230 THE SCIENCE OF LOGIC 



principles of magnitude and multitude in geometry and mathematics, are reached 

 in the way indicated by Aristotle. But have we the same sort of unerring intel 

 lectual insight into &quot; the essence of gold or of an elephant or of a tortoise &quot; l as 

 we have, say, into the essence and definition of a triangle ? Aristotle seems to 

 have regarded it as impossible for the human mind to attain to &quot; absolutely ne 

 cessary &quot; truths about the essences of the multitudinous phenomena that form 

 the subject-matter of the special sciences ; and in his Topics he has indicated 

 various means of reaching and testing those less perfect and less reliable 

 generalizations with which, in the absence of &quot;absolutely necessary &quot; truths, 

 the human mind must rest content. 



He was right in recognizing that we cannot have the same &quot; absolutely 

 necessary &quot; truth about concrete existing facts or phenomena as we have about 

 abstract, possible essences ; for the actual realizations of these latter are con 

 tingent, not necessary. I see that &quot; two and two must be four &quot; because it is 

 intrinsically and absolutely self-evident, and no conceivable sort of experience 

 could contradict it ; I see that &quot; heat must elongate iron &quot; because actual ex 

 perience forces me to believe that heat and iron are de facto so constituted. 

 Aristotle recognized only truths of the former class as principles of demonstra 

 tion and science in the stricter sense ; and these we accept &quot; because our 

 intellect assures us of their truth &quot; a . In a somewhat wider sense, however, 

 he admits &quot; science &quot; of that which, though not &quot; absolutely necessary,&quot; never 

 theless holds good &quot; always, under certain conditions,&quot; or &quot; for the most part &quot;.* 

 This is the domain of those sciences whose laws are established by induction. 

 Now, it has been thought that Aristotle claimed we should have the same sort 

 of intellectual assurance for these &quot; laws &quot; as we have for abstract, self-evi 

 dent axioms, before the former can be recognized as principles of demonstra 

 tive science. He seems to Mr. Joseph to demand the &quot; ipse dixit of an incom 

 municable intuition ... as a means whereby we are to establish the most 

 important of all judgments, the general propositions on which the sciences 

 rest &quot;. 4 But Aristotle could hardly have failed to see that we have no such 

 intuition of what are now commonly known as inductive laws. 5 It was on that 



1 JOSEPH, op. cit., p. 356. * ibid., p. 357. 



3 C/. WINDELBAND, op. cit., p. 143. 4 ibid. 



6 Such laws differ manifestly from geometrical axioms in this, that they are not, 

 like the latter, seen to be true by an absolute, intrinsic necessity arising out of the 

 very nature of reality as conceived in the abstract by the intellect ; and Aristotle surely 

 knew this to be true of all laws established merely by induction, of all generalizations 

 from experience. The evidence for the truth of these lies in our experience of con 

 tingent fact : they are seen to be true by a necessity which is contingent and hypo 

 thetical. Empirical fact forces us to assent to them as true. Such facts might 

 conceivably have been otherwise ; but, being what they are, the only intelligible in 

 terpretation we can put upon them involves our acceptance of the inductively 

 established law as being true de facto. If we are asked why do we believe such a 

 law to be true, we answer that facts force us to believe it. If we are asked further 

 why is it true, or why are the facts (which force us to believe it) such as they are, 

 we cannot answer that the law must be true, or that the facts must be so, by an 

 absolute, inviolable necessity of their very nature, in the same way as &quot;two and two 

 must be four &quot; by an absolute necessity arising from the nature of numbers con 

 ceived in the abstract. We can only answer that the facts are so, and that conse 

 quently the law is true, because the Creator of the actual universe has made the 

 universe so, and not otherwise. Cf. 224, 255. 



