226 THE SCIENCE OF LOGIC 



somewhere &quot;. l The mind which sees the true conclusion only as 

 in the false premisses, and zs following from these, can be scarcely 

 said to possess &quot;truth,&quot; or &quot; conformity with reality&quot; : unless, in 

 deed, when it drops the false premisses and assents to the con 

 clusion absolutely ; and even then it cannot have certitude about 

 the truth of the conclusion, any more than it could about the 

 truth of thefatse premisses from which it inferred them. Besides, 

 the aim of demonstration is to derive a true conclusion from true 

 premisses the natural source of such a conclusion. 



Secondly, demonstration must rest ultimately on first truths or 

 principles, i.e. truths which are not themselves demonstrable, but 

 immediately evident or self-evident. Such principles are called 

 axioms. The concepts embodied in them are so simple that the 

 relations expressed between these concepts are immediately appre 

 hended by the intellect, without recourse to any simpler concepts 

 as middle terms. Were the mind incapable of assenting with 

 absolute certitude to such indemonstrable, self-evident truths, no 

 certitude and no science would be possible. For either the pre 

 misses by which a scientific conclusion is established are immedi 

 ately evident, or their truth has been established by antecedent 

 premisses; about which latter the same question arises. But 

 such a series of conclusions and premisses cannot stretch back 

 indefinitely, for if it did the certainty of any one link could never 

 be established. And if the series is finite, some of its members 

 must be first and indemonstrable. These, moreover, must be 

 self-evident ; if they were not, no conclusions from them could 

 be evident, or therefore certain or scientific. Such self-evident 

 axioms are found involved in all the special sciences. 2 They are 

 called first principles: 3 not in an absolute sense, but relatively to 

 the conclusions they generate in the science that employs them. 



Each science has its own first principles &quot;generating&quot; 

 principles as they are called. But then, also, human knowledge 

 can be unified. Sciences of a lesser scope are subordinate to 

 those of a wider scope, and borrow their initial notions and 

 principles from the latter. 4 And hence the notions that are 

 &quot;absolutely first&quot; are those investigated in the science which 



1 JOSEPH, op. cit., p. 342 n. Cf. supra, 148. 



2 Some sciences may take as their principles truths established as conclusions 

 in other sciences. 



3 A principle is that by which a thing exists or comes into existence (ontological 

 principle) ; or comes into our knowledge (logical principle). 



4 Cf. JOSEPH, of. cit., p. 359, n. 2. 



