue, is not very germane to the failures of neoclassical economics.
I still argue that the real question is why, given the comment of Knut especially, do economists tout this crap as having any intellectual validity at all, and, moreover, push it as policy on the entire world? There lies the real problem. We know this is junk, but we keep on drinking the kool aid or chanting the mantra.
Pace,
David
Again, I agree that “in the beginning there was Walras”. He started it. The mathematical apparatus picked up was just a supplement — the “flesh” as I put it, that was grafted onto the Walrasian “skeleton”. However, I think the authors of the paper have a point that this was a “nice fit” and that the formal style of the argument is worth looking at.
You say that physicists use “actual infinity”. I’m sure they do. But economics is not physics. Economics is a social science, not a hard science and I would argue that when “actual infinity” is posited in economics it is referring to a metaphysical state where everything balances perfectly. This is, I would imagine, somewhat different from the uses made of it in physics.
My guess is that the physicists will observe reality and then build models. In these models they will deploy “actual infinity” to make them work properly. Fine.
Economists, however, and again we’re back to the chicken and the egg (which I agree with you on), do it the other way around. They take the a priori Walrasian system and then use “actual infinity” to portray a mythic, metaphysical or timeless static state. But I think if we stripped away these metaphysical foundations the notion of “actual infinity” would have no place in economics. Why? Because we would have to stop building models.
That’s what really underlies the piece. And its one that some economists that aren’t neoclassicals will dislike. I don’t believe that economic modelling is the way for economics to progress as a science. Nor do the authors of the paper, by my reading. They prefer “on the fly” reasoning based on empirics and rules of thumb. I also think Kaldor was at his best when he dealt with institutions and specifc policy rather than models.
So, there it is. I’ll remove the mask. While modelling may be good for physics, I think that its poison for economics.
Hi agin, Philip.
I have the view that all intellectual descriptions of reality, whether physics or economics, are built on models. Some models may be more robust that others. Physicists take jutifiable pride in their models, but that has more to do with their good fortune that the subject, for whatever reason, can be well described in mathematical terms principally because physical systems can be modeled by reference to very simple structures. Economics, like the other social sciences, can’t achieve the same robustness becuase human interactions are far more complex and heterogenous than, say, quarks or protons, or stars. Proving economic models is correspondingly more complex, and, therefore, much less robust.
For my money, the real question is why anyone would care about descriptions of human activity that are openly addmitted to be nothing but purely intellectual world-building. Why do we put so much of our lives in the hands of economists who knowlingly use models developed by academics who proudly claim their allegiance is to “mathematical” or “logical” “purity” first. I think that is an ugly history of intellectual and moral corruption that we have to face squarely or we’ll continue down the dark road we’ve been following for decades now.
So, I think the issue is not models vs. no models. I think the issue is intellectual honesty and social control. There is a strong vested interest that is trying to “normalize” our behavior to satisfy economic models, rather than admitting that the current economic models are useless and dangerous to mankind. This cannot work. But we either fight the academics and powers now, or suffer the inevitable collapse later. In this regard, I see little value in the arguments presented in the paper.
When will students start fighting back at the professor that teach this tripe? When will the public refuse to fund economics departments and business schools that happily spew this garbage? When will the Nobel Committee stop giving prizes in economics, which is not only not a science currently, but is actively a superstition or religion?
I pretty much agree. Although, I don’t think that all thinking is based on models. However, I recognise that some people thinking in model-oriented terms. Personally, I don’t. I think in linguistically-oriented terms. So, I think this is simply a case of cognitive style and I don’t think there’s much point of getting caught up in it.
However, I think there may be an element to model building itself that inspires the sort of thinking you describe. When you put something down on paper that you think adequately captures a real-world phenomenon as enormous and nuanced as a working economy, you’re inevitably going to have a sort of deferential attitude to the thing you’ve just put down on paper. Now, the neoclassical model is particularly perverse, but I can imagine even the best of models being misused.
Again, though, I recognise that, to some extent, this is a question of cognitive style. And I obviously have my biases like everyone else. But I definitely think that its worth keeping in mind. Kaldor — who was certainly a model-builder (although I think his cognitive style was “mixed”) — was right to point to the “mathematical crystal” as having a particularly hypnotic allure for economists.
I wonder if there’s a difference between the actual infinities used by physical theories and those needed by Debreu’s formalism. In physics you need to justify the use of an actual infinity by saying making a claim that the finitistic, empirical, evidence “converges” on the idealised infinite limit-object; and the metric needed to measure this “convergence” is actually required to be part of the theory.
Hence the success or failure of such a convergence becomes part of the evidentiary basis of the theory. I’d go so far as to say that Ptolemaic astronomy failed when it became clear that repeated addition epicycles-upon-epicycles was not converging to a limit result that could explain the structure of the solar system as we actually observe it.
As far as the equilibrium fixated neoclassicals I’m not sure that such a metric has been given as part of its “theory”. Indeed they seem to spend much of their time explicitly avoiding such question. It would seem to me that the Lancaster & Lipsey “Theory of the Second Best” places some serious obstacles in the way of defining such a metric in Walras/Debreu equilibrium theory.
To summarise: All honest theories that accept actual infinities into their ontologies have to provide an answer to that perennial question from the back seat “Are we there yet Daddy ?”.
Fun question: Maybe Samuelson added the ergodicity assumption in an attempt to get such a convergence-to-infinity to work in the neoclassical space.
This is exactly right. Walras showed how in principle (under highly restrictive conditions) the price and quantity of all things traded in the market are mutually determined. But the only way he could do this was by using simultaneous equations to describe market-clearing conditions. But simultaneous equations imply that everything happens at the same time. Even Walras knew that this was absurd, which is why he called his economics ‘Pure.’ The system provides insight at the cost of an unrealistic assumption. As I used to tell my students, it is another example of the principle that there are no free goods. This holds for theory as well as for other things.
Ever heard of string theory?
Yes,and? why do you mention the string theory in the context of this discussion? it can be understood only by employing a very complicated mathematics, but nevertheless, is a very good alternative to the standard model in physics.
Have any of you actually read Bourbaki?
Yes I have read Bourbaki and studied logic and Set theory. This article is one big confusion. Read william Kneale’s History of Logic or any introducion to math logic and history on the internet.
If you guys are going to insist on engaging in “I’m a bigger mathematician than you” tedium, please make actual criticisms rather than pulling credentials. Also, note very carefully that I only mentioned the Bourbaki School in passing — which, I admit, I’m not hugely familiar with. The main focus is on Cantorian set theory and its use of “actual infinity”.
Walras was also a platonist. Here is the money quote from Elements of Pure Economics (p.61). ‘A truth long ago demonstrated by Platonic philosophy is that science does not study corporeal entities but universals of which these entities are manifestations. Corporeal entities come and go but universals remain for ever. Universals, their relations, and their laws, are the object of all scientific study.
Now THAT is interesting. Thank you, I’ve never seen that before. It looks like M. Walras had some rather unusual ideas about what science was all about…
I had no idea somebody can get a job as a “Philosopher of Economics”.
I thought you had to do that in your spare time — and for free.
Holy Smokes. That means there must be a demand function for philsophers of economics. I wonder who would want to pay for that and how they would judge whether their utility was being maximized. It must be some sort of inner perception of their own mental processes. I wonder if it’s the kind of things that the more you pay for it, the better it seems — like stylish clothes.
I don’t know if anybody noticed this, but I thought Mr. Haldane had a very nice suit on when he gave the lecture back at that INET conference a few months ago, judging by the video. I’m more of a Men’s Wearhouse guy now that Syms is bankrupt, but maybe I’ll upscale to something made by a personal tailor, having been inspired. If you line up an infinite number of apples you certainly can’t contain them all in your field of vision, UNLESS of course, you line the up perfectly one behind the other and then look at them in a perfectly horizontal view. The only problem with that, is if the universe is curved, the line of apples might hit you right in the butt. But that would mean there aren’t an infinite number, or else there’d be room for one more, which their can’t be because your butt is there. This means the universe must not be curved after all.
Well, there certainly is a demand function for comedians. I have no idea how to maximize their utility. But those infinite apples hitting you in the butt line worked for my money. :)
To Philip Pilkington –
So basically you’re clueless.
Obviously not. I clearly have enough of a grasp to discuss the essence of the article with someone quite familiar with mathematics above. The difference being that he appears to appreciate dialogue rather than self-assertion and dick-swinging.
I strongly disagree with a great deal of Milton Friedman’s political philosophy, but any attempt to blame Friedman for this plague of useless abstract models is plain wrong. Friedman was loud and proud in his contempt for the Walras approach. He felt that any economic model that failed reflect reality was worthless, no matter how mathematically elegant.
Check http://delong.typepad.com/sdj/2011/05/milton-friedman-we-curtsy-to-marshall-but-we-walk-with-walras.html
Yes, but Friedmans’ own philosophy of economics as a science was equally squirrely. Arguing that you’re theories are right just because your predictions came true, even if the theories themselves bear no relation to verifiable reality isn’t much better than Walras. It certainly isn’t science. Again, it was just another canard to bamboozle the public (and maybe the elites too) into believing neoclassical hokum.
In engineering this is called a Black Box theory. You deal with a Black Box model solely in terms of its inputs and outputs. You don’t look “inside” the model and you don’t require that what’s inside have a structural resemblance to any aspects of the reality it’s modelling.
As long as the results of the model really do correspond with reality, then it’s doing something useful. Sure, a model that works for reasons you can understand would be better, but you don’t always have those.
The whole economics thing left the rails when they decided they could skip checking their models against reality. Engineers who know Black Box theories know that’s just crazy.
Calling the Middle Ages “Dark” has no basis in reality, and exactly in the same way you say neoclassics has no basis. “The Dark Ages” were a vibrant and lively times, when culture, economy and the people flourished. They are called dark because they are situated between the the “light” of the Roman Empire and the “light” of the Enlightenment and also because we have relatively few historical records of them.
You are right that we currently are like the Middle Ages, but for the wrong reasons. We, too, have prospered, and it is thanks to the system used – whether it was scholastics then or neoclassics now. It is the existence of a system that keeps civilization rolling.
But every system comes to an end and always like this: the clergy in charge of the system becomes corrupted by power. The corruption makes them blind to notice changes in reality and unwilling to adapt to the change. The reality below the system evolves to the point that the system turns from profit to loss. This process is always aggravated by increased rent-seeking by the clergy, but also enlongated by the clergy fighting for their existence.
The troubled end of the Middle ages was resolved when the clergy and the system were replaced. We too should aim for no less! It might be that the neoclassics never looked at the reality. In this case they just had luck, because their simple armchair dreams were close enough to the reality. But they had to be close, because otherwise they would never have run the world! It is just that by now, what was considered trivia now demands to be a part of the system and the reality is no longer able to pay for the system’s upkeep. Since the system is unwilling to reinvent itself, it has warranted it’s replacement. Just as soon as someone figurs out the beginnings of the new one.
I agree with your point – rationalization is a perfectly faceted jewel. But science does not do this. Darwin did not do it – Darwinians did. Survival of the fittest was accomplished in small, conservative increments; in a subtle variety of finch beaks. Duly noted by Darwin.
The term “Dark Ages” to the extent that it has any usefulness applies to the 500 years in Western Europe
after the end of the Western Roman Empire. This is approximately 450-950 AD . It’s use for the Midieval Period
is simply incorrect.
Sorry, I meant Medieval Period.
The distinguishing features of the so-called Dark Ages were the Voelkerwanderung and the onslaught of Arabs, Vikings, and Byzantines on the small successor kingdoms of the Western Roman Empire. This finally came to an end about 950,
the Magyars being among the last of the invading “hordes”.
In the Medieval Ages Europe was relatively secure from external invasions. European civilization prospered during
this time even as the Mongols rained down death and destruction on most of the rest of the Eurasian continent.
Hi all,
I’d say the PP makes some very good points that he encumbers with some unnecessary baggage (Cantorian set theory, Bourbaki, etc). As it happens, I have a number of Bourbaki volumes (not a complete set, if such a thing exists as I think they’re still at it), as well as several works by Debreu, Arrow, et al. I would not care to enter a “my math schlong is bigger than yours” contest, mainly because I think these games are all silly (who’d have guessed in 1904 how big A. Einstein’s schlong was?) but I feel reasonably able to hold my own in discussions of advanced mathematics, not least the fixed-point functional analysis that underpins much of the equilibrium analysis.
That said, I think that there are so many problems with modern economic theory it is difficult to know where to begin, but the very notion that there are economic equilibria is an excellent candidate. Since the neo-lithic period (approx. 10K-8K years ago) we have been on a roller coaster of technological change that dwarfs anything of the previous million years. Furthermore, the periods of technological stasis/stability have grown shorter and shorter ever since. There were few major technological inflection points from 500 BC to 1500 BC but since then we’ve mastered steam, electricity, the atom, quantum mechanics, automatic computers, etc. QUite simply, there is not such a thing as an economic equilibrium anymore, and that is w/o even considering the impact of population growth, environmental degradation, etc.
What I appreciate about PP’s researches and contributions is that he is challenging the complacent orthodoxies that got us into this cluster-f&^k we are today. Sometimes his reach exceeds his grasp (as i think he admits above) on nuances of mathematics, but I’d rather have one PP than a thousand Tom Friedmans or Niall Fergusons.
PS: PP, if you haven’t read him, check out Imre Lakatos’ writings on the methodology of scientific research programmes. He was a colleague/student of Karl Popper and I think one of the most prescient critics of unwarranted confidence (=hubris) is theoreticians of any stripe, and his remarks/ideas are especially relevant to the mess that is modern economics.
Vive la Revolution!
P
That’s very kind of you. Thank you.
Yes, I’m aware of Lakatos’ work — mainly through that of Paul Feyerabend. But it is worth noting that one of his students, Spiro Latsis, focused on economics. His paper “Situational Determinism in Economics” is well-worth a read by anyone interested in neoclassical economics in general and the restrictive determinism that it applies to humans in particular.
http://en.wikipedia.org/wiki/Spiros_Latsis
Also, I’ll certainly admit when I’m ut of my depth. However, I’m not the one making the point about Cantor and the use of “actual infinity”. That was O’ Gorman and Boylan. I nicked it from the paper linked to at the start of the piece. Given that O’ Gorman is a philosopher with credentials in mathematics and mathematical physics, I don’t think you should so quickly reject the idea that “actual infinity” is important. Personally, I think, as I have said above in the comments, that using “actual infinity” in economics probably has exactly the effects O’ Gorman and Boylan attribute to it. Here I’ll quote from the paper at length — excuse the clumsy format, but I think people should pay particular attention to these two paragraphs:
“As we already noted, Hilbert proposed a strict formalist reading of pure mathematics.
In this strictly formalist setting Hilbert proposed an ingenious, non-Platonistic way of
retaining Cantorian set theory. He divided pure mathematics into a finitist part (à la
Poincaré) and an idealized, infinite part (à la Cantor). The idealized infinite part is not
open to interpretation; only the finite part may be interpreted. However, the idealized infinite part is heuristically indispensable as an instrument for deriving finitist results
otherwise unobtainable. In this reading of Hilbert’s ingenious solution, Cantorian
actual infinity is a non-empirical, non-finite, heuristic fiction, justified by its enormous
mathematical power and utility. Crucially for Hilbert such idealized fictions cannot be
arbitrarily introduced into mathematics: the extended system of Cantorian infinity
combined with the finite must be proven to be consistent. In this way one could say
that Hilbertian formalism equates Cantorian mathematical existence with freedom from
contradiction.
Clearly in these Cantorian settings Debreu’s proof is a genuine one. In short in the
context of the Poincaré programme Debreu’s proof is invalid as a piece of mathematics,
whereas in a pro Cantorian framework it is a valid proof! The moral is clear: the
process of the mathematization of economics via Cantorian set theory requires closer
methodological scrutiny. In particular, we are now in a position to address the crucial
methodological question noted above, namely whether or not Debreu’s proof can be
given an economic interpretation? Debreu’s Theory of Value is said to prove the
existence of a set of signals, market prices, in a Walrasian exchange economy, leading
economic agents to make decisions which are mutually compatible. This is the
economic interpretation of Debreu’s mathematical proof. Our thesis, which we call the
P-K thesis (Poincaré-Kaldor), is that there is no justification for this economic
interpretation of Debreu’s ingenious piece of Cantorian pure mathematics. Debreu’s
proof does not support this economic interpretation. Debreu’s so-called economic
equilibrium only exists in the domain of Cantorian actual infinity which transcends any
process limited to socio-historical time. More precisely, since the method of the proof
of existence is inherently non-constructive, i.e. cannot be carried out in a finite number
of steps taken one at a time, Debreu’s equilibrium cannot be given either a finite or a
potentially infinite interpretation.
Debreu’s equilibrium point is merely shown to exist
in a non-temporal, actual infinite Platonic domain, which cannot in any finite effective
way be realized in the socio-historical world in which economic agents operate.
Alternatively, in the language of the Hilbertian formalist, there is no evidence to
support the assumption that the logical possibility, established by Debreu’s proof of
existence, could be realized in any socio-economic system where real historical time
operates.”
Philip,
Just to reiterate, I’m a fan of your contributions here. Modern economics has become a smug, squalid cesspool (a little alliteration there ;-) of self-dealing and intellectual dishonesty since it was coopted by the whole world of business schools and the tight coupling of academia and commerce. The wonderful Charles Ferguson documentary laid that case out better than I can possibly do here.
If I could, I would suggest treading a little more lightly on the mathematical esoterica, especially since it’s not truly required to prove your overarching point(s). In math, we’re taught to always examine your proof to make sure you used all the hypotheses stipulated, and if not to discard them: the result is a broader proof with fewer constraints to its applicability.
BTW, one of the most telling mea culpas about the failure of overly mathematical economics came from its post-war godfather, namely Paul Samuelson. In 2009 he wrote a piece admitting that much of what he and other had built in the past 50 years had failed the ultimate test of any scientific theory: it totally failed to predict the events of 2008-9. It’s time to go back to ground zero and formulate a new theory.
In any case, I always enjoy your posts. Thanks!
P
I appreciate that, but I really have to press this issue. Remember, this is not my hypothesis, it is Boylan’s and O’ Gorman’s — and I’m certainly not defending it out of some patriotic duty.
What they’re doing is NOT attacking a mode of mathematical formalism, but instead they are attacking this formalism as it is applied in economics (see: my comment below to Patricia). The fact is that when economists introduce the notion of the “actual infinite” into their constructions they immediately construct a fantasy world. They imagine something which they call “equilirbium” which means a static state that at once exists and doesn’t exist. That is: it is assumed to exist, but at the same time it is assumed to not be able to be carried out in a finite number of logical steps. Put differentlY: it is projected into the metaphysical beyond.
Now this may be appropriate for mathematics and physics. I don’t know. But I do know that it is absolutely inappropriate for economics.
(P.S. If you want to see a very interesting philosopher go through the implications of the “actual infinite” check out the video I linked to below. Note especially the segment after 1.00.00).
I’m sorry to not renege on this point, but it is important. It is not superfluous. And I cannot simply drop it and hold to the other points made in the piece (they rely on it).
My feeling is that people are rejecing it because they use similar quasi-metaphysical mathematical operations in their own fields. As I said, that may be appropriate in those fields. But I do NOT believe that it is appropriate in economics. It turns it into an unpragmatic and ideological discipline.
Philip
Cool enough. I respect your commitment on this and related issues of the problems w/ econ. We need passion on our side, to make up for vast body of corrupt/coopted economists on the other side. I’ll check out the white paper and vid in more detail.
Best,
P
This is an interesting post and paper. As a philosopher with some background in mathematics and its philosophy but little in economics, I’ve often wondered about the possibility of fruitfully thinking of economics in terms of the philosophy of mathematics in application. I had not thought of tracing the difficulties of economics to particularly classical, as opposed to constructive, mathematics.
For whatever it’s worth, a couple of things struck me as odd in the presentation. In some places the paper authors seem to refer to “Cantorian set theory” as if it were a peculiar or minority enterprise, and as if its peculiarity is based on an association with formalism as a philosophy of mathematics. But it seems like what they are really troubled by isn’t Cantor’s particular views, but rather the idea of doing mathematics with the classical, or non-constructive, method. In that method, which has become standard since the set theory paradoxes were addressed in the early 20th century, one assumes the law of excluded middle for proofs, allows proofs by contradiction, and allows proofs that that do not produce constructions of mathematical objects that are proved to exist.
Classical mathematics is how most mathematics in most subfields is done, and while one can associate that method with formalism or Platonism, one needn’t do so. It may be, for example, that the law of excluded middle represents a useful and apt idealization in the relevant domain. If it does not in economics, that would be something particular and interesting about that domain, rather than something peculiar and divine about a particular mathematical methodology. Recent other possibilities in philosophy of mathematics include mathematical fictionalism and naturalism, both of which generally preserve the classical methodology.
Second, and perhaps relatedly, the paper seems to me to run together the claim about set theory and classical methods with one about the fact that once the mathematics is interpreted in the economics context, the premises are literally false. It’s true in lots of domains that premises are literally false, because of the need to idealize. In science, premises involve things like frictionless planes and infinitely deep water and are literally false as well. Then the question is what makes a given idealization a good one. There may be reasons to think the ones used in economics are particularly bad. But this does seem a separate and distinct problem from the one about classical mathematics. This point echoes some of the points raised above, about models.
Anyway thanks for posting this. I ended up chasing down some of the papers in the footnotes and found some very interesting stuff, such as the work of K. Vela Velupillai, who has written extensively on using constructive mathematics in economics.
“Second, and perhaps relatedly, the paper seems to me to run together the claim about set theory and classical methods with one about the fact that once the mathematics is interpreted in the economics context, the premises are literally false. It’s true in lots of domains that premises are literally false, because of the need to idealize. In science, premises involve things like frictionless planes and infinitely deep water and are literally false as well. Then the question is what makes a given idealization a good one. There may be reasons to think the ones used in economics are particularly bad. But this does seem a separate and distinct problem from the one about classical mathematics. This point echoes some of the points raised above, about models.”
I think that this is the key point. The authors are not so much trying to critique a particular school of mathematics, but instead trying to critique the use of it by economists IN LINE WITH the economist Nicky Kaldor’s demands that economics be a wholly practical discipline which shuns any abstractions about where the economy should “tend toward”.
As you can see from the reply to the post above your’s which contains a lengthy quote from the paper, the “actual infinity” proof is tied to the notion of market equilibrium. In neoclassical economics “equilibrium” is a state in which everything is assumed to “end up” at in the long-run through a teleological process. It’ modelled on a pendulum swinging. After all, we know where it will come to rest. However, an economy operates in a far more complex way to a pendulum and, in reality, we do not know where it will come to rest.
And yes, this is why I brought up modelling in general. Teleological models in economics are, in my opinion, completely useless. You may as well try to teleologically model your best friends actions (i.e. fortune telling). While I don’t think the authors went this far, I believe that is what they were alluding to.
PP wrote: “It’s modelled on a pendulum swinging. After all, we know where it will come to rest. However, an economy operates in a far more complex way to a pendulum and, in reality, we do not know where it will come to rest.”
But as soon as the number of (economic) variables is greater than 2 we now know from Dynamical Systems Theory that this coming to rest at a single point or converging on a stable orbit is in no way guranteed … indeed it appears to be the exception rather than the rule.
P.S — Patricia Marino
Given that you’re a philosopher with a background in mathematics, it might interest you to know why I feel upon this paper — because I’m not usually so interested in these things. This is why: https://www.youtube.com/watch?v=LJ70jKsk3gs
Any comments on Debreu’s approach to first treat the problem as a purely abstract, Hilbertian mathematical exercise, and then (re-)interpret the solution as an economic model as described in the paper at pages 12–16? I find this sort of approach intellectually dishonest, as I’ve written above. But is this fair? Could Debreu have just been naive?
Again, I smell a rat in which, having justified the use of a mathematical approach that cannot be considered relevant to providing physically meaningful results, and then interpreting the result to have physical meaning, Debreu was quite mendacious. And the fact that the entire economics field has happily accepted this canard is quite shocking.
Well, maybe I’m not understanding fully, but it seems to me if you bracket the “Hilbertian” aspect for a moment, this is roughly how most mathematics gets applied. Mathematicians work by defining concepts and proving things about them, in a formal, or at least uninterpreted, way, and scientists use those results by in their models by interpreting the concepts. That explains the continued discussion of the “miracle” of applied mathematics: if mathematicians work in a formal mode and use aesthetic considerations in developing concepts, it seems like the high degree of usefulness of mathematics in science has no explanation. Yet mathematics is highly useful and effective. (Anyone looking for a fun read on this subject should check out Wigner’s classic “On the Unreasonable Effectiveness of Mathematics in the Natural Sciences.”)
And I think one can bracket the reference to Hilbert here because insofar as it’s the non-constructive proofs that are the problem, that’s classical mathematics, as its done all the time by mathematicians, and doesn’t have to do with Hilbert’s particular program.
It’s easy for me to believe (and I think it must be true, though here I’m no expert) that what makes the math work in, say, the physics case doesn’t apply in the economics case. But that seems to me to be about a difference between those domains, not having to do with whether the mathematics is understood in a formal mode or a constructive mode, as the work discussed in the paper at some points seems to imply.
BTW Phillip: Have you considered collecting these thought provoking NC posts & interviews as a book ?
The thought has occurred to me. But I’d feel bad just issuing a rehash of something that’s already been published. I’d have to rewrite and integrate them. I might do it next semester. I’m doing a few other things right now…
“Philosophy is the battle against the bewitchment of our minds by language”. Wittengenstein, “Philosophical Investigations”.
The artificial languages of mathematics are used to convey the patina of validity. The confusion, however, is not some academic matter. While economics makes its central position of strength upon rigorous scientific methodology, confirmed by the language of rocket scientists, its results are less than that of simply throwing darts at newspaper listing of the stock market.
It is not simply enough to plainly see that math has lead economists down a dead end. Additionally, it is MORE important to note the repeated and consistent defeat of any other schools of thought, such MMT or even the practical application of Keynesian spending by the government during dire emergencies. The math traps the earnest who do not know of anything different and the math is used as a filter and a bludgeon by the running dog lackeys of the plutocrats.
There are those who cloak themselves with the abuse of the words ‘Divine Authority’ in which they have arrived at by only using a language whose words which their reason has concoted belong only to a world which is measureable and contradictory, turning that which is sacred – understanding and comprehension, into nothing more than a parody. It will be interesting to stand at Truth’s Libel and Slander suit in all disciplines.
But isn’t the theory of economic equilibrium experimentally supported at the level of economic “nano-scale” (at the level of individual buyers and sellers) by Vernon Smith? And i think that there was no need of complete information and infinite buyers-sellers either http://www.2ubh.com/features/QFsmith.html There is no doubt, experimental economics, behavioral economics (by using some ingenious experimental social psychology techniques), institutional economics (overlapping with sociology and organizational theory) can save the empirical future of economics. There are even further developments in the neuropsychology and neuroscience of economics leading to the new exciting field of of “neuroeconomics”. So, i think that there is a bright future of economics as as science which is rapidly developing at the moment and it is not only based in theoretical mathematical masterbations (co-developing ofcourse with the economentric/observational methods) Furthermore, neo-classical theory is surely no waste. It can be used as a perfect abstract comparator to any other market and act as a bedrock for further, more complicated, theoretical developments such as the “dynamic stochastic general equilibrium” which behaves more like non-linear real-world markets. http://en.wikipedia.org/wiki/Dynamic_stochastic_general_equilibrium Bear in mind that a lot of current cosmology and theoretical physics as as various models of string theory, quantum loop gravity, computational/informational theories of the universe etc. are only mathematical abstractions with no hard evidence whatsoever to support them, and no real applications to the world (since it is “basic” science, not applied). Only time will tell if they have any real “truthness” whatsoever (and the same goes with the Walrasian paradigm, although as i said, there is already experimental evidence that under certain conditions an equilibrium is established)
There’s no good reason why mathematics shouldn’t be Platonist or Aristotelian or Cantorian or Brouwerian or anything else. It is clearly an autonomous discipline that generates its own intellectual norms. Economics, on the other hand, should either decide to be an empirical social science or else shut the fuck up.
Math is a horrible tool, too use, in describe living systems. Especially if you don’t fully understand all the correlations completely and their constantly on the move.
Skippy… increasing fail rates with self autonomy… wada hoot!
In my student days I used to think what has become known as neoclassical economic thought had been carefully put together that way so as to generate continuous mathematical functions in all of their dominions, which, of couse,could be continually derivable. Not the other way around, as one would expect from a method claiming to be “scientific”.
That way the whole gibberish narrative described by neoclassical economics could be supported by some arcane mathematical language that would give it legitimacy, even though, some neoclassical economics practitioners would be quick to disclaim their reasonings were purely abstract. But society expects economists to deal with real world issues relating to, well, real world economics. Those are the moments when epistemological havoc is caused by the economic thought steeped in neoclassical economics.
To sum it up, I used to think there was method in all that madness: to treat economics “higienically”, i.e., to keep the masses affected by it “out of the gates”. And, as a matter of fact, I haven’t changed my mind since then.
Thanks again for you insight. It helps explain an experience of mine from a few years back more fully.
The stage was a bookstore discussion where by chance one of the interviewees to the small group of lefty chatterers was our current head kicking climate change denying leader of the Australian Opposition Liberal Party one Tony Abbot – expected to be Prime Minister next year. He had just been elevated to the post but true to his word turned up in this den of toothless lions.
Anyway it being a bookstore he was asked the obvious question – what books have inspired you? Despite him being a Rhodes Scholar (Rugby, Boxing, Journalism and I think Economics) it was a very short list (Nania, Huck Finn, the New Testament (he is a conservative practicing catholic) and ‘The Wealth of Nations’. In respect to the latter he commented sincerely that he was deeply impressed with ‘The Invisible Hand’ (of God) concept. My reaction at the time was puzzlement as the response conveyed an excessively metaphysical tone. At the time it didnt quite make sense this positing of a link between the christian god and capitalist economics which of course the Church used to damn under the sin of usury.
But now this makes much more sense.