Robert Murphy, like Mises, cannot properly distinguish between (1) pure geometry and (2) applied geometry (on which, see Salmon 1967: 38). When Euclidean geometry is considered as a pure mathematical theory, it can be regarded as

*analytic a priori*knowledge, and asserts nothing necessarily true of the external, real world, since it is tautologous and non-informative. (An alternative view derived from the theory called “conditionalism” or “if-thenism” holds that pure geometry is merely a set of conditional statements from axioms to theorems, derivable by logic, and asserting nothing about the real world [Musgrave 1977: 109–110], but this is just as devastating to Misesians.)

When Euclidean geometry

*is*applied to the world, it is judged as making

*synthetic a posteriori*statements (Ward 2006: 25), which can

*only*be verified or falsified by experience or empirical evidence. That means that applied Euclidean geometrical statements

*can*be refuted empirically, and we know that Euclidean geometry – understood as a universally true theory of space – is a

*false*theory (Putnam 1975: 46; Hausman 1994: 386; Musgrave 2006: 329).

Murphy’s confusion is also confirmed in these remarks below.

The fact that the refutation of Euclidean geometry understood as an empirical theory leaves pure geometry untouched does not help Murphy, because pure geometry per se says nothing necessarily true about the real-world universe, and is an elegant but non-informative system.

Albert Einstein was expressing this idea in the following remarks about mathematics in an address called “Geometry and Experience” on 27 January 1921 at the Prussian Academy of Sciences:

“One reason why mathematics enjoys special esteem ... is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain. At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things. In my opinion the answer to this question is, briefly, this:- As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”If we were to pursue this analysis further as applied to economic methodology, it would follow that praxeology – if it is conceived as deduced from

http://www-history.mcs.st-and.ac.uk/Extras/Einstein_geometry.html

*analytic a priori*axioms – is also an empty, tautologous, and vacuous theory that says nothing necessarily true of the real world. And the instant any Austrian asserts that praxeology

*is*making real assertions about the world, it must be judged as

*synthetic a posteriori*, and so is to be verified or falsified by experience or empirical evidence.

What Murphy fails to mention is that the only way to sustain his whole praxeological program is to defend the truth of Kant’s

*synthetic a priori*knowledge, which, as we have seen from the last post, is a category of knowledge that must be judged as non-existent.

**Note**

* Murphy also conflates (1) the logical positivists’ verifiability criterion for meaningfulness with (2) Popper’s falsifiability criterion for scientific knowledge, but this is an issue I will not bother to pursue here.

**BIBLIOGRAPHY**

Hausman, Daniel M. 1994. “If Economics Isn’t Science, What Is It?,” in Daniel M. Hausman (ed.),

*The Philosophy of Economics: An Anthology*(2nd edn.). Cambridge University Press, Cambridge. 376–394.

Musgrave, Alan. 1977. “Logicism Revisited,”

*British Journal for the Philosophy of Science*28: 99–127.

Musgrave, Alan. 2006. “Responses,” in Colin Cheyne and John Worrall (eds.),

*Rationality and Reality: Conversations with Alan Musgrave*. Springer, Dordrecht. 293–334.

Putnam, Hilary. 1975. “The Analytic and the Synthetic,” in Hilary Putnam,

*Mind, Language and Reality. Philosophical Papers. Volume 2*. Cambridge University Press, Cambridge. 33–69.

Salmon, Wesley C. 1967.

*The Foundations of Scientific Inference*. University of Pittsburgh Press, Pittsburgh.

Ward, Andrew. 2006.

*Kant: The Three Critiques*. Polity, Cambridge.

Hello Lord Keynes,

ReplyDelete"that praxeology – if it is conceived as deduced from analytic a priori axioms – is also an empty, tautologous, and vacuous theory that says nothing necessary of the real world. "

In my opinion, it is wrong to say "that properties deduced from analytic a priory Systems

are tautologous".

I think at least Mr. Pythagoras (or who ever proved the so called theorem) would strongly disagree.

This would also state that everything that (pure) mathematicians produce is tautological.

Best Regards

Siegfried from Germany, (wondering if answers to older post get some attention)

Well, most of classical mathematics can be derived from pure logic and set theory.

DeleteAnd Pythagoras was wrong to think geometry gives you necessary truth of the real external world -- geometry after all is an analytic a priori system.

But perhaps you should read the sense in which even the logical positivists did think that analytic propositions do add to knowledge:

http://socialdemocracy21stcentury.blogspot.com/2014/03/a.html

"Well, most of classical mathematics can be derived from pure logic and set theory."

DeleteOK, but what I meant is that when you start with the 5 euclidian axioms,

make some definitions like: "a triangle is ...", then you can derive a property like:

"The 3 angles of a triangle sum up to 180 degrees"

This, in my opinion ist new knowledge in the "a priory realm" (or we could say in the "Model World") and is not trivial at all.

"And Pythagoras was wrong to think geometry gives you necessary truth of the real external world

-- geometry after all is an analytic a priori system."

I don't know if Pythagoras was thinking what you stated, but do we agree on

that his proof is saying something about pure euclidian geometry?

"But perhaps you should read the sense in which even the logical positivists did think that analytic propositions do add to knowledge:"

I'll have a look at that.

Siegfried