SCIENCE AND DEMONSTRATION 231 



account he excluded them from the domain of demonstrative science proper ; 

 thereby, perhaps, unduly narrowing the scope of &quot; scientific &quot; knowledge. For 

 doing so, we may, in the words of Mr. Joseph, &quot; say this much in his favour. 

 Such an intellectual apprehension of the necessary truth of the principles 

 from which demonstration is to start forms part of our ideal of knowledge ; ] 

 doubtless it seldom enough forms part of the actuality. But Aristotle 

 idealized ; he spoke of what, as he conceived, science in the fullest sense 

 of the term involved, and forgot to state, or failed to see that the sciences 

 did not realize it.&quot; 



There seems, however, to be a more serious deficiency in this Aristotelean 

 conception of science. We can understand well enough by means of it how 

 a body of abstract truths like those of mathematics truths about a system of 

 possible, ideal essences may be derived from ideally necessary axioms and 

 principles, of the widest extension and the simplest or poorest comprehension. 

 But does it enable us to understand how the existing things and concrete facts 

 of the whole actual universe, ourselves included, are derived from, and depend 

 ent on, their real causes ? It does not : a chain of abstract demonstrative 

 reasoning in geometry is hardly an adequate representation of the form in 

 which the human mind possesses a synthetic or philosophical knowledge of the 

 actual universe. In the former the &quot; first principles &quot; are abstract and self- 

 evident, and the mediating concepts or middle terms, which are the &quot; causes &quot; 

 of the successive conclusions, are poorer in their comprehension or fulness of 

 meaning than these latter ; whereas in a synthetic knowledge of the concrete, 

 actual universe, the existence of a First Principle or First Cause, on which all 

 else depends, is not self-evident, but must be proved a posteriori by the principle 

 of causality ; and, furthermore, the First Cause, and all created subordinate causes 

 which serve as middle terms in our synthetic explanation of actual facts, must 

 be richer in comprehension than these latter, inasmuch as they must contain in 

 themselves all the perfections of the latter ; and, finally, the laws according to 

 which these causes act in the production of the actual course of nature, or 

 order of the universe, must be established by induction. No doubt, Aristotle 

 realized the force of a posteriori proof, and utilized it to establish the existence, 

 wisdom, and perfection, of an immovable Prime Mover of the universe. 2 No 

 doubt, also, he propounded the doctrine of moderate realism, which alone makes 

 scientific knowledge of concrete facts possible the doctrine that the reality 

 revealed to the intellect in abstract thought is embodied in the concrete data of 

 sense. 3 But his theory of demonstrative science, which sets forth the connexion 

 of self-evident abstract principles with their conclusions as a representation of the 



114 With this proviso,&quot; the author adds, &quot;that for perfect knowledge all the 

 parts of truth ought to seem mutually to involve each other. In mathematics, where 

 alone we seem to achieve this insight into the necessity of the relations between the 

 parts of a systematic body of truth, we find our theorems reciprocally demonstrable ; 

 and if twice two could be three, the whole system of numerical relations would be 

 revolutionized . . .&quot; (p. 358, n.). A system of truths reciprocally demonstrable in 

 this way, may, perhaps, be allowed to be the ideal of a science of abstract, possible 

 essences. But it certainly has never been proved to be our ideal of human science (in 

 the sense of certain knowledge) of the concrete, existing things that make up the 

 actual universe. 



2 C/. DE WULF, History of Medieval Philosophy, pp. 39-41. 



3 ibid., p. 37 ; WINDELBAND, History of Philosophy, p. 139. 



