178 Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



For if any one X — Z, this with Z — Y, gives X — Y, which is excluded by the second 

 premise. 



To this the objection is that the process is material, for that it is of the matter of the 

 proposition whether give will or will not do : that touch, for instance, will not do. Does not 

 this, — from a living writer who in combination of logical learning and logical acumen is second 

 to none — corroborate my assertion that the logician has the distinction of form and matter' 

 more in his theory than in his practice? I might as well say that 'Every X is Y' is a mate- 

 rial proposition : it is of the matter of X and Y whether it be true or no. In the following 

 chain of propositions, there is exclusion of matter, form being preserved, at every step : — 



Hypothesis. 



(Positively true) Every man is animal 



Every man is Y Y has existence 



, Every X is Y X has existence 



Every X — Y is a transitive relation 



a of X — Y a a fraction < or = 1. 



(Probability /3) a of X — Y /3 a fraction < or = 1. 



The last is nearly the purely formal judgment, with not a single material point about it, 

 except the transitiveness of the copula. But 'is' is more intense than the symbol — , which 

 means only transitive copula : for ' is ' has transitiveness, and more. Strike out the word 

 transitive, and the last line shews the pure form of the judgment. 



The same objection has been raised to the law of inference when the middle term is 

 definitely quantified. If the fractions a and fi of the Ys be severally As and Bs, and if a + /3 

 be greater than unity, it follows that some As are Bs. To this it is objected that whether 

 a + /3 be or be not greater than unity, is material. No doubt it is ; and so is the case of the 

 logician's canon of syllogism, that the middle term must be universal in one or both premises. 

 The logician demands a = l, or j8= 1, or both : he can then infer; but only because he knows 

 that when more in number have been named than there are separate things to name, some must 

 have been named twice. But he does not know this better of 1 +/3 than of |-+ (more than |^): 

 or if he did, the difference of form and matter is not merely difference of arithmetical facility. 

 The writer against whom I am contending declares that, as a logician, he cannot know that 

 2 and 2 make 4. I do not ask him for so much: I do not ask him to know that there are 

 cases in which a + /3> 1. What I say is this, that in every case in which it shall happen (if 

 ever it do happen, which is by hypothesis more than we know) that a4-/3> 1, in each of these 

 cases he is bound, as a logician, to infer that some As are Bs. And this instance is another 

 corroboration of my assertion that the distinction of form and matter is more in the theory of 

 the logician than in his practice. 



As a third instance, I note that the limited universe, and its division into two contraries, 

 are pronounced material, because it is not by logic we learn that when property is the 

 universe, real and personal are contraries. Neither by logic do we learn that every man is 

 animal ; but by logic we analyse our use of this proposition in conversion, in inference &c. 

 Similarly, by logic we learn how we use contraries in inference &c. But what things are 

 contraries, logic no more needs to inquire than law needed to inquire who wore the crown 



