110 PROFESSOR DE MORGAN, ON THE SYMBOLS OF LOGIC, 



into persuasion to command ; and saying ' X cannot persuade any one who can command F' 

 or X cannot persuade Z. 



But, it may be said, this cannot be shewn on the ordinary syllogism ' Z is Y, X is not F 

 therefore X is not Z;' nor on any syllogism in which the negative premise is not expressly 

 composite. This objection I proceed to examine. 



When the copula is means pure identity, as in ' that horse is that horse 1 (in which case 

 I shall write it in capitals) I own that the resolution is so purely formal, and the reality 

 represented under the compound form so elusive of our attempts to mean something more than 

 was meant by the simple form, that I should compare the resolution to that of 1 into lxl in 

 arithmetic. And though this arithmetical resolution be often useful, and even requisite, as a 

 preliminary to clear notion of some higher development of thought, yet the logical type of it 

 might well wait until the time comes when the same may be said of it. " That horse • IS that 

 which IS' that horse" may therefore be abandoned to the objector. But when, as more fre- 

 quently happens, the copula is only denotes some agreement, or something* transitive and con- 

 vertible which is not pure identity, I maintain the actual resolution to be part of the process of 

 inference. Let us take a material instance, which may represent anything objective, as will be 

 admitted : and I think that the process may find its analogue in purely subjective matters. 

 Let is represent agreement in colour. Then it will be instantly admitted that ' Z is F' and 

 ' Z is that which is F 1 are two different propositions. The question is, how do we infer from 

 ' Z is Y, X is not F.' Our second premise is X has not 'the colour which F has: 1 and for 

 the last words we substitute, as an identity, ' the colour which Z has,' the identity being purely 

 subjective. Here the resolution was made : our second premise became ' X is not that which 

 Fis\ 



Logical writers do not collect their copula? : and their processes seem reducible to com- 

 mon form in no way but this. They postulate that the copula? they use (which they take good 

 care shall be transitive and convertible) have the inferential force of the identity IS : they 

 examine and dwell upon syllogisms of identity, thereby giving the opponents of logic some 

 reason for their scoffs at the syllogism, and return with their results to other copulas, by aid of 

 the postulate. To this there can be no objection as to the truth of its results, but much in 

 every other way. This subject however is too wide a one ; and requires the preliminary con- 

 sideration of the manner in which the term has been used, and a disentanglement of the con- 

 fusion of ideas under which logicians speak, in one sense, of man as a partf of the notion 



* In the IS of identity, the transitive and convertible rela- 

 tions are a kind of zero forms. There is not much transition in 

 travelling from York to York and from thence to York : nor 

 much to see, in spite of the Italics, in the proposition that 

 from York to York is the same distance as from York to York. 



f In all that relates to quantity, there is no occasion for the 

 mathematical logician to pay the least deference to the Christian 

 followers of Aristotle; the master himself was a mathema- 

 tician, as were some of his Greek successors. Those who could 

 contentedly put number and speech together, as discrete quart, 

 tily, in opposition to length, as continuous, do not deserve to be 

 listened to, as quantitarians. But this it will be said is in the 

 writings of the master. It is so ; but the question is, whether 



it be not an obvious interpolation. The case stands thus : In 

 the sixth chapter of the Categories, quantity is made discrete 

 or continuous ; the discrete is dpiBfios Kal Xo'yos, the continuous 

 is length, surface, &c. Farther on, \o'yo« is changed into 

 (jitovij — Xe'yw 5e avrov tov fxeTa <pu>vris \6yov yivofievov — 

 and the reason given is that it is measured by long and short 

 syllables. On this I say first, that Aristotle would probably 

 have seen what his determined disciple Crackanthorp after- 

 wards saw, that the time of speaking is not speech; secondly, 

 that it is incredible that he should have used a wrong word 

 and have afterwards corrected himself by a synonyme instead 

 of an erasure ; thirdly, that dpiQads Kal Xoyos, in the language 

 of the time, are integer number, and fractional ratio or ratio of 



