Maybe some Austrians might be interested in a “fresh start” from an empirical point of view with Alfred Marshal as the basis (the inventor of supply and demand). He insisted that logic and mathematics are inseparable (and also saw mathematics as potentially redundant but useful for thinking and prediction).
“(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often.”
Empiricism rules since Newton, so some sort of model for human action may be necessary for the Austrian school to ever become mainstream.
Computer scientist Stephen Wolfram discovered that he could list and search through all sorts of different mathematics using computational models. This means that computational science is one step prior to mathematical science.
Adam Smith, David Ricardo, and Karl Marx made use of the term “supply and demand” years before Marshall was even born. The only thing that Marshall did was draw two lines and set an abritrary “equilibrium point” which does not exist in real markets.
Mathematics is a subsection of logic. How verbal logic is inseperable from mathematics when it comes to subjects which require no advanced mathematics is beyond me.
Empiricism the way you describe it is a self defeating proposition in social sciences. The idea that you can take past experiences that are not controlled for various factors (it’s impossible to control “experiments” in social sciences), form them into theories, and then apply those theories to future events is just plainly absurd.
I agree with the OPer. Mathematics is merely a langugage of philosophy. I never understood why the Austrians are so against modeling per se. I understand their critiques of modern statistical methods (a la the Black Swan). But what’s so wrong with describing axioms as a set of equations? The Austrians did as much, just with words. See Garrison’s graphical expositions, if you don’t believe me.
It’s impossible to do so. You might prefer a to b and b to c, but you might prefer c to a. Mathematics cannot describe this. Likewise, you might prefer one apple to a banana, but you might, at the same time, prefer a dozen bananas to a dozen apples. Then again, you don’t think “oh, well the marginal utility of an apple is [insert ridiculous equation here] so I’ll pick the bananas.” There is no way to use mathematics to describe these relationships.
Garrison simply used neoclassical graphs, e.g. supply and demand as well as opportunity cost, to describe ABCT. He didn’t use absurd neoclassical mathematical models.
No? If you prefer to be, and b to c, but c to a, it’s because time has passed, and prefer simply means choosing. All I need is a parametric equation with time as one of the parameters.
I agree here. It seems that what we have in Mises and Hayek is a verbal description of a sort of equation, but not the sort of equation used in mathematical calculations. Rather, it’s an ordinal equation, and the only place we see this in math is in algebra and set theory. But, since we’re limited to finite situations, set theory has nothing to add, and since human action is a factor, we don’t apply algebra. We can perfectly well draw curves and pictures, as Hayek and Garrison did and do, without claiming to represent a cardinal situation. (Although at times such pictures can be misleading.)
Reread my post. Did I include time? No. Time does not need to pass for you to have seemingly “contradictory” wants.
The problem with mathematics is that the economy is never at equilibrium and human action does not follow mathematical patterns. The way mainstream economists use mathematics in economics is by definition positivist. They take human action and then use some mathematical formula as a representation. It doesn’t have to be a cardinal representation, it can be an ordinal one.
What does such a situation look like? If it is the case that I can, at the very same instant, have seemingly “contradictory” preferences, then why does Rothbard use linear preference scales? Doesn’t this throw out everyone he does from that point on, since he bases the rest of that chapter on the linear nature of preferences? What will this do to Austrian welfare economics, since it will no longer be possible to conclude that triangular intervention is never positive?
In fact, leave aside seemingly contradictory preferences. I don’t see how I can have two non-contradictory preferences at one and the same time. A preference is only expressed in choice, and we don’t assume stability of preference scales over time (if we did, and I choose to watch tv over working out right now, I could never work out), and at time t I can only be making one choice, hence expressed one preference, I see no way to make any two statements about my preference at one and the same time.
I agree with this. Mathematical models need not assume equilibrium, though, and most interesting models don’t. It’s certainly true that human action doesn’t follow mathematical patterns, but I tend to believe that nothing at all follows mathematical patterns. It doesn’t follow that things can’t be modelled mathematically. The planets can be described with calculus, but they don’t move the way they do because of calculus.
Right, that’s the point of mathematical modelling.
Ok, it can be, but then they couldn’t do all the fun things they do with it. If they take ordinal utility seriously, as the Austrians do, they might (for illustration only) still draw continuous demand and supply curves, but they’d never speak about the intersection points (as Rothbard doesn’t.) They’d never take integrals, never try to derive properties of a sequence, never divide - none of these operations are well-defined on ordinals.
The problem with mathematical language is that it rarely has the rigor, accessibility, and conciseness of logic in the verbal form. Though the models of Roger Garrison are excellent learning tools, to completely comprehend the science of economics means one must realize such models are mainly pedological devices. At least that’s my view.
Mathematics can only model that which has some quantity or invariant relationship. In this case, there are some things in human actions in respect to the market that can be modeled such as the relationship of the State’s warping of the market via inflating the currency and other actions as these have quantities to them which don’t necessarily depend on any one agent/individual to instantiate. But if you’re attempting to model the price of a particular product or service or model what the next technological boom will be, you’re out of luck as these things depend on information that is particular to many individuals who often are not in direct communication with each other (due to time, space, interests, and etc). As such, mathematics for modeling their actions is logically impossible.
Since Austrians have identified money and capital to be primary factors, perpahs such a computational model could focus on their behaviour (maybe would also make it less likely that it could be used for socialist purposes). The problem with praxeology as I see it is that it’s not formalized enough to have general credibility (and Austrians also disagree among themselves on some conclusions, as this story illustrates http://mises.org/daily/2936).
@krazy Usually when some one does not know what they are talking about, they admit to that. They don’t proceed to then state the exact opposite of the truth.
When a > b and b > c implies that a > c, we say that the relationship “>” is transitive. It has already been documented by mathematicians that the “utility function” is intransitive. Luckily, there already existed, even before this discovery, of such things as intransitive logics and intransitive relationships in mathematics. You may have already seen some of this in your first year of college. Although I guess you didn’t, obviously.
You could get a detailed explanation on any book in category theory or logic. You can also get a somewhat more cursory mention in popular staples of the mathematics literature as Topics in Algebra by Hernstein, or Principles of Mathematical Analysis by Rudin.
Actually, explaining how the utility function (among others) can arise is the subject of many papers, usually coming to the same conclusion in different ways. Here is an example: “Gambling in a Malthusian Universe: A Game-Theoretic Approach to the Paradoxes of Expected Utility” by Gregory B. Pollock and Keith A. Lewis, published in Rationality and Society, Vol. 5 No. 1, January 1993, pp. 85-106.
Basically mathematics is a language to describe things, and if you can’t model it then you can’t falsify it. I wouldn’t expect you to know about these particular references and the particular research that I mention here if you hadn’t sought them, but then again I wouldn’t have expected you to act like you did.
I’m glad you mention this! I should mention that invariant relationship is a flexible concept, but I would like to quote what you said first:
While I agree with what you say here in one sense, technically (and for more interesting reasons, to me at least) I have to disagree. So I agree that a model will not tell you exactly who what when where why or how the next “big thing” will be. But a lot of mathematics is not about giving exact numbers, but about detailing the specifics of the whole situation. Let me make this more concrete with what I have in mind:
In general, there is a plague with people who use mathematical models. In essence a lot of people are not using them correctly. A brief summary of the most common pitfall: A lot of people will assume that their mathematical model is correct, and assume that all errors in the model are normally distributed. This means that they are due to outside influences and will cancel themselves out in the long run.
In mathematics we say that our errors are “gaussian” and we put a gaussian probability distribution in to our equations that reflects these errors.
The problem with this, of course, is as you mentioned the next “big thing.” There are other probability distributions that deal with this, for example the “power law distribution”. These can be used in a model, but a lot of people don’t like them because it incorporates the idea in to your model that there are big changes that can come and you don’t know when. There is a problem in the business world that if you tell you boss you don’t know what’s going on, he or she may not think highly of that. This is the subject of a book fairly recently published called “The Black Swan” by Nassim Taleb. He discusses events that are really rare. But what’s special about a “Black Swan” event is that if one of these events occurs once, it changes the game forever. For example one can think of the advent of computers, writing, agriculture, as these sorts of unpredicted black swans that have had unpredictable effects on the economy.
I don’t necessarily believe in pure mathematical modeling myself. Keynes himself wrote
“It is a great fault of symbolic pseudo-mathematical methods of formalising
a system of economic analysis, such as we shall set down in section VI of
this chapter, that they expressly assume strict independence between the
factors involved and lose all their cogency and authority if this
hypothesis is disallowed; whereas, in ordinary discourse, where we are not
blindly manipulating but know all the time what we are doing and what the
words mean, we can keep ‘at the back of our heads’ the necessary reserves
and qualifications and the adjustments which we shall have to make later
on, in a way in which we cannot keep complicated partial differentials ‘at
the back’ of several pages of algebra which assume that they all vanish.
Too large a proportion of recent ‘mathematical’ economics are mere
concoctions, as imprecise as the initial assumptions they rest on, which
allow the author to lose sight of the complexities and interdependencies
of the real world in a maze of pretentious and unhelpful symbols.”
But I do believe Austrian economics needs to be more formalized in order to become more mainstream, as I don’t believe in a general mainstream conspiracy but mostly errors in thinking (no doubt there are also politicized economists, but from all sides of the spectrum it seems to me). The general equilibrium theory for example leaves out money altogether as far as I know although corrections have been attempted. A computational model I suppose could even mix boolean or fuzzy logic and mathematics. This way you can perhaps get some falsifiability that would be generally acceptable.