Before I critique the substantive portions of Lord Keynes’ article, I would like to applaud him for taking up the daunting task of attempting to make headway on the philosophy of economics. Although he rejects the method of praxeology, in my opinion erroneously, writings like his are nevertheless to be encouraged because they sharpen the mind and get to the heart of the issue.
As readers may know, I have some experience studying Kantian epistemology, and in particular, the status of the synthetic a priori. This is truly the starting point of praxeology and Austrian economics, and I am grateful for the attempt to render it more comprehensible. In the article, Lord Keynes attempts to force Misesian praxeology into either one of two boxes: the analytic a priori or the synthetic a posteriori. Like the positivists before him, Lord Keynes refuses to acknowledge the possibility of synethetic a priori.
Lord Keynes’s article begins by quoting Mises’ on praxeology and aprioristic reasoning in general. Immediately, LK makes the claim that Kant’s idea of the synthetic a priori is “untenable.” He cites the advance of non-Euclidean geometry as proof that Kant was mistaken to consider geometry synthetic a priori – and this mistake should, according to LK, cast serious doubt on the whole enterprise of the synthetic a priori in general.
Furthermore, he attempts to show by linking from another problematic article, that even if one were to grant plausibility to the category of the synthetic a priori, the “action axiom” cannot be a worthy candidate for it because it incorporates synthetic a posteriori knowledge.
But this is all beside the point. The real meat of the article is to illustrate why Mises fails to understand “Philosophy of Mathematics 101” in his inability to separate “pure geometry” and “applied (physical) geometry.” To describe the distinction, he introduces Rudolf Carnap, a logical positivist. Even further in the article, Lord Keynes correctly notes the limited nature of Euclidean geometry in describing a “universal theory of space.” Euclidean geometry, as we know from the theories of Einstein, instead reflect a special case — a subset — of the larger, more general category of non-Euclidean geometry, which can account for advances made in 20th century physics. LK asserts that because Mises misunderstands the nature of geometry, we can safely disregard his musings on philosophy of economics, and on praxeology in particular. Nowhere in the article does LK refute or directly challenge praxeology as a methodology, because he has no doubt done that elsewhere.
My contribution to this riveting discussion is merely to point out a few errors Lord Keynes makes. I will begin as he began.
In the first place, Lord Keynes begins by inappropriate question-begging. He writes, “Kant’s belief in the synthetic a priori is false, and we know this now given the empirical evidence in support of non-Euclidean geometry: this damns Kant’s claim that Euclidean geometry – the geometry of his day – was synthetic a priori (Salmon 2010: 395).
Notice immediately that Lord Keynes tries to undermine Kant’s notion of the synthetic a priori by use of empirical evidence. This will not do. The synthetic a priori, as Kant formulates it, is a category of knowledge by which we come to understand synthetic claims (claims about the real world) by means of aprioristic reasoning (logical deduction). Pointing to an empirical event as falsifying or refuting a claim about a methodology misses the mark entirely. Kant’s ideas on the synthetic a priori may well be wrong or mistaken, but one must prove so by means of showing where the logical error lies. It is simply poor philosophy to argue that an empirical event can refute epistemic claims. This is a category mistake. Epistemic claims — claims of how we understand knowledge — are of an altogether different category than claims of knowledge themselves.
In the second place, Kant’s musings on pre-Einsteinian geometry are fascinating, but hardly foundational for the synthetic a priori paradigm. As Mises says, men can make mistakes in their logical deductions. Just because Kant did not, or could not, imagine non-Euclidean geometric theorems does not invalidate his notions on the category of the synthetic a priori in general. For years, I too considered pure geometry to be analytic a priori; as an edifice of logic that does not necessarily refer to real constructs. This excerpt by Hans Hoppe is worth considering, however, given the context we are discussing:
“[T]he old rationalist claims that geometry, that is, Euclidean geometry is a priori and yet incorporates empirical knowledge about space becomes supported, too, in view of our insight into the praxeological constraints on knowledge. Since the discovery of non-Euclidean geometries and in particular since Einstein’s relativistic theory of gravitation, the prevailing position regarding geometry is once again empiricist and formalist. It conceives of geometry as either being part of empirical, aposteriori physics, or as being empirically meaningless formalisms. Yet that geometry is either mere play, or forever subject to empirical testing seems to be irreconcilable with the fact that Euclidean geometry is the foundation of engineering and construction, and that nobody there ever thinks of such propositions as only hypothetically true.”1
“Recognizing knowledge as praxeologically constrained explains why the empiricist-formalist view [of geometry] is incorrect and why the empirical success of Euclidean geometry is no mere accident. Spatial knowledge is also included in the meaning of action. Action is the employment of a physical body in space. Without acting there could be no knowledge of spatial relations, and no measurement. Measuring is relating something to a standard. Without standards, there is no measurement; and there is no measurement, then, which could ever falsify the standard. Evidently, the ultimate standard must be provided by the norms underlying the construction of bodily movements in space and the construction of measurement instruments by means of one’s body and in accordance with the principles of spatial constructions embodied in it. Euclidean geometry, as again Paul Lorenzen in particular has explained, is no more and no less than the reconstruction of the ideal norms underlying our construction of such homogeneous basic forms as points, lines, planes and distances, which are in a more or less perfect but always perfectible way incorporated or realized in even our most primitive instruments of spatial measurements such as a measuring rod. Naturally, these norms and normative implications cannot be falsified by the result of any empirical measurement. On the contrary, their cognitive validity is substantiated by the fact that it is they which make physical measurements in space possible. Any actual measurement must already presuppose the validity of the norms leading to the construction of one’s measurement standards. It is in this sense that geometry is an a priori science; and that it must simultaneously be regarded as an empirically meaningful discipline, because it is not only the very precondition for any empirical spatial description, it is also the precondition for any active orientation in space.”2
I will conclude before the conversation becomes unwieldy. To my understanding, LK makes two errors: one minor and one monumental. The minor error he makes is to give us a red herring; that is, he attempts to use Mises’ misunderstandings (or not – depending on if Hoppe is correct) on the epistemic status of mathematics and geometry to entirely discount his contributions to philosophy of economics, and praxeology in particular. His larger and more alarming error is in not recognizing the validity of the category of the synthetic a priori. In so doing, Lord Keynes forces his mind into considering knowledge in only two ways: either analytic a priori (empty formalisms, logic games of which no relation to reality can be made) or synthetic a posteriori (real-world empirical claims, of which continuous testing is done to falsify or confirm a hypothesis). He does not recognize that action necessarily renders us knowledgeable of its logical implications, and because human action is a real world phenomenon, does indeed give us knowledge of the real world through the use of the rationalist, deductive process. Hoppe writes elsewhere that action — the substitution of one state of affairs for another — necessarily implies that the actor understands and comprehends a teleological, means-ends framework, and the existence of “time-invariantly operating causes” (the category of causality). No actor could make a decision about whether to interfere or not without understanding that events are connected in a casual framework. Even making empirical observations requires that the observer understand a causal framework, simply in order to make sense of his observations. The understanding of causality is thus inherent and irrefutable within every action. This renders causality to the status of the synthetic a priori and — that every event is interconnected with other events and causes — is both true logically, because every action demonstrates the actor must know this, and it also gives us usable and important information about the real world.
1. Hans-Hermann Hoppe, Economic Science and the Austrian Method, pg. 30.
2. Hoppe, ibid, 31.