234 THE SCIENCE OF LOGIC 



application of arguments in the second figure of syllogism (209, 

 212). Hence, it is by this process of indirect proof we know 

 that inductively verified laws are de facto true, even though we 

 may not be able to explain the latter, or show why they are true 



(247). 



In dialectical discussions, when one of the disputants makes use (provision 

 ally, and without necessarily assenting to them himself) of premisses admitted 

 by the other, in order to disprove the latter s main contention, the former is 

 said to be arguing &quot; ad hominem &quot; or making use of the &quot; argumentum ad 

 hominem &quot;. This latter expression is, however, also used, in quite a different 

 sense, to designate a special form of the fallacy known as Ignoratio Elenchi 

 (275, A, a). 



(c) Pure, Empiric, and Mixed Demonstration. This is a divi 

 sion of direct or ostensive proof, and is based upon the nature of 

 the judgments which are employed as premisses. Pure demon 

 stration is that into which none but metaphysically necessary 

 judgments enter (85-90, 198). It is exemplified in abstract 

 metaphysics and mathematics. Empiric demonstration is that 

 in which the premisses are synthetic judgments, truths of fact, 

 inductively established generalizations, as in the physical sciences. 

 Such demonstrations must, of course, conform to the a priori and 

 absolutely necessary laws of thought ; and each step or syllogism 

 must contain at least one universal premiss, endowed with some 

 degree of necessity ; but these need not be analytic or metaphysic 

 ally necessary propositions (198). 



Mixed demonstration is that which contains both pure or 

 abstract, and empirical or concrete premisses. The major states 

 some metaphysically necessary principle ; the minor asserts an 

 empirical application of it ; and the conclusion infers some con 

 sequence categorically. Such, for example, is the line of proof by 

 which the existence of God, as the uncaused First Cause, is estab 

 lished : A series of efficient causes, directly subordinate to one 

 another in their activity, cannot exist without an independent and 

 uncaused First Cause. But we see in the world concrete ex 

 amples of the existence of such series. Therefore an independent 

 First Cause exists, namely God. 



This is, perhaps, the most important of all forms of proof. By 

 means of it we can apply the rational principles of abstract thought, 

 the great necessary truths of the ideal or conceptual order, to the 

 concrete facts and data of our sense experience. And it is only 

 by such a process of proof we can infer from &quot; the things that 



