METAPHYSICS AND THE OTHER SCIENCES 237 



implication between truths, is only one species of a wider genus, 

 order in general by the side, for example, of spatial, temporal, and 

 numerical order, and thus that logic is one subordinate branch of 

 the wider science of metaphysics. Such a view, of course, implies 

 that there are a plurality of ultimately independent forms of order 

 irreducible to a single type. Whether this is the case, I must confess 

 myself at present incompetent to decide, though the signal success 

 with which the principles of number have already been deduced 

 from the fundamental definitions and axioms of symbolic logic, and 

 number itself denned, as by Mr. Russell, in terms of the purely logical 

 concept of class-relation, seems to afford some presumption to the 

 contrary. Or it may be held that the difference is purely one of the 

 degree of completeness with which the inquiry into order is pursued. 

 Thus the ordinary symbolic logic of what Schroder has called the 

 "identical calculus," or "calculus of domains," consists of a series 

 of deductions from the fundamental concepts of class and number, 

 identical equality, totality or the "logical 1," zero or the null-class, 

 and the three principles of identity, subsumption, and negation. The 

 moment you cease to accept these data in their totality as the given 

 material for your science, and to inquire into their mutual coherence, 

 by asking for instance whether any one of them could be denied, 

 and yet a body of consistent results deduced from the rest, your 

 inquiry, it might be said, becomes metaphysics. So, again, the dis- 

 cussion of the well-known contradictions which arise when we try to 

 apply these principles in their entirety and without modification to 

 classes of classes instead of classes of individuals, or of the problem 

 raised by Peano and Russell, whether the assertions "Socrates is 

 a man " and " the Greeks are men " affirm the same or a different 

 relation between their subject and predicate (which seems indeed to 

 be the same question differently stated), would generally be allowed 

 to be metaphysical. And the same thing seems to be equally true 

 of the introduction of time-relations into the interpretation of our 

 symbols for predication employed by Boole in his treatment of 

 hypotheticals, and subsequently adopted by his successors as the 

 foundation of the "calculus of equivalent statements." 



However we may decide such questions, we seem at least driven 

 by their existence to the recognition of two important conclusions. 

 (1) The relation between logical and metaphysical problems is so close 

 that you cannot in consistency deny the possibility of a science of 

 metaphysics unless you are prepared with the absolute skeptic to 

 go the length of denying the possibility of logic also, and reducing 

 the first principles of inference to the level of formulae which have 

 happened hitherto to prove useful but are, for all we know, just as 

 likely to fail us in future application as not. (Any appeal to the 

 doctrine of chances would be out of place here, as that doctrine is 



