Guttenberg’s response to my critique of Austrian methodology displays a large degree of carelessness and misunderstanding of the nature of logic. Guttenberg fails to respond to my thesis; he states it, claims it is “demonstrably untrue,” and then never mentions it again. Claiming an argument is “demonstrably untrue” requires you to demonstrate that it is untrue. Nowhere in his response does he say anything about whether knowledge we gain from the use of pure deduction can be an appropriate means towards our goals. It is telling that Guttenberg portrays my discussion of knowledge-as-means as opposed to knowledge-as-end as simply “some interesting thoughts” as if this is unrelated to my thesis.
My argument is that pure deduction by itself cannot give us appropriate knowledge-as-means, or knowledge that we value because it enables us to better serve our goals. Without any empirical knowledge there is no way we can apply the conditional knowledge gained by logical deduction. What we use as knowledge-as-means is ultimately empirical knowledge because we act in the real world, on the basis of knowledge about the real world. By itself, conditional knowledge tells us nothing about the world that we could use. The only way in which conditional knowledge can ultimately be knowledge-as-means is by expanding our knowledge of the real world given some knowledge of the real world. With conditional knowledge, we can take a few empirical facts and deduce from them many empirical facts that must also be true. But without any means for attaining empirical knowledge, logical deduction is useless. It can only be valued as knowledge-as-end.
But no one to my knowledge sees economics as knowledge-as-end. Economics is valued because it can inform our decisions by giving us knowledge about the real world. The Austrian economists are no exception to this rule. Any time the Austrian theory of the business cycle is applied to a real-world business cycle, every time an Austrian economist comments on economic policy, and whenever Austrian economics is used to try to predict the outcomes of given real-world events, Austrian economics is being treated as knowledge-as-means. One of the more prominent Austrian economists, Guido Hülsmann, has in fact said “The necessary assumption of any research activity [is] that research will make a difference. Whoever sets out to develop a model of human behavior necessarily assumes that his findings will have some impact on either his own action or the actions of other persons (otherwise this research would be senseless).”*
There is of course no discussion of anything like this in Guttenberg’s response, rather, he takes issue not with my thesis but with much more fundamental claims about logic and deductive reasoning. Guttenberg’s naïve understanding of logic, and of its most well drawn-out application, mathematics, is present at every stage of his response to my critique, as I will show.
The first claim I make that he takes issue with is my thesis:
The process of pure deduction, as a methodology, should not be valued in this regard. As we will show, it cannot be applied because it cannot yield appropriate knowledge-as-means.
However, after asserting it is “demonstrably untrue,” he never mentions it again. Somehow, in a mere half page of writing, he completely forgets about this. Indeed, in his next paragraph he has so forgotten about it that he claims:
$A = A$ is a tautology, just as all deduction is. Whether Eric thinks logical tautology can give us usable or meaningful knowledge is another thing.
No. It is not “another thing,” it is central to my thesis.
The second claim I make that he takes issue with is this:
Pure deduction can only yield conditional knowledge. Only with foundational assumptions, or with things that are ‘given,’ can logical deduction yield any results at all.
Now, the fact that he takes issue with this is rather disturbing. He says in response to this that:
Pure deduction, as a matter of fact, can yield quite a bit of certain knowledge. The understanding of mathematics and geometry are based on pure deduction from an incontestable axiom: the law of identity.
Here, Guttenberg takes issue with my claim without even being able to figure out the negation of my statement. If someone disagrees with this claim, they are claiming that without any foundational assumptions at all, they can deduce something. He claims that “mathematics and geometry,” as if geometry is not part of mathematics, is an example of deduction not from any foundational assumption, immediately before stating the foundational assumption on which he believes they are based. “Axiom” in fact means “foundational assumption.”
We cannot, contrary to Guttenberg’s proclamation, derive mathematics from the “law of identity.” There are many axioms on which mathematics is based, and some of them are very intensely contested, such as the famous axiom of choice. The “law of identity” is something that is true by assumption: we essentially define it to be true. The identity relation is something which we define as a binary relation such that for a set X, { (x,x) | x element of X}, and the symbol “=” simply denotes this binary relation. That A = A is a simple result that is “derived” from this definition. It follows trivially from it. With a different definition, the statement could easily be false, viz., in some conceivable world the statement is false. To the extent that it is “derived,” it is derived from the definition, and is thus conditional on that definition.
None of this implies that the statement “A = A” is an empirical hypothesis, subject to continual testing or experimentation, or anything of the sort. Guttenberg simply does not understand that “conditional knowledge” is not the same as “empirical knowledge.” Conditional knowledge is knowledge of a conditional statement, an if-then proposition. If I am “given” something that satisfies the condition, then I also know something else. If I am given a right triangle, then I know how to relate their side lengths as the Pythagorean theorem describes. It is a conditional statement, and it is conditional knowledge because we know it to be true, but nothing about it is empirical. This confusion is Guttenberg’s.
The third claim I make he takes issue with is:
Conditional knowledge becomes proper knowledge when the conditions it is base on are known to be satisfied. How this knowledge comes to be known is a problem that is outside of the realm of pure deduction: it is necessarily empirical. This is the interesting epistemological problem.
Now, the simple example of the Pythagorean theorem was used to demonstrate how logically true and certain conditional knowledge can come to be used as knowledge-as-means, or useful knowledge. Since Guttenberg has ignored the whole problem my critique raises about useful knowledge, he says that:
What empirical testing and experimentation can do is to verify whether certain theorems fit into a specific case, not whether certain theorems are true or false.
This is of course, exactly what I had just said, and yet Guttenberg says of the paragraph in which I talk about this that it “is untrue in all of its parts.” Guttenberg has clearly contradicted himself. The remainder of his paragraph attempts to portray my work as claiming that the truth of logically deduced claims is somehow dependent on reality. Once again, Guttenberg’s confusion between “conditional knowledge” and “empirical knowledge” leads him to falsely characterize my critique.
The remainder of Guttenberg’s response to my critique is largely repetition, and is similarly poor in its interpretations and arguments. There are, however, several more erroneous notions of which Guttenberg needs to disabused. First, merely because something is true, does not make it useful. For example, if I am given that P is false, then the statement P implies Q is true vacuously. Yet this statement is obviously not useful because P is false. Another example pertains to an apocryphal story told in my math department: supposedly, some poor MIT student’s Ph.D. thesis was on functions satisfying an inequality of the type |f(x) – f(y)| <= |x-y|^k where k > 1. Allegedly, more than 100 pages were written on the properties of such functions. And at his oral defense he was asked for a non-constant example of such a function. (There aren’t any). You can guess at the outcome of his defense. However true his claims, they are nonetheless useless. The same can be said of praxeology without some justification for why it can be applied.
The second is the “proof” that Hoppe gives for the principle of diminishing marginal utility. A basic understanding of the logic of a proof demonstrates that Hoppe’s argument does not constitute a proof even though Guttenberg thinks otherwise. The principle of diminishing marginal utility does not follow from the principle of human action; there has been, in this instance, a “flaw in the process of deduction.” Simply because actors prefer what satisfies them more over what satisfies them less, does not mean that each unit of a good that they use will give them less satisfaction than the previous one. It is all the more outrageous to believe that such things as the time-preference theory of interest or Austrian business cycle theory follow logically from simply the principle of human action.
Now, as well practiced as Guttenberg seems to be at calling statements “wrong,” “unqualified,” “demonstrably untrue,” etc., he is completely ignorant of what “conditional knowledge” and “axiom” mean, among other things. This is hardly acceptable for anyone, but much less someone who feels the need to share their views on logic and epistemology and to critique others’ views on these subjects. Guttenberg would be wise to study these matters more carefully.
* Hülsmann, “Economic Science and Neoclassicism” Quarterly Journal of Austrian Economics vol. 2, no. 4 (Winter 1999): 3-20, p. 13.