CHAP. VI.] OF INTERPRETATION. 97 



may be suggested to our minds by the meaning of the terms 

 employed, as distinct from their expressed connexion. Thus it 

 seems obvious to remark, that " They who have voluntarily sa- 

 crificed then: freedom are not free," this being a relation implied 

 in the very meaning of the terms. And hence it might appear, 

 that the first of the two independent relations assigned by the me- 

 thod is on the one hand needlessly limited, and on the other hand 

 superfluous. However, if regard be had merely to the connexion 

 of the terms in the original premiss, it will be seen that the re- 

 lation in question is not liable to either of these charges. The 

 solution, as expressed in the direct conclusion and the indepen- 

 dent relations, conjointly, is perfectly complete, without being 

 in any way superfluous. 



If we wish to take into account the implicit relation above 

 referred to, viz., " They who have voluntarily sacrificed their 

 freedom are not free," we can do so by making this a distinct 

 proposition, the proper expression of which would be 



w = v (1 - z). 



This equation we should have to employ together with that 

 expressive of the original premiss. The mode in which such an 

 examination must be conducted will appear when we enter upon 

 the theory of systems of propositions in a future chapter. The 

 sole difference of result to which the analysis leads is, that the 

 first of the independent relations deduced above is superseded. 



17. Ex. 4. Assuming the same definition as in Example 2, 

 let it be required to obtain a description of irrational persons. 



We have 



z + w 



Z + W - X 



- XZW -f XZ (1 - W) -f X (1 - Z) W - J? X (1 - Z) (1 



'2 



with xzw = 0, x (1 - z) (1 - w) = 0. 



H 



