Proofs are properties of axiomatic systems. Axiomatic arguments are complete by definition. Proof and completeness are why axiomatic systems merely state internal consistency not external correspondence. As such axiomatic systems allow us to construct proofs – not truths.
One cannot prove a theory, only falsify it. A theory corresponds with reality, but is forever incomplete, or it is not a theory but a tautology. Axiomatic arguments are bounded only by the imaginary, and theoretic arguments are bounded by correspondence with reality.
This is why axiomatic systems are argumentatively weak (as we have seen in postwar physics) and theoretic arguments are strong: because the set of all possible and falsifiable theories is smaller than the set provable axiomatic statements.
This delta in ability is why axiomatic systems are useful for assisting us in the construction of theoretical systems. Mathematics for example can represent more possible relations than the universe can represent since the combinations of elementary particles is smaller than can be represented by natural numbers. Logic can represent more combinations of language than humans can organize into meaningful statements. In both language and mathematics external correspondence is required, and axiomatic arguments are merely exploratory devices to help us in the further construction of theories.
Economic statements allow us to test the rationality of actions and incentives. And we must always retest them if they are more than reductio statements, because no economic circumstance is unique enough that we can categorize it. That human interpretations are constant is not the same as saying that the circumstance is constant.
Problem Theory Test stated correctly would be:
Intuitive pattern->Imagination->theory->test of internal consistency->test of external correspondence->test of falsification->increase in knowledge->new intuitive pattern.
Hoppe’s arguments for example make these same errors: (from “Economic Science and the Austrian Method – Praxeology and Economic Science”
1 —” Whenever two people A and B engage in a voluntary exchange, they must both expect to profit from it. And they must have reverse preference orders for the goods and services exchanged so that A values what he receives from B more highly than what he gives to him, and B must evaluate the same things the other way around.”—
However, this is not correct. They must expect satisfaction from it, not profit. As an axiomatic statement it is false.
I’ve been corrected by a reader since Hoppe is referring to ‘psychic profit’. On the other hand I do not think blackmail gives us a psychic profit, and blackmail is a voluntary exchagne. As such, I think that the statement fails since voluntary exchange is not a sufficient test of ethical and moral exchange and therefor politically possible property rights.
–“Whenever an exchange is not voluntary but coerced, one party profits at the expense of the other.”—
This is not correct. All we can know is that on party is unsatisfied with the exchange. Involuntary restitution is unsatisfying or it would be unnecessary. The statement is not axiomatic, it’s false.
—“Whenever the supply of a good increases by one additional unit, provided each unit is regarded as of equal serviceability by a person, the value attached to this unit must decrease.”—
Subjective value is not moderated on a unit basis but on a utility basis. As such this statement is not axiomatic (its false)
—“Of two producers, if A is more productive in the production of two types of goods than is B, they can still engage in a mutually beneficial division of labor. This is because overall physical productivity is higher if A specializes in producing one good which he can produce most efficiently, rather than both A and B producing both goods separately and autonomously.”—
But demonstrably this is untrue, since the effort to produce an inferior good at a lower profit does not remove it’s portfolio value, and as such profibabilty is a property of the set of effort and risk involved, not the price and profiablity of any element of the portfolio of goods and services. Again, this statemetn is not axiomatic, and it’s false.
—“Whenever the quantity of money is increased while the demand for money to be held as cash reserve on hand is unchanged, the purchasing power of money will fall.”—
First, the question remains as to whether demand for cash on hand CAN remain constant, or if there is value to holding it constant, because while money is neutral, it is only neutral over time, and as such it is not unclear that even savers benefit (profit) if consumption is increased during the period, OR whether it is moral to refrain from encouraging consumption simply so that savers can obtain higher interest rates than consumers can consume and producers profit. So no, the statemetn is not axiomatic and I at least suspect it is either questionably moral, if not empirically false.
—” is the validation process involved in establishing them as true or false of the same type as that involved in establishing a proposition in the natural sciences?”—
Evidently, yes. As we have just seen, economic statemsts are set-theoretical and incomplete, general rules. Not axiomatic, complete, and open to deduction absent empirical test.
What separates economic science from the physical sciences both of the material world (physics et al) and cognitive science, Is that we require instrumentation to test statements about the physical world to compensate for the limits of our sense and perception, and likewise we require instrumentation to test the mind – since our senses are limited at the act of introspection. HOwever, economic statements that are reduced to operational language – a series of steps of human action in sequence – are universally perceptible or we could not take those actions.
As such economic statements are testable by sympathetic experience. We are marginally indifferent in our reactions to specific circumstances, and as such over subjective sympathy can be expressed as a general rule (theory). But given the uniqueness of every experience in time, these can never be more than general rules (theories), and are subject to testing each example incident.
One may say that economics is a science in which we need not rely upon instrumentation for testing statements. One may say that we can produce a logic of human action, consisting of the empirically derived theories.
Man’s reaction may be consistent throughout time, and consistent across all humans – at least to some degree. But since no two instances are the same, economics remains a theoretical rather than axiomatic discipline. Theories do not require completeness and axioms do by definition.
This post should be one of the more profound arguments that you will have encountered on a FB – that’s pretty likely from my experience.
The Propertarian Institute
(PS very dense above. I may have to edit and expand it for additional clarity. But as an argument it’s pretty rock solid. And eventually I expect to put a permanent bullet in Misesian nonsense with it.)