SCIENCE AND DEMONSTRATION 233 



this &quot; proof of fact &quot;. Such are the proofs by which Aristotle and 

 the Schoolmen have argued from the existence of motion, causa 

 tion, and contingent being, to the existence of an immovable 

 Prime Mover, a First Cause, a Necessary Being, distinct from the 

 universe. 



Strict or causal demonstration is also commonly known as 

 &quot;a priori proof&quot; ; while &quot; proof of fact &quot; is known as &quot; a posteriori 

 proof&quot;. Causal proof is called &quot; a priori&quot; because it proceeds 

 from what is naturally or really prior, to that which is naturally 

 or really posterior. And since the effect is naturally or really 

 posterior to the cause, an argument which proceeds from effect to 

 cause is called &quot; a posteriori&quot;. 



When the middle term is really neither prior nor posterior to 

 the conclusion, when the passage of inference is from one of two 

 concomitant connected facts, or abstract aspects of reality, to the 

 other, the argument is called an &quot; a simultaneo argument &quot;. The 

 great historic example of this is the argument by which St. 

 Anselm (1033-1 [09) sought to prove the existence of God from 

 the notion we have of His infinite perfection. In the domain of 

 induction, a part arguments, arguments from Example, and from 

 Analogy, are in a certain sense &quot;a simultaneo&quot;; while in the 

 domain of deduction, proofs that are based upon reciprocal pro 

 perties and relations (spatial or numerical) might also be regarded 

 as &quot;&amp;lt;2 simultaneo&quot; (258). 



(b} Indirect Proof or Reductio ad Imposstbile. 1 The forms of 

 proof already examined prove the truth of their conclusions 

 directly. Where this cannot be done, it may be possible to show 

 indirectly that a judgment is true, by showing that if it were false 

 and its contradictory true, something impossible, absurd, or self- 

 contradictory would follow. This method of establishing a truth 

 by disproving its contradictory, is, obviously less satisfactory and 

 less scientific than direct proof; for it does not give the mind 

 any insight into the positive, intrinsic causes or reasons why the 

 established proposition is really true. Nevertheless, it is of great 

 importance as a path to certain knowledge, and it is used ex 

 tensively in every department of research. It is, as we saw, the 

 sort of consideration underlying inferences in the second figure 

 of syllogism (169). We have seen, too, that laws are discovered 

 and verified inductively by disproving alternatives through the 



1 tis rb aSvvarov iirayuiyf), Cf. Anal. Prior., i., c. xxiii. [xliv.], 2 ; supra 169. For 

 a different use of the term cnrayuyji cf. Anal. Prior., ii., c. xxvii. [xxv.j. 



