An argument such as this helps to make intelligible why logicist philosophers of mathematics sought so strenuously to prove that all propositions of mathematics were analytic by showing how they could all be derived from axioms governing the single non-logical primitive concept of set. But the same argument serves also to make intelligible one peculiarly controversial feature of Austrian economics in the formulation that was given to it by Mises, the leading figure in the twentieth-century renaissance of Austrian economics in the United States. For Mises held that there is but one single non-logical concept (or ‘category’ or ‘essence’) of that general theory of human action which he calls ‘praxeology’:
All that is needed for the deduction of all praxeological theorems is knowledge of the essence of human action … The only way to a cognition of these theorems is logical analysis of our inherent knowledge of the category of action … Like logic and mathematics, praxeological knowledge is in us; it does not come from without. (1966, p. 64; see also Rothbard 1957)
Mises, as we shall see shortly, has here drawn together in illegitimate fashion the two concepts of the a priori and the analytic.
Even a discipline whose axioms are constructed on the basis of only one non-logical primitive need not be analytic however. Consider, for example, the case of mereology, the theory of part and whole, which we can assume to have been built up from the single primitive concept part. The latter is a formal concept, in the sense that it can be applied, in principle, to all matters without restriction. But it is not treated as a logical concept in the standard textbooks, and nor can it be defined in terms of the logical concepts which are standardly recognized as such. Thus it seems that the concept part is a non-logical primitive. Consider the proposition
If a is part of b, and b is part of c, then a is part of c,
which asserts that the corresponding relation is transitive. This is, to be sure, a ‘trifling proposition’ in the sense of Locke. Yet it is not analytic, for there is no law of logic to which, when defined terms are removed, it would correspond as a substitution instance. But it is surely also a priori.
Kantians and positivists conceive the a priori as a matter of relations between concepts which enjoy a purely mental existence and as being in some sense a contribution of the knowing subject. The Husserlian, in contrast, conceives the a priori as a matter of intrinsically intelligible relations between species or structures of objects in the world, relations which would obtain even if there were no minds to apprehend them. And where Kantians and positivists hold that a priori knowledge is either empty (‘analytic’) or a reflection of the fact that we see the world through ‘conceptual spectacles’ which somehow allow us to make sense of that world, the Husserlian holds that a priori knowledge is read off the world, reflecting the fact that certain structures in reality are intrinsically intelligible.
When once they are properly understood, however, the two conceptions of a priori judgments or propositions need not be irresolvably in conflict. It may very well be that, even in a world which manifests structures of an intrinsically intelligible sort, there might still be room for certain dimensions of noncontingent (conventional?) structures that are read into the world in the way the Kantian would require. Moreover, it may be that the Kantian notion of an epistemological a priori itself requires a foundation in an ontological a priori of the sort here defined. For if Kantian a priori formings and shapings are read into reality, then we know at least that reality must be dispositionally such that it can bear such forms, and the fundamenta of the relevant dispositional properties would then constitute something like the a priori in re that is admitted by Husserl and Reinach. Moreover, even if the world in itself were infinitely elastic in the sense that it would be capable of bearing any and every sort of forming and shaping, then it seems that there must still be some residual a priori structure in the Husserlian sense on the side of the mind that is responsible for this forming and shaping. For if the latter is not itself entirely random, then the mind itself must possess some structures of its own, and these cannot themselves be the result of forming and shaping in the Kantian sense, on pain of vicious regress.