I did not write this but saw this floating around on various places today. Thought I would share and see some feedback from the peanut gallery.
The Problem with Praxeology
Praxeology is founded on the premise that “humans act,” & by “act,” they exert their will with the intent to accomplish goals. Because this is taken as axiomatic - that is, because this proposition is taken as an independent, stand-alone, self-evident truth - by the Austrian school, it is argued that a whole system of thought can be derived from this axiom purely through deductive means, akin to any given branch of pure mathematics.
The problem is though, that this “axiom” is anything but self-evident. Many cognitive scientists believe that the will, intent, & goals are just illusions pre-fabricated by our brains, & indeed, Praxeology just assumes outright that we have free will. Now, whether or not those cognitive scientists are correct is beside the point - the fact that it’s even possible that the action axiom is wrong means that if it’s true, it’s an empiricalfact, not an axiomatic one. As such, Praxeological methodology is rendered invalid, & thus the study of human action, as well as of economics in general, must be conducted through largely inductive (empirical) means, like any other science.
Now, there’s another angle to this, namely, Goedel’s Incompleteness Theorem. The Incompleteness Theorem states that in any axiomatic system, there are always going to be true conclusions relevant to said system which can’t be derived from the axiom(s). This means that Praxeology is subject to the Incompleteness Theorem. In other words, if the proposition that humans act is an axiom, then not everything which is true about human action can be derived from Praxeology; if, however, the proposition that humans act is an empirical fact, then everything which is true about human action can be inferred as an implication of said fact.
Not only does that mean that an empirical “Praxeology” would be more complete than an a priori one, but an a prioriPraxeology is squarely at odds with reality, as it leads to the conclusion that not every implication of the proposition that humans act is really an implication thereof. And this isn’t a flaw that can be contained to whatever conclusions that Praxeology can’t reach, either, for if one methodology leads to a partially accurate but false result, & another, radically different, methodology, leads to a true result, then it can be concluded that there is a rather profound flaw in the former methodology that casts a shadow on the whole enterprise.
To put it another way, conceiving of human action as axiomatic (assuming that from it you can derive all of its implications) leads to the conclusion that the action axiom cannot predict all of its own implications, & indeed, that only a radically different methodology can, so Praxeology is thoroughly self-refuting.
So there you go, two logical proofs that Praxeology is bunk.
Oh my have the amateurs come out to play? I’d like him to quote Mises showing where Mises says praxeology requires free will (on this read from p.37 of the document I’ll link), and also explain what exactly it is these cognitive scientists are up to when they say intent and goal are “illusions” fabricated by our brains? So why should their “beliefs” be taken as important if they have no intent or goal of discovering truth and applying a sound methodology to reach it? What would his denial of the action axiom be if not an action? An involuntary reaction? If so, it’s hot air, literally. So the first one is utter tripe.
Second one. This argument doesn’t even make sense, is he pulling this out of his rear? Here’s Hoppe on Goedel (p.74):
Maybe he shouldn’t try bringing up arguments Mises had already considered in the first 100 pgs of HA?
A few comments and insights for our anonymous praxeology bunker.
The positive, existential, or ontological proposition that other people act is not required for praxeology. A cognitive scientist is free to deny that he aims at goals utilizing means. Praxeology only applies when its given assumptions are present. If a cognitive scientist were to aim at no goals or ends, and utilize no means towards them, then praxeology will be of no use to him, just as mathematics will be of no use to those who seek to arrive at no particular location or time.
Regarding Goedel’s Theorem and how it applies to praxeology, this much I believe I can say:
Praxeology seeks to ascertain the incontestable implications of various means of action. Here are two simple examples:
If by means of walking I intend to arrive at some location, the incontestable implications of these means is that I must necessarily depart another location.
If by means of making a car more aerodynamic I intend to increase its fuel efficiency, the incontestable implications of these means is that the car now travels further before coming to a stop.
The means utilized have “logical” co-presences which it is possible the individual is not aware of.
Praxeology applies this same kind of reasoning to social phenomena as well.
Regardless of the abstract claim that Goedel’s Theorem limits or invalidates praxeology, we should be able to apply this theorem to the two examples above.
If we apply Goedel’s Theorem to these examples of the implications of the means of action, maybe this will give us insights we are currently unaware of.
Doing so may help to clarify the problems involved more concretely, as opposed to an abstract comparison of praxeology and Goedel’s Theorem.
Praxeology doesn’t assume that the will is absolutely free and that we are in absolute control of our actions. There is space for constraints on that either of a cultural or biological nature. This doesn’t howeve imply that people are like functionalistic automatons.
These sorts of articles are really insulting. It seems to me that they think they can debunk a whole school of thought by one evening of thought and no real research. Mises and other thinkers spent decades developing and defending these theories, and some guy comes a long like no one has ever brought up either of these ideas.
I think this reveals the author does not really understand the use of logic in science. I may start off with a law that has been demonstrated to hold quite well (like the first law of thermodynamics), and very well deduce the consequences following therefrom in the construction of my theories. This DOES involve the use of deductive reasoning, and theories that are at variance with our most basically emprically attested laws are not entertained but ruled out and left for the cranks to chew on.
There is no such thing as inductive science, otherwise all kinds of superstitous hogwash could qualify as it.
The only main difference I can see between Praxeology and the natural sciences is the way in which deductive reasoning is predominantly applied in both to produce theories. In the natural sciences the main causes of phenomena are not available to us. Hence, we proceed to gain knowledge of nature by producing hypothetical premises, from which we build up a chain of causation to relate physical observations, from which we may deduce predictions. Since from a true premise in a correctly framed argument, only true conclusions can follow, if our conclusion is false, this falsifies our hypothetical premise. This is the general structure of arguments used to build up theories in the natural sciences and physics, whether one is talking about relativity or thermodynamics.
In Praxeology, what we start of with the basic synthetic a priori notion of action, and we can deduce what would follow from this in different scenarios. Despite being a prioristic, the conclusions produced are certain as long as the initial statements can be held to be reflected in empirical reality. The truth of this requires understanding not measurement, e.g. realising whether indirect exchange is an institutional condition for the society in question. The structure of logic used to produce correct statements here is far more straightforward, since we begin with the basic causal phenomena already known, that of teleological action, we may trace its consequences. Hence we start with a true statement, and if our additional premises are true as well, and our chain of reasoning is correct, then our conclusions are also true.
What is not trivial however in this analysis however, is establishing the nature of the historical conditions and factors at play in any given scenario; which requires historical understanding. Since prefect knowledge of these can never be acquired, despite this knowledge being synthetic a priori, since it is reflected in actual actions, it can never produce predictions of the form found in the natural sciences.
Sort of, if a chemist was asked if this particle would combine to form air -no one could really know that because no one really has perfect knowledge of particulars and not because chemistry is wrong?
Kind of, though I think a better way to state the comparison would be to ask if a certain sample of gas produced from air would relight a glowing splint; without allowing the chemist to identify the distribution of constituent gases, since only a sample with a high concentration of Oxygen would do the trick. If the chemist had mistakenly thought or was told the sample was almost completely nitrogen, his wrong prediction would not falsify Chemistry.
Even if that statement on it’s own was correct, the one that following would be moot.
So what? We able to derive economic laws, and probably not other true things. Saying that the incompleteness theorem debunks praxeology is like saying the incompleteness theorem debunks math.
Perhaps it would be more accurate to say that the incompleteness theorum limits the plausible scope of claims that praxeology can make, I.E. it demarkates it from the whole of social science.
This is nothing but a huge piece of either sophistry or ignorance or both.
OK let’s take it paragraph by pragraph:
Paragraph 1: so far so good
Paragraph 2:
I don’t believe anyone could really think something so stupid. If I would go over and punch the guy who wrote this in the face, he would expect an apology, I am certain. But why? I had no free will.
Free will is a universal assumption since the beginning of time in any legal system, any ethical system, and every person’s gut feeling. So the burden of proof is on thee, mad scientist, to show we don’t have it.
Sure, the 19th century thinkers figured that the mind is just a bunch of atoms subject to all physical laws, and so are as bound by the inevitable as the apple falling to the ground, but we know better. The atomic level of reality is not really understood, it is full of paradoxes and randomness and uncertainty. So lets all grow up.
Now if a professional physicist here could enlighten me with more precise knowledge I would appreciate it, but my layman’s readings led me to write the above.
More paragraph 2:
Here’s where the author shows clearly that he knows not of what he speaks. So let’s get the background info set up, and the scales will fall from our eyes:
There are two things going on in a serious study of reality, such as Physics or Geometry.
The first is observations of reality, collecting facts in a plastic bag and saving them up. This is done in the real world, and does not need thinking. A camera, a robot, a thermometer, can be set up to do this while we sleep.
The second is attempting to understand what is happening, how all these facts fit into a scheme of some sort. This occurs ONLY in the minds of the thinkers.
Mathematics is, of course, part of the second thing, the thinking and understanding. The great genius Euclid showed us all the way how to do this. One makes up a set of axioms [meaning assumptions that we are not going to prove, cause we gotta start somewhere], uses universally agreed on rules of logical thinking, and deduces the consequences of the axioms.
Now not all axioms are created equal. It is part of the art of the Mathematician to choose his axioms cleverly. If he does it well, he creates a little world of Math, his axioms and their consequences, WHICH ACTUALLY MATCHES SOME PART OF REALITY.
For example, Isaac Newton said, “Let me assume three axioms. [the famous F=ma, and the other two laws of motion.]” As a mathematician, he studied the logical consequences of those three axioms, and all physicists to this day keep doing it. The result: Big fat calculus books full of formulas and pictures.
Again. all this was going on his head. It was a purely mathematial thingy, exactly like high school geometry. His place in history is assured for that alone.
But now comes something mindboggling in the extreme. Newton said, “Guess what, guys?” F=ma is not only an “axiomatical fact” [to use the language of the OP. Of course there no such thing as an axiomatical fact. An axiom is by definition an unproven assumption], but an empirical fact as well!
In other words, since F=ma is true, IN THE REAL WORLD, AS SHOWN BY EXPERIMENT AFTER EXPERIMENT, and so are both my other axioms, then my whole big fat calculus book which deduced the consequences of the axioms is also 100% true in the real world, every last word of it. For if the axioms are true, then by all humkan knowledge that mankind has painfully saved from savagery over the ages, the conclusions MUST BE true.
OK now we have that all clear, the sophistry of the OP [and I know it’s not the sender of the post, he’s only quotiing] is obvious. Just as F=ma is an “axiomatic fact” AND an “empirical fact”, so too is the praxeologic axiom that humans act both those things. The two concepts “axiomatic fact” and “empirical fact” are not opposites.
More paragraph 2:
That was not my experience studying physics. I spent a trivial amount of time in the lab, and heaps and heaps of time studying that big fat calculus book.
How much time should be devoted to empirical work, and how much to thinking about the empirical work and trying to sort it out into part of a big picture? Who knows? Usually what happens is a lot of time is spent initially just gathering facts, which doesn’t advance the science very much as far as being able to predict things. Then some genius puts the pieces of the puzzle [the collected data] into place, by assuming an axiom and studying it’s consequences. If he chose his axioms wisely, the things he deduces from the axioms can be interpreted as predictions about reality, and then tested. If they indeed match reality time after time, his set of axioms is accepted as a working theoretical model of the real empirical world.
So that to say that any other science is conducted largely through inductive (empirical) means is just ignorance of the facts of how science is pursued.
On to Paragraph 3:
This is wrong. Not every axiomatic system is incomplete. The simple uncomplicated ones are not. Godels Theorem states that in any axiomatic system AS RICH IN AXIOMS AS ARITHMETIC, there are going to be unprovable conclusions. Every axiom system has to be tested seperately for incompleteness. At least that was the state of Mathematical Logic when I studied it decades ago. Probably advances have been made in this cutting edge branch of Math since then. As for praxeology, I don’t know enough about it [or enough Math] to know if it is incomplete or not. But one thing is for sure, not every axiom system is incomplete.
However, all that is small time stuff. The real whopper, the incredibly ignorant false statement is what follows:
The key to his mistake lies in the tiny word “inferred”. Remember the long intro you may have skipped, about there being a real world observable by cameras and such, and a world inside the thinkers head, where axioms and their consequences are deduced? Where do you think “inferences” happen? Not in the real world. Inferences are done by thinkers. [Now dont confuse the issue by saying a computer can be built to list the logical conclusions of axioms. The computer too is a thinker, by which I mean the computer is not out there studying falling apples, but studying dry abstract axioms and using the recognized rules of logic to spew out the deductions]
Anyway, inferences are done by thinkers. The only way in the whole wide world to make an inference is to take a statement and assume it as an axiom, apply the rules of logic to it, and get the inference. What I’m saying is that an “empirical fact” is not some magical assumption to which Godels Theorem does not apply. Once introduced into an axiomatic system [as it must be in order to draw inferences from it], it is just like any other axiom, and Godels Theorem will pounce on it too. It’s laughable to think otherwise, hard to convey how totally ridiculous this is.
Paragraph 4:
OK guys, if you grasped the above stuff you already know this line is wrong, and why.
What a mess this sentence is! OK lets get the record straight.
Godels Theorem says that any set of axioms and rules of logic as rich as simple arithmetic will have unprovable theorems. He shows that assuming simple things like “2+2=4” and “A+B = B+A for every whole number A and B” will lead to unprovable theorems. Does this mean 2+2 is NOT equal to 4? Or that A+B is NOT equal to B+A? Of course not. Godels Theorem does not say the axioms are false. Also, it DOES NOT say that we will come up with FALSE conclusions. It merely says that some complicated Mathematical statements will not be provable. They will be forever elusive.
So that asserting saying “2+2=4” is not “at odds with reality” just because Godel showed it’s incomplete. Similarly, the axioms of praxeology are not “at odds with reality.” What a ridiculous notion, to try to conclude that from Godel’s Theorem.
This is not at all different in other areas of science. Do we know everything yet? Of course not. Will a time come when we do? Maybe, maybe not. We may never know everything. Does it mean that what we do now is mistaken? Not neccesarily.
So now we also know why the next piece of Paragraph 4 is nonsense:
Godels Theorem does not say there will be false results. That was an easy one.
And we know enough to know why this piece is wrong too:
The gross error here has already been discussed. Using an “empirical axiom” does not protect one from the dragon of Godels Theorem.
The conclusion follows from your assumptions, but we have shown that BOTH your assumptions are false. Fail.
OK final Paragraph, which restates his previous misunderstandings, and adds in a new one for good measure.
Geometry is axiomatic. Set theory is axiomatic. Every area and sub-area of Mathematics is axiomatic. But after Godels Theorem shocked the wrold, no one assumes anymore “that from it you can derive ALL of its implications”. Mathematicians now have a much humbler demand of an axiomatic system: That it produce “important” theorems. What is “important”? Ones that increase our understanding of the subject being studied. Yes, it’s rather vague, but it’s all we have. Math has an element of Art in it, always has.
Applying that test to praxeology, is it a succesfull axiom system? Hey, if tells us how to get out of this reccesion, I’d say yes.
As I said earlier, an axiom system consisting of a single theorem is probably not rich enough for Godels theorem to apply. In any case it is no embarrassment to an axiom system that Godels Theorem applies to it. Thats just the way it is. It applies to all of Math. So what? Does this post intend to say that all of Math should be tossed in the rubbish bin? [LOL, all of you who dislike Math, don’t nod so vigorously].
C’mon guys, this is the third time he’s restating this error, you should know by now why it’s wrong.
Nope, as shown above.
Last paragraph has nothing new, already shown false.
The OP was trying to use Godels Incompleteness theorem.
Hoppe’s footnote is referring to a completely different theorem of Godel’s, and is not discussing the problems raised by Godels Incompleteness Theorem that the OP mentioned.