Monday, September 2, 2013

Mises’s Non Sequitur on synthetic a priori Knowledge

We can find it here in Mises’s book The Ultimate Foundation of Economic Science: An Essay on Method (1962):
“The essence of logical positivism is to deny the cognitive value of a priori knowledge by pointing out that all a priori propositions are merely analytic. They do not provide new information, but are merely verbal or tautological, asserting what has already been implied in the definitions and premises. Only experience can lead to synthetic propositions. There is an obvious objection against this doctrine, viz., that this proposition that there are no synthetic a priori propositions is in itself a—as the present writer thinks, false—synthetic a priori proposition, for it can manifestly not be established by experience.” (Mises 1962: 5).
The proposition that “there are no synthetic a priori propositions” would appear to be synthetic a posteriori, for one could indeed refute it by successfully demonstrating the existence of synthetic a priori knowledge.

Alternatively, it could be verified by demonstrating empirically that all alleged examples of synthetic a priori knowledge are untenable and can be refuted by empirical evidence. And, in fact, the latter has been the fate of all alleged kinds of synthetic a priori knowledge, such as, for instance, Euclidean geometry.

Even the Kantian idea of necessary, deterministic causation as a universal truth known a priori is untrue given modern quantum physics (Melnick 2006: 229; Anscombe 1993), which now separates the notions of causation and determinism (Weinert 2004: 260).

At most, the strict notion of deterministic, necessary causation is probably true of the macroscopic world – a limited domain – but breaks down at the level of the quantum world. But we only know this a posteriori (empirically), and not as an a priori or a necessary truth.

If this isn’t bad enough Mises then proceeds to shoot himself in the foot, and demonstrates how his own statement above is highly dubious, by admitting that modern science has questioned the synthetic a priori status of Euclidean geometry:
“The whole controversy is, however, meaningless when applied to praxeology. It refers essentially to geometry. Its present state, especially its treatment by logical positivism, has been deeply influenced by the shock that Western philosophy received from the discovery of non-Euclidian geometries. Before Bolyai and Lobachevsky, geometry was, in the eyes of the philosophers, the paragon of perfect science; it was assumed that it provided unshakable certainty forever and for everybody. To proceed also in other branches of knowledge more geometrico was the great ideal of truth-seekers. All traditional epistemological concepts began to totter when the attempts to construct non-Euclidian geometries succeeded.

Yet praxeology is not geometry. It is the worst of all superstitions to assume that the epistemological characteristics of one branch of knowledge must necessarily be applicable to any other branch. In dealing with the epistemology of the sciences of human action, one must not take one’s cue from geometry, mechanics, or any other science.

The assumptions of Euclid were once considered as self-evidently true. Present-day epistemology looks upon them as freely chosen postulates, the starting point of a hypothetical chain of reasoning. Whatever this may mean, it has no reference at all to the problems of praxeology.” (Mises 1962: 5).
Come again? The collapse of Euclidean geometry as synthetic a priori knowledge has “[n]o reference at all to the problems of praxeology”? The stupidity of this passage beggars belief.

The issue of whether Euclidean geometry is synthetic a priori knowledge is absolutely of great relevance to the epistemological status of Mises’s praxeology, because Mises needs to prove that synthetic a priori knowledge exists.

But, having assured us that there is good reason to believe in the truth of synthetic a priori knowledge, Mises then immediately seems to concede that Euclidean geometry – the leading paradigm of the synthetic a priori – was not actually synthetic a priori at all, which destroys much of the alleged evidence for the existence of the latter.

Mises’s statement that “[p]resent-day epistemology looks upon [sc. the assumptions of Euclid] … as freely chosen postulates, the starting point of a hypothetical chain of reasoning” seems to be a tacit admission, or veiled reference to, the finding of modern science that Euclidean geometry as a universal theory of space is false.

Without any convincing evidence for the truth of synthetic a priori knowledge, Mises’s whole system of praxeology is left hanging in the air, without foundation, and must come crashing down.

Anscombe, G. E. M. 1993. “Causality and Determination,” in Ernest Sosa and Michael Tooley (eds.), Causation. Oxford University Press, Oxford.

Melnick, Arthur. 2006. “Kant’s Proof of Substance and Causation,” in Paul Guyer (ed.), The Cambridge Companion to Kant and Modern Philosophy. Cambridge University Press, Cambridge. 203–237.

Mises, Ludwig von. 1962. The Ultimate Foundation of Economic Science: An Essay on Method. Van Nostrand, Princeton, N.J.

Weinert, Friedel. 2004. The Scientist as Philosopher: Philosophical Consequences of Great Scientific Discoveries. Springer, Berlin and London.


  1. Euclidean geometry is used to prove the existence of non-Euclidean geometry.

    Non-Euclidean geometry did not "refute" Euclidean geometry. It expounded on its a priori status by making it clear that X does not have any meaning unless ~X exists and has meaning.

    Euclid is what grounds our understanding of non-Euclidean spacetime.

    1. "Euclidean geometry is used to prove the existence of non-Euclidean geometry. ...

      False. Non-Euclidean geometry starts with different axioms.

      "Non-Euclidean geometry did not "refute" Euclidean geometry. "

      Right: the empirical evidence from the real world vindicating Non-Euclidean geometry did that.

  2. When he says "Whatever that may mean" he is taking a shot at "modern epistemology" by saying essentially "freely chosen postulates" is meaningless, or rather he can see no meaning in them.