204 



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



This is one of those questions which it is very important to ask because they cannot be answered. 

 We ought however to think it possible that we have made a converse to the Irishman's blunder, 

 For though one went before and the other behind. Sir, 

 They set off cheek by jowl at the very same time, Sir. 



XXI. I have had much occasion to point out that the logician is, by his own choice, no 

 more* than a mathematician : not too mathematical, in fact not mathematician enough, if he will 

 be nothing more. One error forces a metaphysical notion within the mathematical boundary, 

 as a concept the sum of all its attributes. One is the presentation of a mere transformation — 

 ' Some animal is all man' from ' All man is some animal' — as transition from the mathematical 

 to the metaphysical. One grand error | yet remains, though not, I judge, so widely received. 

 Before proceeding to it I remark that the logician, in thus making mathematics a present of 

 his science, does it under protest that the mathematician is not to plant it, and make it grow : 

 above all, that he is not to use any symbol-manure. Those who make a concept the sum of 

 its attributes are indignant at the appearance of A + B : though, had they had a mathemati- 

 cian's power over the distinction of A + B and AB, they would never have fallen into the 

 mistake. 



The attachment to mathematical quantity has become so strong that this Aaron's rod has 

 swallowed up all the others. We are told that predication is nothing more or less than the 

 expression of the relation of quantity in which notions stand to one another ; that we think 

 only under determinate quantity ; that all thought is comparison of less and more {Achilles 

 killed Hector, for example) ; that an affirmative proposition is merely an equation of the 

 quantities of its subject and predicate, and the consequent declaration of the coalescence of 

 terms in a single notion ; that a negative proposition is a non-equation — whatever that may 

 mean — of quantities, and an announcement of non-identity of terms. The word equation is 

 often followed by identification, in a manner which would lead us to suppose that the two 

 words are taken as convertible. 



Quantity, to confront the old logicians with the new ones, was left undefined by Aristotle 

 for several reasons: the first, that it is a summum genus, and therefore cannot be defined ; we 

 may excuse them all the rest. The followers gave various definitions, one of which would 

 palliate the preceding use of the word equation : it is res per se divisibilis in partes, which 

 confounds quantity with its subject of inhesion. Others, passing to another extreme, made 

 quantitas the abstract notion on which we say of anything that it is or has quantum: and 



* From the thesis that the mathematics contain a sufficient 

 study of logic, and the answers which have been made to it, I 

 equally dissent. But the discussion would require a volume. 

 Every branch of learning certainly grows a crop of logical 

 habits, that is, of habits of the form of thought : a majority 

 good, a minority bad. Nothing but the study of logic as a 

 science, simultaneously with other studies, will prevent tares 

 from growing up with the wheat. 



■)- I might dwell on some strange uses of mathematical 

 language : but there is only one which really makes a diffi- 

 culty ; it is the use of the word numerical. Many writers on 

 logic call the distinction between one thing and another — their 



not being the same thing — a numerical distinction. Thus 

 they say that a perception is numerically different from the 

 thing perceived; and that the hunger of to-day is numerically 

 different from the hunger of yesterday. Now though it may be 

 true that Hrst, second, third, &c. are called by grammarians 

 ordinal numbers, it is equally true that the phrase will not stand 

 the smallest reflexion. The seventh, the twentieth, are not 

 numbers : the distinctions are ordinal, because they are arrang- 

 ed in order ; but they are not numerical distinctions ; they do 

 not allow predication of more and less. The ordinal numbers, 

 so called, are of a pronominal character : this, that, the other, 

 supply the place of the first three. 



