248 THE SCIENCE OF LOGIC 



special way of its own with first principles. Each of these antecedents gives 

 a &quot; cause &quot; of the conclusion, i.e. something which is nearer to first principles, 

 and more evident, than the conclusion itself; or, at least, something which 

 helps us to understand why the conclusion is true, by showing forth some 

 intrinsic connexion of the latter with the whole system of reality to which it 

 belongs. In proportion to the depth and clearness of our insight into this 

 system, we shall be able to see the mental, rational relations that obtain among 

 those antecedents themselves, and between these and their antecedents and 

 consequents. When these relations are reciprocal, the antecedent cannot be 

 said to give a &quot; cause &quot; of the consequent (254, a). &quot;Still,&quot; writes Mr. 

 Joseph, 1 &quot; the reasoning is deductive, since our premisses display to us the 

 rational necessity of the conclusion, and do not leave it resting on a mere 

 necessity of inference &quot; ; that is, on the necessity of an inference which is 

 &quot; based on an appeal to facts which might conceivably have been otherwise &quot;. 2 



In the mathematical sciences, where we deal with conclusions arising from 

 self-evident intuitions of Quantity (&quot; magnitude &quot; and &quot; multitude &quot;), truths are 

 often reciprocally related, so that the distinction between antecedent and con 

 sequent practically vanishes. Not only can we, having demonstrated a truth, 

 A, from first principles, use it in turn to demonstrate another truth, C, but 

 we can embrace the alternative of demonstrating C from first principles and 

 then using it to demonstrate A. If we know two such propositions to be re 

 ciprocals, i.e. such that the truth of either involves the truth of the other, 

 and if, further, we know one of them to be true, we can prove the truth of 

 the other by showing that the latter as antecedent proves the truth of the 

 former as consequent. 



&quot; Thus in proving a theorem, or solving a problem which is supposed to 

 be set before us, we take the result provisionally for granted as a starting- 

 point, and say ; If this be true then would that, and if that be true so would 

 some other ; and so on, until we come to some already recognized truth. 

 The fact of being led back to this point establishes the conclusion &quot;. 3 The 

 process might be symbolized thus : &quot; If Z then F, if Fthen X, . . . if Z? then 

 A ; but A ; therefore Z &quot;. The validity of this inference depends on the 

 assumption that the truth of the consequent involves that of the antecedent : 

 an assumption not guaranteed in ordinary thought, of which alone the formal 

 canons of inference take cognizance. It is, however, often admissible in mathe 

 matics &quot; where most of our propositions are of the nature of equations, rather 

 than ordinary predications,&quot; * and are, therefore, reciprocal and simply con 

 vertible. 



259. MORAL CERTITUDE IN THE &quot; HUMAN &quot; SCIENCES. In 

 the foregoing sections (249-58) we have been considering the 

 sources, conditions, and limitations of those sorts of &quot; scientific &quot; 

 knowledge about which we can have metaphysical or physical 

 certitude. But there is also a sort of knowledge which is rightly 

 called &quot; scientific,&quot; about which we have moral certitude. Among 

 the many more or less closely allied meanings of&quot; moral certitude,&quot; 

 we may distinguish these three : (i) firm or certain assent to 



l op. cit. p. 505, n. 2. *ibid., p, 410, n. i. 



3 VENN, Empirical Logic, p. 369. * ibid, p., 370. 



