One of the striking features of (propertarian) libertarianism, especially in the US, is its reliance on a priori arguments based on supposedly self-evident truths. Among[^1] the most extreme versions of this is the “praxeological” economic methodology espoused by Mises and his followers, and also endorsed, in a more qualified fashion, by Hayek.
In an Internet discussion the other day, I was surprised to see the deductive certainty claimed by Mises presented as being similar to the “certainty” that the interior angles of a triangle add to 180 degrees.[^2]
In one sense, I shouldn’t be surprised. The certainty of Euclidean geometry was, for centuries, the strongest argument for the rationalist that we could derive certain knowledge about the world.
Precisely for that reason, the discovery, in the early 19th century of non-Euclidean geometries that did not satisfy Euclid’s requirement that parallel lines should never meet, was a huge blow to rationalism, from which it has never really recovered.[^3] In non-Euclidean geometry, the interior angles of a triangle may add to more, or less, than 180 degrees.
Even worse for the rationalist program was the observation that the system of geometry (that is, “earth measurement”) most relevant to earth-dwellers is spherical geometry, in which straight lines are “great circles”, and in which the angles of a triangle add to more than 180 degrees. Considered in this light, Euclidean plane geometry is the mathematical model associated with the Flat Earth theory.
The discovery of non-Euclidean geometry led to the rise of formalism as the dominant philosophical approach in mathematics. The key point of formalism is that axioms like Euclid’s parallel postulate are neither true nor false. They are merely sentences in a formal language that can be combined and manipulated to form new sentences (theorems). A set of axioms may be useful if the theorems it yields turn out to provide a good model for some real world phenomenon, but this is not a mathematical question (though it helps keep mathematicians in work).
Mathematical formalism reached its high point with the Hilbert program in the early 20th Century. Despite the negative results of Godel, who showed that the more ambitious aims of the program could not be fulfilled, it was still dominant when I was taught mathematics in the 1970s.
I believe mathematical formalism has lost some ground since then, but if so, the effects have yet to filter through to economics. Mainstream (neoclassical and Keynesian) economics, since its mathematical reformulation by Samuelson and Arrow in the 1940s and 1950s, has been entirely formalist in its approach. Its axioms are not treated as self-evident. Rather the standard justification is that of modus tollens: if the theorems are descriptively false, we can trace our way back to work out what is wrong with the axioms.
The formalist program in economics hasn’t lived up to its expectations. It turns out to be much trickier than was hoped to work out what is important and what is not, and the formal clarity of deductive argument doesn’t necessarily translate into clear thinking. Still, this program is in far better shape than that of the Austrian School, and the methodological failure of a priori reasoning is a large part of the reason.
Having written this piece, I did a better Google search and found, as usual, that much of it is not new aand indeed goes back to Keynes. (Mises reply to Keynes seems entirely unconvincing). But the point that Austrian economics is genuinely related to Flat Earth geography (as opposed to the use of this term as simple abuse) seems to be new.
Update The reference to Keynes above was the result of reading too quickly. The “Lord Keynes” in question isn’t John Maynard, but the contemporary blogger to whom I linked. And the weak reply is not from Mises but from one of his epigones, Hans-Herman Hoppe.
[^1]: As I read him, Nozick is equally extreme. An ethical theory that disregards consequences seems just like an economic theory that disregards data. Nozick seems to me to get more respect from other philosophers than Mises gets from economists. Reader
[^2]: Some presentations are more careful, referring to a triangle on a Euclidean plane. But that only shifts the problem one step back. Without the empirical proposition (false for the surface of the earth) that the subject of inquiry is a Euclidean plane, we don’t know (as Russell said) what we are talking about when we refer to Euclidean triangles. And, as Einstein showed, the situation isn’t improved by thinking of the earth as an object in three-dimensional Euclidean space.
[^3]: The most famous name here, immortalized by Tom Lehrer, is Nikolai Ivanovich Lobachevsky.
John Quiggin 
Thanks for the great fill-in. One thing one has to wonder is what would have happened if Keynes had lived long enough with his uncertainty/probability background/perspective to consider developments in scientific method not long after his death in 1946 – aka.
– Popper’s return to the world after mulling things over at the University of Woolloomooloo (sorry Christchurch NZ) in 1946 – and subsequent wider circulation of his ideas on falsifiability e.g. in the The Logic of Scientific Discovery (published much earlier but in German at a non so great period).
– Thomas Kuhn’s ideas crystalized in The Structure of Scientific Revolutions developed in the 1950s and published in 1962.
Looking from the sidelines the reason why formalism still dominates seems to be that economics by its nature, and complexity – is prone to being captured by vested interest even more so today even than in Keynes’ time.
i.e. if you as an economist say things and develop theories that suit the powerful and wealthy that justify their comfy jobs and privilege you will in turn be showered like any good courtier with money and accolades and even ersatz Nobels to keep producing/recycling more of the same.
Whereas if you throw in curly issues from say a Marxist viewpoint in a non-Marxist state – you will not be a beneficiary of such largesse.
Its doesn’t even need to be personal/political. Its just good business if it keeps us dancing to the music of capitalism for another round then that is all that is required. And if it works to suppress or simply crowd out alternative ideas from teaching syllabuses too then even better. One of the great things about University course certification / standardization too is it promotes orthodoxy as effectively as any capture of the citation lists.
For me the only way to break this ‘natural selection’ vice would be the development of a new economics ‘atomic theory by a theory + technique giant comparable to Keynes. Alas we are still waiting. Picketty for all his accolades doesn’t seem yet to qualify as (if I understand this correctly) he really has still been saying the bleeding obvious to anyone who reads history and doesn’t work inside economics – albeit very well. The fact he is being embraced by part of the mainstream is a worrying indication he will soon be sequestered back into the economic fold in the role of loyal opposition. I’d like to hope otherwise.
@Newtownian
My thanks too. I would immediately have thought of the arts if presented with the words rationalism and formalism and indeed so does Lord Google when presented with rationalism versus formalism.
I shall enjoy following up your idea that “rationalism” was dealt a fatal blow by non-Euclidean geometers. I may try it out on a friend who is close enough to the subject to have written at length on the Riemann Hypothesis. (No sign of the Andrew Wiles yet to master what I believe is the last of Hilbert’s great unsolved mathematical problems of about 1900).
With great hesitation I beg to doubt Newtown’s explanation for the prevalence of formalism. Wouldn’t William of O see that it was just a way of keeping things simple enough to handle? Not that any technique which can be bent to meet the demands of those who dispense the goodies of this world won’t be made to do that service. That would be common ground with those who think the IPCC’s model makers have been effectually bought!
Like all economists the Austrians say many things which are true, and even important, at least some of the time. But someone please help me get my head round the sectarian differences between Austria and the freshwater boys (mostly boys – and including Hayek from memory) of Chicago.
see What Austrian Economics IS and What Austrian Economics Is NOT with Steve Horwitz
@Jim Rose
what’s the tldr version?
@Nevil Kingston-Brown
Probably something like “The Austrians will fix everything by sprinkling free market pixie-dust on it.”
Good to see a clear example of capitalist ideology contradicting itself so blatantly.
While it is a nice platitude to claim that only individuals choose, markets are spontaneous, prices reflect society and that cost and utility are subjective – all of this is contradicted by the other claim in this confused video, namely that: institutions and rules condition how this operates.
In effect Austrian economics self-implodes.
In the real world individual private commercial property does not really exist and is outcompeted by huge social concerns made up of millions of shareholders and superannuation funders. Again the institutions and rules surrounding these social entities then determine how they operate independently even if this contradicts the long run interests of the rest of society. Fossil fuel combustion, in the interests of huge social companies, is one result.
A superior form of economics is constructing enterprises that share all the benefits amongst all citizens – public health, public banks, public schools.
We do not want to go back to the old system where fire brigades only put out fires in houses covered by membership of private entities. But this is the essence of Austrian confusion. Prices must not be used to allocate fire brigade services, ambulance services, schools, and policing and access to justice.
The Austrian claim that price is a “knowledge surrogate” is naive. Price only represents some knowledge namely cost and demand. It does not indicate knowledge of institutions and rules that condition costs and create demand. So here is a further example of Austrian confusion.
A good example would be two equivalent tins of jam. If one is priced at $5 and the other is at $4, society has insufficient information to judge whether subsequent transactions threaten economic stability. The price does not indicate whether the cheaper tin of jam was manufactured by slave labour or not. The price does not indicate whether it is set at these levels only because consumers have increased their level of credit.
“Considered in this light [as detailed in the thread], Euclidean plane geometry is the mathematical model associated with the Flat Earth theory. (Term in square brackets added.)
Neat.
Some might consider Riemann a more famous name than Lobachevsky.
Great post, but regarding this:
“Having written this piece, I did a better Google search and found, as usual, that much of it is not new and indeed goes back to Keynes.”
A slight misunderstanding here. Actually in the post you link to called “A Red Herring on Praxeology: A Reply to Lord Keynes”, the “Lord Keynes” (the handle I use) is me — the author of the original post here:
http://socialdemocracy21stcentury.blogspot.com/2013/08/mises-fails-philosophy-of-mathematics.html
@Lord Keynes
Oops! I’ll fix this
Also, some more thoughts — in support of you — here:
http://socialdemocracy21stcentury.blogspot.com/2014/07/john-quiggin-on-apriorism-in-austrian.html
Another minor point: it seems that Hayek rejected Mises apriorism. But this this doesn’t effect your main argument at all.
I have never read Hayek, Mises, or even Rand. But I know I don’t like them, because I don’t like their followers.
Rand fiction is popular with those who don’t read. Even conservatives find her stuff without discernible merit
@John Quiggin
I think you may still be reading too quickly. The weak reply to Lord Keynes purported to come from one Mattheus von Guttenbrrg. Not that it matters if you didn’t realise he was an epigone’s epigone.
Pretentions ofmany members of the Austrian school to logic has always struck me as somewhat odd, since they make it clear in their exposition of Austrian ideas that they haven’t kept up with the developments in logic in the 20th century. You rightly alude to non Euclidean geometries here, but even the incompleteness theorem destroys the whole program of praxeology. What I mean is, Gödel showed us the futility of trying to deduce all the truths of arithmetic from pure logic, which one would think is going to be as certain as anything else. Next to that, the notion that praxeology can attain anything like apodictic certainty about something as complicated as human behavior strikes me as pure folly. Perhaps that isn’t something to be surprised at since it comes from the same scholastic tradition as Aquinas. Austrian economists warnings against the expansion of credit also echo the old Catholic prohibitions of usury. They really are the Rationalists of the economic world, sharing all the faults of that tradition while masquerading them around virtues.
They come by their pseudoscience legimately; Mises held that verification or falsification was irrelevant to economics.
It may be useful to quote Mill on prices:
“There is no proposition which meets us in the field of political economy oftener than this—that there cannot be two prices in the same market. Such undoubtedly is the natural effect of unimpeded competition; yet every one knows that there are, almost always,*33 two prices in the same market. Not only are there in every large town, and in almost every trade, cheap shops and dear shops, but the same shop often sells the same article at different prices to different customers: and, as a general rule, each retailer adapts his scale of prices to the class of customers whom he expects. The wholesale trade, in the great articles of commerce, is really under the dominion of competition. There, the buyers as well as sellers are traders or manufacturers, and their purchases are not influenced by indolence or vulgar finery, nor depend on the smaller motives of personal convenience, but are business transactions. In the wholesale markets therefore it is true as a general proposition, that there are not two prices at one time for the same thing: there is at each time and place a market price, which can be quoted in a price-current. But retail price, the price paid by the actual consumer, seems to feel very slowly and imperfectly the effect of competition; and when competition does exist, it often, instead of lowering prices, merely divides the gains of the high price among a greater number of dealers.”
@John Brookes
I think reading Rand when you’re a teenager is actually a good thing (see also: rough sex is the highest form of capitalism). It’s like getting a vaccine. I don’t mind admitting that I was captivated for a few weeks at age 17 or so, until the fridge logic of it all caught up with me.
Pete Boettke’s entry on “Austrian Economics” at the Concise Encyclopedia of Economics, also offered 10 propositions that define Austrian economics:
1. Only individuals choose.
2. The study of the market order is fundamentally about exchange behaviour and the institutions within which exchanges take place.
3. The “facts” of the social sciences are what people believe and think.
4. Utility and costs are subjective.
5. The price system economizes on the information that people need to process in making their decisions.
6. Private property in the means of production is a necessary condition for rational economic calculation.
7. The competitive market is a process of entrepreneurial discovery.
8. Money is non-natural.
9. The capital structure consists of heterogeneous goods that have multispecific uses that must be aligned.
10. Social institutions often are the result of human action, but not of human design.
@Jim Rose
There are clearly an awful lot of unstated propositions if this set of quite general statements is supposed to lead to the prescriptions of Austrian economics. Most of which appear to be extra beliefs snuck in under proposition 8.
In particular, the non-neutrality of money is a core tenet of Post-Keynesian thought, as is that capital is heterogenous, that institutions matter, that the future is uncertain and therefore beliefs, expectations and discovery processes matter: and yet post-Keynesians have extremely different conclusions and views of appropriate policy than Austrians.
@Jim Rose
Perhaps I have misunderstood something, but on the face of it proposition 3 suggests that for a social scientist investigating, for example, witch-hunting, it is a fact that people were believed to have intercourse with devils, but it is not a fact that people didn’t really have intercourse with devils. I would like to see how this approach could be justified.
@Nevil Kingston-Brown
This is quite clever.
“There are two novels that can change a bookish fourteen-year old’s life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves Orcs.”
John Rogers
My response to Boettke, from 2009
https://johnquiggin.com/2009/03/18/austrian-economics-a-response-to-boettke/
Off topic but topical, I saw this interview this afternoon. I’d previously read comments from Nick Hanauer, and was pleased for the effort
http://www.pbs.org/newshour/making-sense/why-capitalism-has-nothing-to-do-with-supply-and-demand/
Now move your viewer to a room with no heavy objects and take in the Libertarian perspective from Law Professor Richard Epstein.
http://www.pbs.org/newshour/bb/top-middle-debating-key-economic-growth/
Sorry I broke the 2 link rule. I just forgot about it. Now to move on to the “on topic” rule, but what would a thread be without a token zombie and a slayer.
http://www.pbs.org/newshour/bb/top-middle-debating-key-economic-growth/
The parallel postulate is an axiom, and the real world is more easily described by non-Euclidean geometry. This is not to say that Euclidean geometry doesn’t apply to the real world.
To say that only Euclidean or non-Euclidean geometry applies to the real world are both metaphysical statements. There is no evidence that denies Euclidean geometry from applying to the real world, because nothing says its impossible for you to describe space and light as Euclidean.
In fact, no evidence can prove or disprove whether Euclidean geometry applies to the real world or not. It would be silly to attempt this. Its an arbitrary designation made for modeling.
However, to say that the mind perceives things as Euclidean is correct. You cannot visualize any non-Euclidean geometry, without visualizing it as Euclidean geometry. That is mental capacity of our mind, and is an inductive observation.
I can prove this by asking you to draw an instance where the parallel postulate is invalid. Since its not possible for you to draw this, then its sufficiently proven.
Schopenhauer had similar arguments shown here: http://en.wikipedia.org/wiki/Schopenhauer%27s_criticism_of_the_proofs_of_the_Parallel_Postulate
So when people say the universe is Euclidean, it is the same as saying the mental capacity of the human mind only perceives Euclidean space. Objectively, the universe is not necessarily Euclidean, non-Euclidean, or any geometry at all. Any geometry is a mental analytical conception.
This is where the confusion arises. Mises never used the term “axiom” because the basis of praxeology is formed of statements about the nature of how humans perform actions, which is inductive.
Everything derived from this is a priori, and is based on the analysis of the causal factors of human actions.
This isn’t like geometry because these are not constructions for the purposes of modeling reality. They are observations about reality itself. They are inductions from introspection that are validated by literally asking any person.
Mises did not invent the a priori. John Stuart Mill, in fact, explained why the the a priori method is valid in “On the Definition of Political Economy and the Method of Investigation Proper to It,” written in 1836. And Cartwright defended this method in “Nature’s Capacities and their Measurement,” written in 1989.
The Austrian position is simply that no economic statistics can possibly measure all the causal factors involved in society. These types of econometric statistics can in no way invalidate basic a priori economic laws because these tests simply don’t address the content addressed by the a priori laws.
Bollocks.
Visualise this. Take an orange. Draw an equator around it. Draw two lines at right angles to the equator. Since they are both at right angles to the equator, they are parallel with each other. Extend the lines all the way around the orange. They cross at the poles. Euclid’s parallel postulate does not hold in this everyday visualisation/drawing. QED.
For further applicability to the real world, imagine you are living on the surface of something spherical. It shouldn’t be too hard, unless you are Austrian.
The claim that a bunch of white male elderly privileged anglo-saxon-austrian-american economists could derive universal laws of human behaviour by contemplating their navels is even more ridiculous. I refer you to this well known paper, “The Weirdest People in the World?”, which documents just how little the findings of actual psychological tests (not just introspections) about very basic things (like, inter alia, concepts of “fairness”, “work”, “space” and “geometry”), which were taken to be universal, apply to people who aren’t residents of US university campuses.
PS If real spacetime could be correctly described as Euclidean then both General and Special Relativity would be falsified. You could stilldescribe it that way if you wished, much like conservative economists keep describing US inflation as an imminent danger and/or already here, but being covered up by the FED; it’s just that you would be wrong.
@John Quiggin
This reply to Pete is a nice reply about were people have honest disagreements.
Nevil, that’s a dumb argument. There is no reason special and general relativity must be “falsified.” This is based on what? Yes, it would require a difficult and impractical model, but this is not to say its impossible. To you, it seems impossible because you have a difficult time visualizing it, and so do I. However, look at Eddington’s experiments. The light beams do bend according to how our mind interprets them.
As further evidence of your confusion, economists and scientists don’t describe anything as dangerous. This is normative. Its not descriptive, its prescriptive.
@Hank
I’m not sure this is correct. I can certainly visualise a triangle on the surface of a sphere, which I’m led to understand is non-Euclidean.
@Tim Macknay
…although I note that this could be a terminological issue as, on a brief scan of online material, some sources identify spherical geometry as being non-Euclidean, whereas others say that it is ‘not truly a non-Euclidean geometry’. At this point I’ll hand the discussion back to trained mathematicians (!).
@Tim Macknay
Spheres are Euclidean. There are also 4 dimensional spheres which are non-Euclidean impossible to visually construct.
@Hank
The predictions of general relativity would be falsified if spacetime was not curved. There is no internally consistent way to calculate the curvature of light around Mercury (etc) which is consistent with a Newtonian/Euclidian universe.
Quibbling about adjectives is a red herring. “an imminent event” if it makes you feel better (ps I note that Peter Boettke describes inflation as “socially destructive” in his encyclopedia definition of Austrian economics quoted earlier, so maybe you should take this up with him).
I noted earlier, but it seems to be stuck in moderation:
“Visualise this. Take an orange. Draw an equator around it. Draw two lines at right angles to the equator. Since they are both at right angles to the equator, they are parallel with each other. Extend the lines all the way around the orange. They cross at the poles. Euclid’s parallel postulate does not hold in this everyday visualisation/drawing. QED.”
@Nevil Kingston-Brown
Nevil, it is important. Many economists have opinions. Its perfectly fine to have opinions. “dangerous” is not a scientific term.
You are conflating Euclidean and non-Euclidean. Yes the two lines cross because they are were not straight (according to Euclid’s definition). You simply redefined straight to what normally means curved. There’s nothing wrong with that, but you are conflating it.
@Nevil Kingston-Brown
Regarding mercury, just because it doesn’t follow the laws of Newtonian gravity doesn’t mean its impossible to derive new equations explaining its motion.
Even if you can’t derive these equations, then the movement of Mercury would merely be unpredictable according to a Euclidean universe. There is nothing wrong with this, its just not very satisfying.
@Hank
I think you will find that elliptical (eg on the surface of a sphere) and hyperbolic geometry are usually referred to as “non-Euclidean geometry”. You can come up with your own personal definition – much as Austrians have recently attempted to redefine the word “Inflation” – but you are unlikely to convince anyone.
On your second point, its hard to see this as anything but a flat rejection of Occams razor and enlightenment thinking generally. Consider this restating from a comparable paradigm shift: “Regarding Cholera, just bwvause it doesnt follow the wind patterns of miasma doesn’t mean that we can’t derive a new miasma to explain it. Even if we can’t, outbreaks of cholera would just be unpredictable by miasma theory. There is nothing wrong with this, it’s just not very satisfying”.
To expand on Nevil’s point, you can’t as a matter of empirical fact, rescue the actual geometry of the Earth for Euclid by treating it as a spherical object in Euclidean 3-D space. That’s because, thanks to Einstein, we know that space isn’t Euclidean, any more than the surface of the earth is a plane.
It might be worth reading Feynmann on armchair philosophers who claim to derive relativity theory from a priori argument rather than observation. The Austrians are exactly in this position.
@J-D
Well, maybe Tom Lehrer is not a popular as he used to but he made Lobachevsky far more famous, at least in the English speaking world. Mind you when I first heard of Lobachevsky I did not even know he was a mathematician. But the lyrlcs are great, and worthy of describing a Wegman.
“worthy of describing a Wegman.”
Gold. It’s a pity his name doesn’t scan
@Nevil Kingston-Brown
Nevil, first of all, you are missing the point. But I’ll follow up on your point regardless.
I agree with Occams razor. Occams razor is a normative statement about how scientist’s OUGHT to do science. I agree that non-Euclidean geometry is better applied to the universe and can probably describe more than what the rules of a Euclidean universe allow for. I’ve said that numerous times, so to say I “reject” Occams razor is patently false.
To say whether any geometry exists in the physical universe makes no sense, because geometry only exists as an analytic concept. It exists in the human brain, not in the physical universe.
So you are once again confusing two things. You can say its “correct,” as in the analytic concept is correct, or you can say its “correct” as in it follows the normative principle of Occams razor. One is a scientific statement, one is not a scientific statement.
However, as I already stated, the economic a priori principles are not axioms, like in geomtry. They are inductive observations. These causal factors exist in our physical universe. Therefore, you’re arguments about geometry don’t necessarily apply to what I was trying to say in my original comment.
@John Quiggin
“thanks to Einstein, we know that space isn’t Euclidean.”
Einstein was a physicist, not a metaphysician. To say that the outside universe is “Euclidean” is a metaphysical statement. No evidence can possible “say” that the universe is any geometry because geometry only exists conceptually.
Einstein developed a non-Euclidean model that can be accurately applied to the universe. Strictly speaking, this isn’t even accurate! The measurements of galaxy rotation contradict his model. Do you come to the conclusion that the “universe” is not “non-Euclidean”? No, because your statement about geometry “existing” in the physical universe is made arbitrarily, without any demonstration.
@jrkrideau
Among Lehrer fans — in which category I include myself — Lobachevsky must be one of the most famous mathematicians ever.
On the other hand, if I do a Web search for ‘famous mathematicians’, my top hit is a list somebody has compiled of the greatest mathematicians, on which Riemann is ranked 5th and Lobachevsky 110th. Obviously that’s a single observer’s opinion, but what I wrote was not about what everybody thinks, but rather about what some people think, an observation I stand by: some people rate Riemann higher than Lobachevsky. (And if Lobachevsky’s name is a bigger one than Riemann’s because of the Lehrer song, then it’s not because of relative contributions to non-Euclidean geometry.)
If you love Tom Lehrer’s work, you will know Lobachevsky’s name and don’t need to know Riemann’s. But if you’re interested in the history of non-Euclidean geometry, you should know Riemann’s name.
@Jim Rose
Between alternatives presented to them and based on their budget constraint. In other words the system determines how individuals choose. Public expenditures are examples where social groups choose.
Exchange behaviour is determined by budget constraint and is impacted by anti-competitive behaviours.
The facts of social sciences are objective facts of wealth and poverty and of working poor arrangements and unemployment.
Injustice is an objective standard essentially based on the “Golden Rule” or its breach.
Utility is subjective, costs are objective.
The price system corrupts the information needed to make sustainable decisions. If a market event occurs due to price there is no information whether the price figure was constructed of real sustainable value or in part of unsustainable debt.
Capitalist private property of means of production can never produce rational economic calculation. In the absence of additional debt, capitalist prices always exceed society’s final consumption expenditures. In the presence of additional debt – the economy is driven to catastrophe.
Monopolists, government agencies and planners produce discoveries.
This makes no sense. Who claims that money is natural.
Capital only has to earn the same rate of profit in the long run. Nothing needs to be aligned except capital and profit rate.
All social institutions operate within the law and therefore well and truely are the result of deliberate design.
@Hank
It would seem that part of our dispute here is terminological, and part is philosophical.
Terminological: I (and I think JQ) am using “the universe is non-Euclidean” as a sort of shorthand for “the universe can most accurately be described using the mathematical framework of non-Euclidean geometry” and you are objecting to this, or rather, you are inferring from it that I think of “geometry” as an empirical thing. I agree that geometry per se, whether euclidean or non-euclidean, is a formal mental construct not susceptible to empirical proof or disproof. Indeed that was part of the point of JQ’s original post.
However, the accuracy, precision and “scientific beauty” in the form of the least number of rules explaining the widest range of events, with which the physical universe can be described using various geometries is very much an empirical question, and claiming that the universe can’t be described as “non-Euclidean” because “non-Euclidean” is the name of a formal geometry is to mistake the terminological for the ontological. Your statement “In fact, no evidence can prove or disprove whether Euclidean geometry applies to the real world or not.” is simply wrong. No empirical evidence can prove or disprove the formal internal consistency of Euclidian geometry, but empirical tests of whether physical space is accurately described by Euclidean geometry, or in other words whether Euclidean geometry “applies”, are very much possible. Saying “the universe is non-Euclidean” is a shorthand for “the universe can most accurately be described using non-Euclidean geometry”, deal with it.
Getting back to the more philosophical issues, the question “what can the human mind visualise” is ALSO an empirical question. Just because you (or, my physics degree being long behind me, I) have difficulty visualising four-dimensional space-time curvature doesn’t mean that someone else with a better imagination and more mathematical training can’t do it. This so-called induction from introspection is really nothing more than an argument from incredulity, similar to people who say that they can’t possibly imagine all life evolving from a single cell 4 billion years ago and therefore Darwin must be wrong, or (in the normative sphere) that they can’t imagine homosexual sex in any positive way, therefore it must be evil.
Moving on to the next steps of your argument, you appear to be trying to have your cake and eat it. When you say “This [Mises’ premises from inductions] isn’t like geometry because these are not constructions for the purposes of modeling reality. They are observations about reality itself.” you appear to be a) contradicting Mises (“Its [praxeology’s] statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori.”) and b) claiming that they are simultaneously a priori, which is, by definition, not derived from observations and experience, and empirical, which does consist of observations of reality. You can’t have it both ways – synthetic a priori is an empty box, as Lord Keynes elucidated.
Claiming that various premises are embedded in the structure of the human mind is not a justification for a priori-ism, but an empirical claim about the structure of the human mind. Enough research has been done on how widely minds vary across cultures, genders, classes, ages, etc (see the Heinrich et al paper I linked to above in post 27) to make any claim to universality of human understanding of economic action (and, for that matter, geometry) extremely dubious. Unless you are also going to adopt mysticism and claim that the human mind can never be empirically studied or understood (in which case, how would introspection work?), and by implication dualism, then this attempt to provide a non-empirical connection to the real world fails.
You appear to then claim that Austrian economics is a formal system not susceptible to empirical proof or disproof (although your argument that Austrianism is not a formal axiomatic system but some kind of set of non-axiomatic statements and deductions appears to undermine this – how can you have deduction without axioms anyway?) but then you have to accept that Austrianism has no more relevance to the real world than Euclidean geometry as a formal system does. It is not about the actual economy, it is about an imaginary economic system that Mises introspected out of his navel. It may be very interesting to join him in contemplation, but it’s not anything that can guide study of the actual economy in any way – as you appear to admit when you say that economic statistics have no relevance to it. In which case, what’s the use of it except as a subset of abstract art, and why do Austrians keep making claims about what economic policy should be followed?
@Nevil Kingston-Brown
“Euclidean geometry “applies”, are very much possible.” Saying its possible, doesn’t make it possible.
“Saying “the universe is non-Euclidean” is a shorthand for “the universe can most accurately be described using non-Euclidean geometry”, deal with it.” Again, I never once disagreed with this statement. You pretend I disagreed with this for some reason. I don’t think I even attributed the view to you, yet you feel as if you need to defend yourself against nothing.
“ALSO an empirical question.” Correct. In addition, it has never been falsified.
“imagination and more mathematical training can’t do it.” Again, it has nothing to do with math or imagination. Its a simple (and empirical) fact that you, nor anyone, sees a fourth dimension.
“introspection is really nothing more than an argument from incredulity,” Here, you are denying empirical evidence as valid. Introspection is empirical. Psychologists frequently draw from introspection.
“they can’t possibly imagine” Introspection and imagination are completely different things.
“have your cake and eat it.” I would if I could.
Yes, I admit its hard to comprehend. Mises says, “Its [praxeology’s] statements and propositions are not derived from experience. They are, like those of logic and mathematics, a priori.” He’s saying that economic propositions made from basic praxeological concepts are a priori. These statements are the analysis from PRIOR concepts, aka a priori.
“claiming that they are simultaneously a priori” I didn’t claim that basic economic postulates are a priori. In fact, as you already noted, I said they were inductive.
“Enough research has been done on how widely minds vary across cultures, genders, classes, ages, etc (see the Heinrich et al paper I linked to above in post 27) to make any claim to universality of human understanding of economic action (and, for that matter, geometry) extremely dubious.” This is easily demonstrated as false.
Action has been a topic of research by cognitive science, psychology, and philosophy for decades. http://plato.stanford.edu/entries/action/
“But the view that reason explanations are somehow causal explanations remains the dominant position.” You see? This is precisely the same causal mechanism described by Mises in Human Action. These causal mechanisms are universal for all deliberative actions. This is an inductive argument and has never been falsified by any evidence.
Again, read Nancy Cartwright in Nature’s Capacities and Their Measurement for a full explanation on the reasons why singular causes, not general causes, are the important starting point in science.
“how can you have deduction without axioms anyway?”
This horse is white.
This different horse is white.
This horse is the same color as the other horse.
This is a deduction without axioms. Is there some sort of logical law preventing deduction without axioms I am unaware of?
“imaginary economic system that Mises introspected” Again, equivocating introspection and imagination seems fundamental to your argument.
“guide study of the actual economy in any way” Every economist who studies the economy relies on basic fundamental postulates. You literally cannot use the term “value” without defining what “value” is. Once you understand that “value” is a completely subjective phenomenon, you must accept that the causal mechanism is the purpose these valuations have. Otherwise, you must unscientifically, arbitrarily, objectively determine value, or cease to use the term whatsoever.
@Nevil Kingston-Brown
In addition, the idea behind intentional an unintentional action is relied on in courts of law. In your world, there would be no difference between first degree murder and manslaugher. If deliberate action was really subject to “cultures, genders, classes, ages, etc” then you can live in a world where there is no legal concept of mens rea: http://en.wikipedia.org/wiki/Mens_rea
@Hank
If geometry only exists conceptually and not in the physical universe, then any system of economics that is analogous to geometry in this respect also only exists conceptually and not in the physical universe.
“Some presentations are more careful, referring to a triangle on a Euclidean plane. But that only shifts the problem one step back. Without the empirical proposition (false for the surface of the earth) that the subject of inquiry is a Euclidean plane, we don’t know (as Russell said) what we are talking about when we refer to Euclidean triangles.”
True, we cannot be certain that human beings act. Therefore, we can only be as certain of any conclusions we deduce from this axiom as we are in the correctness of the axiom and of our logical reasoning. The relevant question is then, are we more or less confident that human beings act than we are in the outcome of the latest regression analyses?