1. Skip to navigation
  2. Skip to content
  3. Skip to sidebar

Mises Economics Blog

Mathematics Versus Economic Logic

July 10, 2009 8:01 AM by Mises.org Updates (Archive)

If this antagonism between the logical and the mathematical economists were merely a disagreement concerning the most adequate procedure to be applied in the study of economics, it would be superfluous to pay attention to it. The better method would prove its preeminence by bringing about better results. It may also be that different varieties of procedure are necessary for the solution of different problems and that for some of them one method is more useful than the other. FULL ARTICLE

Bookmark/Share | Comments (45)

Comments (45)

  • Daniel J. Fallon Daniel J. Fallon

    Lew Rockwell, his post on LRC, turned me on to the Nobel winning physicist Richard Feynman. Please enjoy this short clip (under 2 mins) of Feynman discussing social "science":

    http://www.youtube.com/watch?v=_EZcpTTjjXYPer

    Published: July 10, 2009 8:54 AM

  • RWW RWW

    That should be

    http://www.youtube.com/watch?v=_EZcpTTjjXY

    Published: July 10, 2009 9:08 AM

  • Daniel J. Fallon Daniel J. Fallon

    Thanks RWW. I should have checked closer before posting.

    Published: July 10, 2009 9:39 AM

  • Russ Russ

    If Feynman didn't have much respect for people who claimed to be social scientists but didn't back up their theories by putting them through the rigor of repeatedly trying to empirically falsify them, what do you think he would have thought of people who claimed to be social scientists but don't think that their theories *can* be subjected to such rigor? Like most scientists, he would probably think that a "deductive science" that is "apodictically true" is really no science at all.

    Published: July 10, 2009 12:57 PM

  • Inquisitor Inquisitor

    Feynman seems to be a typical positivist to me... and I am not even sure what he is getting at. He should stick to physics.

    Published: July 10, 2009 1:25 PM

  • Russ Russ

    Inquisitor wrote:

    "Feynman seems to be a typical positivist to me... and I am not even sure what he is getting at."

    What he's getting at, as far as I can tell, is the same thing that many here are getting at when talking about mainstream mathematical economics. He's saying that social scientists are mainly people who assume the mantle of physical science and use its "forms" (i.e. complex mathematical theories) because physical science is so respected and unarguably successful, even though they aren't really using scientific methodology or doing real science. In other words, he seems to be criticizing scientism, although he doesn't use that word.

    The problem with an Austrian trying to use this clip to criticize mainstream economics is that Feynman's main objective to social science does not seem to be that it uses mathematics. As a "typical positivist", he would probably consider that a good thing. His main objection, which he gives with his example about organic foods, seems to be that the claims of social science are not rigorously emprically tested. So, I doubt he'd think much of Austrian economics, either, were he still alive.

    Published: July 10, 2009 2:05 PM

  • Russ Russ

    Arrgh. I meant to type "objection" in my last post, not "objective".

    Published: July 10, 2009 2:08 PM

  • Inquisitor Inquisitor

    To his detriment.

    Published: July 10, 2009 3:00 PM

  • Eric Eric

    Mises is too absolutist. While much of what he states here makes sense, he also makes statements that don't agree with his own argument. For example,

    "Moreover, money is not a standard for the measurement of prices; it is a medium whose exchange ratio varies in the same way, although as a rule not with the same speed and to the same extent, in which the mutual exchange ratios of the vendible commodities and services vary."

    What does he mean by "as a rule"? Is this really a logical deduction from his axioms of action? Or is this a measurement of history that he is using "as a rule".

    If prices are all subjective based on values, how can this statement be made based on logic? The value of money, being just another commodity, albeit with medium of exchange value, is still subject to the same subjective human values as other commodities. If one cannot use mathematical arguments about subjective value, then how can he make a statement that claims the "speed" of adjustments in exchange ratios between money and other things change more or less quickly than the ratio of any other two economic things.

    It is this sort of contradiction that is troubling. On the one hand, he states that one cannot make statements from history to prove a claim, and then does the same thing himself.

    If he meant "as a rule - in the past" I might be less inclined to criticize, but he didn't and Mises is well known for using obscure wordings because he felt it was necessary in order to be more precise. Well, this doesn't sound very precise to me.

    After all, Mises does not use the sort of precise step by single step logic of mathematical proofs, such as in say, Euclidian geometry. If he did, then Human Action would be a million pages long. And without this sort of extreme detail in logical deduction, it is very easy to make a mistake. One has to constantly interpret his terms - like the above mentioned "as a rule". This makes it nearly impossible to check all of his logic for potential errors.

    I believe it is for this reason that the mathematical types ignore even his good points.

    Published: July 10, 2009 3:12 PM

  • Russ Russ

    Eric wrote:

    "While much of what he states here makes sense, he also makes statements that don't agree with his own argument."

    My favorite statement that doesn't seem to agree with his own argument is this: "Reasoning and scientific inquiry can never bring full ease of mind, apodictic certainty, and perfect cognition of all things." (Page 25 of the 3rd revised edition of Human Action, Comtemporary Books, 9th paragraph of the section "Alter Ego" in Chapter 1.) While I agree with this quote, the rest of Human Action seems to argue that praxeology is apodictically certain, like logic or mathematics, and yet capable of making empirical predictions, which mathematics and logic cannot.

    "I believe it is for this reason that the mathematical types ignore even his good points."

    I believe that the reasons they ignore Mises and Austrianism in general are twofold: #1) They believe that economics has to be a "hard" science to be useful, i.e. they believe that economic theories have to be empirically testable (falsifiable) to be science. #2) They believe that hard science has to be mathematical, since physics, the most successful hard science so far, is mathematical.

    I agree with #1 above, but I do not agree with #2. It doesn't matter whether a scientific theory was arrived at by means of mathematical modelling, verbal logic, or ancient Babylonian astrology. What matters is that it is capable of making specific (i.e. "hard") empirical predictions that can be used to test the theory. If verbal logic (or ancient Babylonian astrology, for that matter) does so, it's still a scientific theory, as far as I am concerned, and still worth considering.

    My problem with mainstream economics calling itself science is that when its predictions are falsified, they don't discard the theories. The late '70's should have been the last time anybody ever heard of Keynesianism, for instance, but that's not the case.

    But I'm not sure that Austrian theory is any better, since its predictions don't seem to be falsifiable at all, since they are not specific enough. For instance, if ABC theory makes predictions that X causes recessions, and the government does X, and *eventually* a recession occurs, that does not prove that ABC theory is correct. Austrian economists might as well be shamans predicting rain. Eventually it will rain.

    Published: July 10, 2009 4:08 PM

  • Roark Roark

    Hey everyone, if you are looking for a good laugh stop by thinkprogress.org and comment on some of their posts. Real funny stuff with all those crazy democrats.

    Published: July 10, 2009 4:21 PM

  • Sherman Sherman

    Russ: "But I'm not sure that Austrian theory is any better, since its predictions don't seem to be falsifiable at all, since they are not specific enough. For instance, if ABC theory makes predictions that X causes recessions, and the government does X, and *eventually* a recession occurs, that does not prove that ABC theory is correct. Austrian economists might as well be shamans predicting rain. Eventually it will rain."

    The problem is not theoretical specificity. The problem is control of variables. The most important phrase in the Austrian dictionary is: ceteris paribus. How can such a thing be accomplished in any "real" life experiment, or in any dissection of economic experience?

    Economic reasoning is no less specific or predictive than the physics of, say, meteorology. Both tell us with certainty "if A then B." The problem is in the real world of human action (and weather) "A" does not exist in isolation.

    Moreover, as Mises pointed out, "value" in economics is ordinal, based as it is on human preference. Thus, economics unlike the hard sciences is not quanitifiable.

    Published: July 10, 2009 5:19 PM

  • Jeremy Jeremy

    Russ,

    “Reasoning and scientific inquiry can never bring full ease of mind, apodictic certainty, and perfect cognition of all things.”

    I didn’t see that quote in the portion posted but as I read the sentence Mises is saying that there can never be “apodictic certainty, and perfect cognition OF ALL THINGS.” Mises may have argued that economic propositions can be apodictically certain, but here is talking about perfect cognition of ALL THINGS in this sentence, not just economic propositions. This is certainly true and in no way contradictory to his argument in Human Action.

    Minor point, but anyway...

    Published: July 10, 2009 5:22 PM

  • Russ Russ

    Sherman wrote:

    "The problem is not theoretical specificity. The problem is control of variables."

    If it is the case that economic theories cannot be falsified because of the problem of control of variables, then it is my contention that economic theories (including Austrian ones) are not scientific. That is all that I am saying. I don't have a problem with the Austrian methodology, per se. It gives logically plausible explanations for how economies work. That's better than nothing. I just object to the idea that Austrian theory is "science" if it is not falsifiable.

    I do think there is also a problem with "theoretical specificity", though. For instance, I can't see how ABC can tell with any specificity when a recession will start, or how deep it will be. It only predicts that, given certain conditions, one will eventually happen.

    Jeremy wrote:

    "I didn’t see that quote in the portion posted..."

    I didn't mean to imply that it was. That's why I gave a reference to where it can be found. I was reading Human Action recently, and that quotation caught my attention, that's all.

    "...Mises is saying that there can never be “apodictic certainty, and perfect cognition OF ALL THINGS.""

    That's certainly one way to look at it. But look at the section of Human Action that I quoted. Mises believed that praxeology is based on "reasoning and scientific inquiry". I hope we can agree on that. That being the case, my interpretation is that Mises is confessing that neither the mechanistic/causal approach to science (analyzing blind cause and effect in the manner of physics) nor the teleological/praxeological approach (analyzing purposeful action) will give "apodictic" certainty about anything, including economics. But I could be wrong, and Mises is unfortunately no longer around to mediate the disagreement.

    Published: July 10, 2009 6:31 PM

  • FTG FTG

    Russ,
    But I'm not sure that Austrian theory is any better, since its predictions don't seem to be falsifiable at all, since they are not specific enough.

    This begs the question - what's "enough"?

    Also, theories are not judged by their predictions entirely except when they pretend to explain regularities, but for how they explain the existing evidence. There is no way to use current evolutionary theory to make predictions on future species, nor current geology to predict what a future mountain will look like (current theory has not been able to predict geological phenomena like volcano eruptions, yet.) However, there is no denying both evolutionary theory and geology explain current evidence, the same way ABCT explains monetary-expansion recessions.

    What Feynman was criticizing was the pretense of social "scientists" to explain human action through reductionist theories, as if humans acted in regular patterns. IF they did, THEN you could use rigorous experimentation and falsifying of hypothesis to arrive at a theory. But since they DON'T, then the normal scientific method cannot be used, and the social scientists cannot say their theories are "scientific" as theories in physics and chemistry are scientific - that would NOT be the case.

    Published: July 10, 2009 8:15 PM

  • Russ Russ

    FTG wrote:

    "This begs the question - what's "enough"?"

    To take the shaman analogy again, if a shaman were to say "It will rain again here this month", I wouldn't be that impressed, even if his prediction turns out to be correct. If he says, "It will rain again here, next Tuesday at 11:39AM EST", and turns out to be correct, I would be much more impressed. So, I can't say how much specificity is "enough", but more is certainly better. And complete lack of specificity equals complete lack of falsifiability, as far as I can tell.

    "However, there is no denying both evolutionary theory and geology explain current evidence, the same way ABCT explains monetary-expansion recessions."

    But geology and evolutionary theory are fields that respect the idea that they are falsifiable with empirical evidence. I don't think that Mises thought that with regard to praxeology.

    And although you are right that evolutionary theory can't predict what future species will look like, it does make certain predictions. For instance, it predicts that we will never find "fossil rabbits in the Pre-Cambrian", to steal a phrase from J.B.S Haldane. Does Austrian theory make any falsifiable predictions, even about what we won't discover about the past, such as the "Haldane prediction"?

    "What Feynman was criticizing was the pretense of social "scientists" to explain human action through reductionist theories, as if humans acted in regular patterns...."

    That's not what I took from that short clip. What I got out of it was that he was criticizing them for calling themselves scientists, but either not having testable theories, or not doing the testing.

    Published: July 10, 2009 8:51 PM

  • Inquisitor Inquisitor

    "I just object to the idea that Austrian theory is "science" if it is not falsifiable."

    TBH who cares how you choose to label it? Mathematics is not empirically "falsifiable" yet it is a body of knowledge. Economics (praxeology) is falsifiable in that it is built on certain axioms and deductions thence, which if incorrect can be corrected. How is this not "falsifiable"? It is good that Austrian econ is circumspect with regard to what it does say, rather than blithely assuming one can have control of the variables and make very specific quantitative predictions. If you think this is akin to "shamanism", too bad really. The theory is falsifiable as far as its axioms and their corollaries go. Mises definitely believes praxeological theorems can be apodeictically certain if correctly formulated and deduced. A better way to view Austrian theory is that it rejects the hypothetico-deductive model alleged to be in use by the natural sciences in favour of a more classical Aristotelian notion of empiricism... which treats concept-formation as ultimately abstraction from elements in the world, which then are operated upon by deductions. It is no fault of Austrian theory that it does not - like a charlatan - pretend to offer more than is possible. You wish to falsify an Austrian economic theory? Find errors in the concepts it uses or its deductions. It is incredibly stupid to insist that economics must use the method of physics and other such sciences when its subject-matter is not amenable to them... and this is what Mises argues, modernist fetishism with the word "empirical" notwithstanding.

    I still think Feynman is full of positivist garbage. In fact he did not even give a very credible example of a social scientific theory, suggesting to me when he says he is not sure of what he says that he is dead on...

    Published: July 10, 2009 9:13 PM

  • LibertyVini LibertyVini

    It is quite easy to resolve the seeming contradiction - humans do not, principally act in the same homogeneous way as schools of fish of flocks of birds, not at the macro level anyway. And we know next to nothing of the microeconomies of flocks of birds. We know nothing of the response of fish schools to incentives beyond food or sex urge-fulfillment. Neither the microeconomies of schools of fish, of flocks of birds, nor of groups of men can be predicted empirically through mathematical models, though their macro movements may be observed, quantified, and some predictions made mathematically

    Published: July 10, 2009 9:30 PM

  • FTG FTG

    Russ,
    To take the shaman analogy again, if a shaman were to say "It will rain again here this month", I wouldn't be that impressed, even if his prediction turns out to be correct.

    You are still begging the question - is the theory to satisfy YOUR standards? To impress YOU?


    But geology and evolutionary theory are fields that respect the idea that they are falsifiable with empirical evidence. I don't think that Mises thought that with regard to praxeology.

    Well, you have accepted that theories not need to be predictors, that they can also be valid if they conform to existing evidence.

    And although you are right that evolutionary theory can't predict what future species will look like, it does make certain predictions. For instance, it predicts that we will never find "fossil rabbits in the Pre-Cambrian", to steal a phrase from J.B.S Haldane.

    Wouldn't such a prediction be impossible to falsify?

    Does Austrian theory make any falsifiable predictions, even about what we won't discover about the past, such as the "Haldane prediction"?

    Again, the Haldane prediction is in itself impossible to falsify - in order to achieve it, it would require tearing apart the very Earth to be exhaustive. So it becomes ironic you would ask for a similarly "falsifiable" theory as the Haldane "prediction".

    Published: July 10, 2009 9:39 PM

  • Evan Evan

    This question of falsifiable predictions is not as pertinent to ANY field of science, much less to social science. The difference is that physical sciences can get relatively more accurate predictions than the social sciences.

    To make a strong claim: no social science can ever yield falsifiable predictions. The reason is simple. You cannot reliably *control* for a variable, repeat an experiment with the same initial conditions, or even nail down the substance of your variable in the social sciences.

    The difference between austrian economics and other schools is the lesser degree of 'junk' floating around. ABCT for example will correctly tell you that inflation induced booms lead to busts rather then sustainable growth. However ABCT cannot tell you what level unemployment will be during the bust or which sector will see the most bogus capital expenditure, because there are too many variables to account for. Unemployment could be 50% say if the minimum wage is raised so high that 'traditional' employment is no longer doable. Or, unemployment could be 0% if they institute universal conscription (or communism).

    Published: July 11, 2009 12:16 AM

  • Inquisitor Inquisitor

    "#

    It is quite easy to resolve the seeming contradiction - humans do not, principally act in the same homogeneous way as schools of fish of flocks of birds, not at the macro level anyway. And we know next to nothing of the microeconomies of flocks of birds. We know nothing of the response of fish schools to incentives beyond food or sex urge-fulfillment. Neither the microeconomies of schools of fish, of flocks of birds, nor of groups of men can be predicted empirically through mathematical models, though their macro movements may be observed, quantified, and some predictions made mathematically"

    Good points.

    Published: July 11, 2009 5:33 AM

  • Sherman Sherman

    Mises' last word on this subject can be found in his: "Ultimate Foundation of Economic Science" (available free online from LVMI). I believe it is his last book. I believe it is his best.

    Virtually every comment made in this thread is addressed therein.

    Published: July 11, 2009 7:33 AM

  • Russ Russ

    Inquisitor wrote:

    "Mathematics is not empirically "falsifiable" yet it is a body of knowledge. Economics (praxeology) is falsifiable in that it is built on certain axioms and deductions thence, which if incorrect can be corrected. How is this not "falsifiable"?"

    Yes, mathematics is a body of knowledge, but it is not a science. It is "falsifiable" in the sense that statements can be proven true or false (except when they can't, thanks to Godel). But this has nothing to do with science. The truth or falsehood of scientific statements is contingent on reality, not logical deduction. The phrase "deductive science" is an oxymoron.

    Math is still useful, however, because it is used in science to construct theories that make empirically falsifiable predictions. But that is *applied* mathematics, not pure mathematics. What is needed to convince doubters (like me, or like mainstream economists) is something like "applied praxeology".

    "It is incredibly stupid to insist that economics must use the method of physics and other such sciences when its subject-matter is not amenable to them... and this is what Mises argues, modernist fetishism with the word "empirical" notwithstanding."

    I think it is stupid to insist that an economic theory be based on mathematics (although I also think it's stupid to insist that it eschew math), but I don't think it stupid to insist that a theory that claims to make empirical predictions be empirically falsifiable. If the theory doesn't make empirical predictions, then it's not of much use. If it does, then there should be a way to determine how accurate those predictions are, or again, it's not of much use. Saying "If you do X, then Y will happen, all other things being equal, but all other things never are equal, so there's no telling", which is what praxeology seems to do, is useless.

    I don't accept the idea of the synthetic a priori category. Either a statement is true by definition and has no empirical content, or it has empirical content and its truth is contingent on reality. I can't accept the idea that a statement can be true by definition, and still have empirical content.

    FTG wrote:

    "is the theory to satisfy YOUR standards? To impress YOU?"

    Ummm, if it is to convince ME, YES!

    "Well, you have accepted that theories not need to be predictors, that they can also be valid if they conform to existing evidence."

    No, I have not accepted that theories need not make empirical predictions to be scientific. You have misunderstood me. Evolutionary biology does make empirical predictions. They may not be the ones that, say, a creationist would insist upon, but they do exist.

    "Wouldn't such a prediction [Haldane's "pre-Cambrian rabbit" prediction] be impossible to falsify?"

    Wouldn't it be falsified if fossil rabbits *were* found in pre-Cambrian strata?

    Evan wrote:

    "This question of falsifiable predictions is not as pertinent to ANY field of science, much less to social science."

    Not true. The labor theory of value was falsified by the diamond-water paradox, for instance.

    "The difference is that physical sciences can get relatively more accurate predictions than the social sciences."

    Yes, which means it's easier to falsify the claims of physical theories. As I said before, lack of specificity basically means lack of falsifiability. If a theory says that given X, a recession will occur some time in the future, but it never says when exactly, there's no way to falsify that claim. The theorist could simply claim "Well, it hasn't happened YET, but it WILL!".

    Anyway, getting back to Eric's comment about why "mathematical types" reject Mises. I think it's deeper than Eric thinks. I think the mainstream rejects Mises mainly because Mises explicitly rejects empirical science with respect to economics, not just because he rejects mathematics, or because his chains of logic are hard to verify. I do think the other two factor in, though. If a theory uses no math, specificity is hard to achieve. OK, so theory says that given X, prices will go up. OK, by how much? Don't know? Then how do you test the predictions of the theory? And long chains of logic? Lots of smart people used to think that the labor theory of value was "logical", or "stands to reason", until Messrs. Menger, Jevons and Walras came along. So long chains of logic aren't trusted so much anymore, either.

    Published: July 11, 2009 9:28 AM

  • Inquisitor Inquisitor

    "Yes, mathematics is a body of knowledge, but it is not a science. It is "falsifiable" in the sense that statements can be proven true or false (except when they can't, thanks to Godel). But this has nothing to do with science. The truth or falsehood of scientific statements is contingent on reality, not logical deduction. The phrase "deductive science" is an oxymoron."

    Science merely means body of systematically collected and organised knowledge... and the truth or falsehood of everything is contingent on whether it corresponds to reality, yet then again Mises calls praxeology an axiomatic-deductive science - if he calls it deductive it is only careless phraseology.

    "Math is still useful, however, because it is used in science to construct theories that make empirically falsifiable predictions. But that is *applied* mathematics, not pure mathematics. What is needed to convince doubters (like me, or like mainstream economists) is something like "applied praxeology"."

    There's a lot of that, particularly by Robert Murphy, Roger Garrison, Hulsmann, Walter Block &c. Doesn't change the epistemic status of praxeological theorems...


    "Saying "If you do X, then Y will happen, all other things being equal, but all other things never are equal, so there's no telling", which is what praxeology seems to do, is useless."

    Or, it makes it a matter of interpretation whether certain events come under a certain theory. Praxeology is already "falsifiable"... Mises was attacking the notion that economics follows the hypothetico-deductive method, whereas it follows an axiomatic-deductive methodology. His arguments are specifically against the idea that using the h-d methodology one can derive economic theorems, not that one could not make purely contingent, historically situated predictions based on praxeological theorems. Either Roderick Long's book on Mises or Wittgenstein or Selgin's book Praxeology and Understanding sheds light on this, as well as Hoppe's The Economic Science & the austrian method or Mises's UFOES or The Epistemological problems of economics.

    "I don't accept the idea of the synthetic a priori category. Either a statement is true by definition and has no empirical content, or it has empirical content and its truth is contingent on reality."

    What is the status of this statement? "Empirical" (i.e. borne of direct observation)? Analytic? No, it's neither. What are the law of non-contradiction and the principle of inference? "Empirical"? Again, no. It either has basis in that it's synthetic a priori, or it has no epistemological basis whatsoever and therefore there is no such thing as knowledge.

    Published: July 11, 2009 10:27 AM

  • RWW RWW

    It never ceases to amaze me when people define science in such a way that pure mathematics is excluded. Such definitions are usually simply formed without thinking deeply enough about their consequences, but it is even more alarming when someone directly asserts that mathematics is not science. But it gets worse: some time ago, one of my students (in a mathematics course) brought up the "question" of whether mathematics is knowledge. Apparently his philosophy professor had asserted that it is not.

    This is the mindset that economists are often up against.

    Published: July 11, 2009 11:10 AM

  • Russ Russ

    RWW wrote:

    "It never ceases to amaze me when people define science in such a way that pure mathematics is excluded."

    It never ceases to amaze me when people define science in such a way that pure mathematics is INcluded.

    Yes, mathematics is a very "hard" field. Most mathematical statements are either provably true or provably false. But how does that make mathematics science? It doesn't make empirical claims at all, and doesn't look to empirical testing for proof.

    Inquisitor wrote:

    "Science merely means body of systematically collected and organised knowledge... "

    Under that definition, stamp collecting is science. I don't buy it.

    "It either has basis in that it's synthetic a priori, or it has no epistemological basis whatsoever and therefore there is no such thing as knowledge."

    This is nonsense. Either a statement is analytic a priori, synthetic a posteriori or synthetic a priori. If it's synthetic a priori, it's claiming that the nature of reality can be divined by pure reason, which is completely unscientific. If it's analytic a priori, it can be proven true or false deductively. Hence, there is an "epistemological basis" for saying it's true or false. If it is a synthetic a posteriori statement, it can possibly be proven false by checking it against reality. That may not be enough of an "epistemological basis" for those who are looking for "apodictic certainty" in the real world, but to requote Mises and extend the quote: "Reasoning and scientific inquiry can never bring full ease of mind, apodictic certainty, and perfect cognition of all things. He who seeks this must apply to faith and try to quiet his conscience by embracing a creed or a metaphysical doctrine."

    I believe this is what Austrian economics has turned into; a metaphysical doctrine. Mises is to economics what Rand is to philosophy. Both offer complete certainty that theirs is the one true way. That, in a nutshell, is why most economists reject Mises, in my opinion.

    Published: July 11, 2009 12:17 PM

  • RWW RWW

    It doesn't make empirical claims at all, and doesn't look to empirical testing for proof.

    Why do you insist that the word "science" (from Latin scientia, or knowledge) carry some connotation of empiricism?


    Mises is to economics what Rand is to philosophy. Both offer complete certainty that theirs is the one true way.

    I am not entire clear on what you mean by this. What "way" are you referring to? Unlike Rand, Mises explicitly rejects the idea that there are objective values for which all men must strive. Are you referring to the fact that his claims as to the consequences of certain actions are proved with apodictic certainty?


    That, in a nutshell, is why most economists reject Mises, in my opinion.

    Right, it has nothing to do with the fact that Mises' conclusions are inconvenient. You have a very optimistic view of most state-sponsored economists.

    Published: July 11, 2009 1:05 PM

  • End the Fed End the Fed

    "Yes, mathematics is a very "hard" field. Most mathematical statements are either provably true or provably false."

    Only when given the axiomatic framework. But who says which set of axioms are the "correct" axioms? You can make up just about any axioms that you want, and prove anything you want.

    Published: July 11, 2009 3:42 PM

  • Inquisitor Inquisitor

    "Under that definition, stamp collecting is science. I don't buy it."

    Couldn't care less whether you "buy" it or not. Stamp collecting is a science in its own way and the word solely refers to a body of organised knowledge. The fetish to refer to it as what is characterised by hypothetico-deductive inquiries is but that - a fetish.

    "This is nonsense."

    No, it's true. Deal with it.

    "Either a statement is analytic a priori, synthetic a posteriori or synthetic a priori. If it's synthetic a priori, it's claiming that the nature of reality can be divined by pure reason, which is completely unscientific."

    No, it's saying it can be intellectually grasped, not "divined".

    " If it's analytic a priori, it can be proven true or false deductively. Hence, there is an "epistemological basis" for saying it's true or false. If it is a synthetic a posteriori statement, it can possibly be proven false by checking it against reality. That may not be enough of an "epistemological basis" for those who are looking for "apodictic certainty" in the real world, but to requote Mises and extend the quote: "Reasoning and scientific inquiry can never bring full ease of mind, apodictic certainty, and perfect cognition of all things. He who seeks this must apply to faith and try to quiet his conscience by embracing a creed or a metaphysical doctrine." "

    You didn't really get it - checking against reality presupposes that facts are as they are, i.e. that they're not both the case and not the case. So the LNC is presupposed by the empirical approach, else it dwindles into nonsense. I still wish to know - what is the epistemological status of your own statement? Analytic? If so, it is arbitrary, merely tautological (how does one even "check" against reality wrt to such a statement?) Empirical? Surely it is not the result of direct observation. Which fact of the world is it that informs you of this? So then what is it? A string of meaningless words you compiled?

    "I believe this is what Austrian economics has turned into; a metaphysical doctrine. Mises is to economics what Rand is to philosophy. Both offer complete certainty that theirs is the one true way. That, in a nutshell, is why most economists reject Mises, in my opinion."

    Actually, it exposes the nonsense and inconsistencies in opposing epistemological viewpoints, causing some people to label it a "metaphysical doctrine", for how dare it raise these questions and put into doubt the validity of mathematics and the h-d methodology wrt the social sciences... how dare they! Neither Rand nor Mises preached infallibilism. Anyone more than superficially familiar with their work would know this...

    Published: July 11, 2009 9:28 PM

  • Orfeu Orfeu

    I don't understand a word from what Russ is saying.

    I kept on reading and I just don't get his logic. He uses all those strange words and weird formulation, but he just doesn't make sense to me. The thing that truly escapes me is his desire to "falsify something." What is that?

    And most of all, why so much effort in contradicting someone that doesn't understand his own opinions? If he uses all those fancy words, it doesn't mean that he is smart or something, just that he is in love with hearing himself speaking.

    Published: July 12, 2009 2:18 AM

  • RWW RWW

    You can make up just about any axioms that you want, and prove anything you want.

    True, and what you are proving is "Given these axioms, this statement follows." This is scientific knowledge. Besides, the vast majority of mainstream mathematics, if you will, is based on Peano's Axioms, which are as innocuous as the foundations of praxeology.

    Published: July 12, 2009 10:12 AM

  • Anonymous Anonymous

    This document from Mises was written decades ago, before almost all of the currently supported economics using mathematics was thought of and written. In it, Mises takes some guesses as to how mathematics would be used in economics and what mathematical economics would say.

    Those guesses are completely, dead wrong. For Mises to have written these ideas back when he wrote them was not stupid, just wrong. For a Mises admirer in 2009 to oppose the mathematical statements in the well-written, currently assigned, year 2009, graduate level economics textbooks on the grounds described in this document is flat out wrong and stupid, and deserves to be called this (straight to its face).

    I suspect there might be some readers of this website who would do exactly that, and I would urge them not to do that.

    I would suggest that any students reading this go and get a current textbook, like Jehle/Reny or Mas-Colell/Whinston/Greene. Then, learn the definitions and theorems for all of the mathematical concepts used in that book. Then, read very carefully which mathematical concepts are used, and how the mathematical concepts used in those books are used in the text. You will find that they do not fit what Mises wrote here decades ago. Some of it you will recognize as the same thing Mises supported.

    You will find in those textbooks: methodological individualism, revealed preference, subjectivism, ordinal utility, marginal analysis, and conclusions that are reached basic on deductive reasoning from simple assumptions that we take as true.

    The expression "Human Action" is a reference to the elegant way that Mises explains the concept of revealed preference. And, quite exactly the same concept of revealed preference is firmly stated and supported in the current mainstream textbooks, include the most mathematical ones.

    Mises was a very intelligent man. If he were alive and young today, he would be smart enough to carefully read and understand a 2009 textbook like Jehle/Reny. I think he would understand the definitions, read very carefully which mathematical concepts are being used, and how they are being used. I think he would notice that those are the same as the basic economic concepts that Mises supported back in the 1920's through 1940's.

    Published: July 12, 2009 9:43 PM

  • newson newson

    to anon:
    if there are no constants in human behaviour, how can any mathematics serve? i can't see mises is dated in the slightest.

    Published: July 12, 2009 11:11 PM

  • anonymous anonymous

    newson,
    I have studied a variety of branches of mathematics. Never have I seen a type of mathematics that asserts there must be constants in human behavior. Never. If you are assuming that economics using mathematics must assert that this is the case, then that probably means you are familiar with little (if any) modern mathematics. Even with the mathematics available when Mises wrote, no such thing was true. There might be cases where a textbook example is shown assuming a constant value relevant to human behavior, but those are pedagogical examples used to illustrate a concept, and not assertions that human behavior follows defined constants in real life. In fact, mathematical mainstream economics textbooks say the opposite of that about, and they say so in mathematical language.

    It is very possible for economic theory to be written in mathematical language without ever asserting that there are constants in human behavior. If you would like to see how, you should look at any of the currently most popular mathematical mainstream economics textbooks. Such as the ones by Jehle/Reny or Mas-Colell/Whinston/Greene.

    Those two books cost money to obtain legally. If you want to see a mainstream economics textbook illustrating this, which is available online for free, you should carefully study the one by Ariel Rubinstein. He is a mathematical mainstream economist who works at NYU and Tel Aviv University. His book can be seen here:

    http://arielrubinstein.tau.ac.il/Rubinstein2007.pdf

    If you study and understand the contents of that free online book, you will then have, more or less, an accurate idea of what current mathematical mainstream economics looks like.

    If you carefully read that textbook and understand all of it, you will find the concept of revealed preference (a.k.a. "Human Action") stated in Chapter 1. But, not as eloquently as it was done back when Mises showed us his way of explaining that widely accepted, basic, mainstream economic concept.

    If you read and understand Chapter 2, you'll also see in that chapter ideas equivalent to ideas supported by Mises, in Human Action.

    Published: July 13, 2009 12:46 AM

  • newson newson

    to anon:
    thanks for the tip. but i don't understand what possible benefit mathematics can bring to economics that can't be done by verbal logic. if it can't be expressed verbally and make sense, then mathematizing it won't help.

    Published: July 13, 2009 1:42 AM

  • newson newson

    ...actually i had a look at the rubenstein book. it reminded me of university. if you first dream up the curves, then you can use calculus. what if the curves aren't continuous, then what? what if the curve shape is unknowable and changing?

    Published: July 13, 2009 2:16 AM

  • anonymous anonymous

    The advantages and disadvantages of mathematical vs. verbal language seem to vary. They vary based on what you're studying, the skills and interest of the student, what you're trying to express et cetera.

    When students first learn a text like Rubinstein, some of them have a reaction that is like, "I can see how this is the same as what the intuitive verbal books say, but this just seems like a waste of time. It's not even wrong, I just don't like it."

    I think it's one of those cases where you have to look backwards to the complaints economists were making before they made the shifts they made. When economics was written only in words, it was common for them to read a paper and jump to lots of different assumptions about what the author really, really, really meant. This is not as common when the same general concepts are stated in mathematical language.

    Some of the econ professors most enthusiastic about the mathematization of economics are old guys who did grad school before the mathematization happened. Robert Solow of MIT is an example of this. Some of them make sure to remind people that the 'good old days' weren't as 'good' as you might think. And, that economists back then had problems that today's grad students don't have to experience in the first place.

    The important thing to recognize is that neither language, math nor words, makes economic theory automatically right or wrong.

    In my view, students should start in words and then shift to math later on. Some very mathematical economists recommended that I start out learning from words-only books, or else I wouldn't have a good feel for the intuition. Then, I should study mathematics, separately from economics. Then, I should study economics that has been mathematized. Once I'm fluent in the math and already have a flavor for the real-world intuition, then I'd be able to read econ papers written mainly in math, and read them for their real-world intuition, just as if I were a pre-school kid reading a picture book. Experienced economists say they get used to the math that is most commonly used in economics, and, after a while, they read it just like they're reading a novel.

    If I had to advise a 14-year old aspiring economist, I'd tell them to read Steven Landsburg, Russell Roberts, Milton Friedman, Thomas Sowell, and Henry Hazlitt when they're in high school. Then, do a bachelor's degree mainly in mathematics and statistics, studying it by itself, without thinking about econ yet. Maybe take just the basic undergrad courses in micro, macro, game theory and econometrics, but mostly stay away from undergrad econ courses, and especially business/accounting courses. Then, switch more seriously from the math department into economics by studying stuff at the level of the Rubinstein text I posted. Rubinstein is typically assigned at the first-year grad student level.

    Published: July 13, 2009 2:25 AM

  • pbergn pbergn

    Very sad!

    Mathematics is the foundation of all sciences!

    The Austrians' claim that some processes in nature, such as social processes, are too complex, an therefore cannot be accurately formulated in mathematical terms, completely disregards the cyclical nature of the universe.

    I am amazed that the Austrians do not see a great contradiction in pushing forward their economic theories, and trying to predict business cycles, and future trends, such as devaluation of currency with the increase of money supply, or rise and fall of prices based on supply and demand variations, and not being able to admit that they are some repetitive trends in human action as well...

    In my opinion, anything that is based on hierarchical, and ultimately on cyclical nature can be rationally evaluated by analyzing the previous cycles.

    I assume, it is undisputed that there are certain patterns even in such complex systems as chaos systems (e.g. it is possible with more and more accuracy to predict weather patterns, patterns of behavior of groups sharing certain character traits, etc.). While the outcome of each individual iteration is not predictable in general, the outcomes of sufficiently many iterations can be mathematically (quantitatively) estimated (for example, from Theory of Probability we know that the law of large numbers is being upheld, and can be theoretically and empirically proven)...

    The point: while incorrect or inaccurate mathematical models tell little to nothing about economic processes, to use this as a definitive proof that mathematics is inapplicable and is irrelevant when dealing with complex social processes is intellectually dishonest and is utterly reactionary.

    The Catholic Church used to blame the science as witchcraft for it was not always able to explain the miracles of creations, so it tried explaining everything through the existence of super being, that is God, and tried to convince people that all efforts to understand God and his ways were futile and misgiving.

    It is twenty-first century outside, and yet I am afraid, Austrians are advocating for similar approach that is of Catholic Church, to the Science of Economics - that is one cannot explain the human action, for it is too complex, so let us treat it as a work of supernatural forces (or, as spontaneous exchanges, that have no explanation whatsoever, short of, perhaps, supernatural).

    This kind of approach goes against the very nature of science - which is based on rigorous enquiry, and is driven by the unquenched curiosity of millions of individuals seeking to better understand this world...

    Published: July 13, 2009 2:53 AM

  • newson newson

    anonymous, that's one of the most convoluted bits of reasoning i've seen in a long while. if it's unclear in english, how is mathematizing going to make it less clear?

    Published: July 13, 2009 4:20 AM

  • newson newson

    ...i mean, less unclear.

    Published: July 13, 2009 4:22 AM

  • Duh! Duh!

    This hostility to metrics does the Austrian schools reputation no good. Austrian economics is like the physics, mathematics, and philosophy of economics. Their criticisms of mathematical models are valid. The criticisms of how these models cannot meaningfully be extrapolated accurately to the "real world" are less convincing. Economics is faced with a simple problem in parallel with physics. A relatively simple set of rules, which are simple and intuitive, render very good predictions when subject to minor manipulations (all other things being equal). These models however crumble before the n-bodies problem. In economics n is just too large, the system is not closed, and practically none of the determinants are known!

    However to state that nothing can be measured, and nothing can be predicted, is an untenable nihilist one. Please spare a thought for a less lofty and more practical economics. One less poor, but better suited to us lowly peasants, who must ply our trades far from the ivory towers of the LVMI. Help us hack together a workman's economics, woefully inaccurate for the lofty perfection of pure economics. But good enough for us to craft our lowly tools so that our economic burdens may be lightened.

    Please don't fight the Chicago school, they ain't perfect, but their pragmatic outlook makes them good companions. They will happily throw aside their models when they are not fit to the task. (And more importantly they consider Krugerman a Keynesian cult figure, too)

    Published: July 13, 2009 5:55 AM

  • newson newson

    to pbergn:
    the church also used to use latin to mystify the scriptures and remain the gatekeepers to the faith. this is similar to the economic orthodoxy of today with their attachment to mathematics.

    anybody who feels that economics, austrian or otherwise, will lead to predictive success should hurry off to new york to test his ability with the best of the hedge-funders. they're awaiting your black-box model.

    Published: July 13, 2009 9:52 AM

  • Daniel J. Fallon Daniel J. Fallon

    Duh

    "However to state that nothing can be measured, and nothing can be predicted, is an untenable nihilist one."

    You say nothing convincing in support of this statement. Mises is merely setting down what can be vs. what cannot be measured given our current reality. It is not anti-science to define what economics is vs. other forms of knowledge.

    You almost state the unbridgeable problem yourself, the "n-bodies". Mises does not declare that modeling is unhelpful for forecasting- but puts it in the category of entrepreneurial understanding. Mises states that no economics, no laws, may be derived from this experimentation.

    But then you are probably challenging the idea that there can be economic laws? Or is it the law that everything in economics is hypothetical? But then we are back to square one. Mises categorically states that humans act purposively- they make decisions and have human will. No metrics may represent the subjective side of these decisions- never mind the impossibility of recreating an experiment. The outside phenomena cannot be completely known, exist in the past anyway, and relate to an unrepeatable mindset of that particular place in time.

    Your belief, in rejecting praxeology, is closer to nihilism. It is the empirical schools that keep having to invent fictions just to make their models work. It is Mises who assumes that humans act with purpose.

    No matter how complex the math becomes it is still just math. It will only reveal mathematical knowledge. This is why economics is unique. Unless there is some kind of evolutionary change or divine intervention this remains the reality.

    It is ironic how you seem to have so much faith in the possibility of econometrics while admitting and forgiving the pragmatics of the Chicago School. The hope that someday they might get something right is highly misplaced.

    Published: July 13, 2009 10:48 AM

  • anon-basher anon-basher

    The book by Rubinstein referred to above by "anonymous" starts off with some strange stuff (as expected).

    Consider the mathematical "definition" of preferences Defn 1. (pg. 19 of the pdf).

    Using the notation that "f(x,y)= I" signifies indifference between x and y, Defn 1 requires the following property to hold for any 3 elements x, y and z:

    "if f(x,y)= I and f(y,z)=I, then f(x,z)=I"

    Due to this constraint, the definition for preferences does not even adequately cover preferences expressible as a partial order on a set.

    Supposing that silver is at $10/oz

    1. Indifferent between 1oz silver and 1 10$ note

    2. Indifferent between 1oz silver and 10 1$ notes

    3. Definitely prefer 1 10$ note to 10 1$ notes

    The situation above cannot be modeled using Rubinstein's Defn 1 (and Defn 2) of preference functions.

    I don't know how much this sort of oversight affects the results of further analysis in the book, but I don't expect much from any mathematical analysis which fails to handle such seemingly trivial situations even at the outset.

    Published: July 15, 2009 1:52 AM

  • anonymous anonymous

    anon-basher,

    First of all I want to apologize for having been so heated and confrontational in this thread. Mises.org is not my website, and I truly regret having been such a belligerent and obnoxious 'guest' when I put comments here. The policy said I must be "civil", and I violated that, so *sorry*.

    On p. 20 of the pdf, Rubinstein acknowledges that humans behave in ways that violate transitivity, so he presents that concept as imperfect with respect to real world relevance. He at least acknowledges that in the text, and the student reads that acknowledgement, which I think is good. Experiments done in psychology and marketing departments and by experimental econ people have found that people behave in inconsistent ways. So, if you consider that type of human behavior (a guy preferring a $10 bill to ten $1 bills) important enough to make Rubinstein's book and his work generally untrustworthy, and if you are a fair and consistent person, then I speculate you would end up also concluding that the books by Mises and Rothbard are untrustworthy. If you look around long enough, I'm guessing you'd find a psychology or marketing department experiment that would show humans behaving inconsisently in a way that would prove problematic even with the definitions found in Mises and Rothbard (i.e. you could come up with a scenario that makes a statement about value scales false or questionable).

    I also would suggest looking at the "Summary" section on p. 25. Rubinstein reveals there that the formalization for preferences on p.19, to which you refer, was not essential, could have been omitted, and was there for a demonstration. So, if that is your biggest concern about the book so far, I don't see it as a huge, highly important problem. Your observation is interesting, but I don't yet see that it is important enough to adopt low expectations for the book. I'd recommend that students at Tel Aviv University remain enrolled, and continue to act like normal students.

    I've never seen or read an economist who adopted conclusions about the real world based on the opinion that it did not matter whether or not the assumptions made were realistic, but I've also never seen an economist whose assumptions were all perfect with no uncertainties, variations or exceptions.

    Published: July 15, 2009 7:19 PM

Post an intelligent and civil comment

(Please allow up to one minute for your comment to be processed.)