=Call in the assistance of intuition, for instance our five fingers.=[274]--This statement, repeated from the _Prolegomena_,[275] does not represent Kant’s real position. The views which he has expressed upon the nature of arithmetical science are of the most contradictory character,[276] but to one point he definitely commits himself, namely, that, like geometrical science, it rests, not (as here asserted) upon empirical, but upon pure intuition.[277] Except indirectly, by the reference to larger numbers, Kant here ignores his own important distinction between image and schema.[278] The above statement would also make arithmetic dependent upon space. =Segner: Anfangsgründe der Arithmetik=,[279] translated from the Latin, second edition, Halle, 1773. =Natural science (physica) contains synthetic a priori judgments.=[280]--There is here a complication to which Vaihinger[281] has been the first to draw attention. In the _Prolegomena_[282] Kant emphasises the distinction between physics and pure or universal science of nature.[283] The latter treats only the _a priori_ form of nature (_i.e._ its necessary conformity to law), and is therefore a propaedeutic to physics which involves further empirical factors. For two reasons, however, this universal natural science falls short of its ideal. First, it contains empirical elements, such as the concepts of motion, impenetrability, inertia, etc. Secondly, it refers only to the objects of external sense, and not, as we should expect in a universal science, to natural existences without exception, _i.e._ to the objects of psychology as well as of physics.[284] But among its principles there are, Kant adds, a few which are purely _a priori_ and possess the universality required: _e.g._ such propositions as that _substance is permanent_, and that _every event has a cause_. Now these are the examples which ought to have been cited in the passage before us. Those actually given fall entirely outside the scope of the _Critique_. They are treated only in the _Metaphysische Anfangsgründe_. They belong to the relatively, not to the absolutely, pure science of nature. The source of the confusion Vaihinger again traces to Kant’s failure to hold fast to the important distinction between immanent and transcendent metaphysics.[285] His so-called pure or universal natural science (nature, as above noted, signifying for Kant “all that is”) is really _immanent metaphysics_, and the propositions in regard to substance and causality ought therefore to be classed as metaphysical. This, indeed, is how they are viewed in the earlier sections of the _Prolegomena_. The distinction later drawn in § 15 is ignored. Pure natural science is identified with mathematical physics, and the propositions which in § 15 are spoken of as belonging to pure universal natural science are now regarded as metaphysical. “Genuinely metaphysical judgments are one and all synthetic.... For instance, the proposition--everything which in