320 THE SCIENCE OF LOGIC 



identical with the conclusion. &quot;Whatever has a soporific quality 

 induces sleep&quot; is a tautology ; &quot; opium has a soporific quality &quot; is 

 the same as the conclusion to be proved : &quot; Opium produces 

 sleep &quot;. 



When the conclusion is separated by more than a single step 

 of inference from the assumption, the fallacy is called the circulus 

 in demonstrando, circulus vitiosus, or arguing in a circle. Thus, 

 if we were to prove the immortality of the soul from its simplicity 

 (as Plato does in the Phaedo], and then prove its simplicity from 

 its immortality (as he does in the Republic], we should be arguing 

 in a circle. It may be expressed thus : &quot; M is P t S is M, . . S is 

 P ; and M is P because 5 is P and M is S.&quot; 



(2) The second, and perhaps more common, form of petitio 

 principii, consists not in assuming the very conclusion itself to 

 be proved, but in assuming, without independent proof , some wider 

 principle which involves the latter, arid which could not have been 

 proved or established otherwise than through a prior knowledge of 

 the latter. To this head we may refer all cases wherein the as 

 sumed proposition, whether wider than the conclusion or not, 

 is such that it could not have been known or established other 

 wise than through a prior assumption of the truth of the con 

 clusion. 



We have already dealt with Mill s contention that all syllogism 

 commits this form of petitio principii (195-6). We saw there, how 

 ever/that the fallacy is really committed only when a premiss is 

 assumed which could not be established otherwise than through 

 a knowledge of the conclusion ; that this is usually the case when 

 the premiss in question is a mere collective proposition ; but that 

 genuine universal premisses can be known with certitude inde 

 pendently of any knowledge of instances to which they are 

 applicable, arid otherwise than by enumeration of these in 

 stances. 



A few examples will suffice here to illustrate this form of the 

 fallacy. Galileo accuses Aristotle of having committed it in the 

 following argument : &quot; The nature of heavy things is to tend 

 towards the centre of the universe, and of light things to fly from 

 it ; experience proves that heavy things tend towards the 

 centre of the earth, and that light things fly from it ; therefore 

 the centre of the earth is the centre of the universe &quot;. Spencer, 

 in his work on Education, after distinguishing two values in any 

 branch of study value for knowledge imparted, and value as a 



