THE THEORY OF SYLLOGISM, ETC. 



Ill 



animal, and in another of animal as part of the notion man. The " integrate or mathematical 

 whole" which, according to Sir William Hamilton, " the philosophers contemned," and which is 

 seen in ' All men are animals', must take its proper place : and " philosophy", which " tends 

 always to the universal and the necessary" must be taught that the universal belongs to the 

 mathematical whole, as surely as the necessary to the metaphysical whole. 



The admission of relation in general, and of the composition of relation, tends to throw 

 light upon the difference between the invented syllogism of the logicians and the natural syllogism 

 of the external world. The logician, tied to a verb of identity, from which if he wander it is 

 never quite out of sight, is bound to subject and predicate of the same class ; objective both, or 

 subjective both. He cannot say the rose is red, for his is would require the inference that some 

 red is the rose. He has nothing but a method of reducing his predicate to an object : the rose is 

 a red thing; some red thing is a rose. The common man uses a copula which ties the object 

 up in relation to a more subjective predicate; not reading inversely by intension, not dwelling 

 on redness as an attribute of the rose, but directly by extension, thinking of the family rose as 

 his external object, and the sensation red as one condition under which it appears to his senses. 

 Again, an ordinary person says that the rose is red, and red is pretty, so that the rose is pretty. 

 The logician's pupil, when not far advanced, will interpret him as saying that ' The rose is a red 

 thing ; a red thing is a pretty thing, &c.' thus committing him to an opinion upon red cabbage 

 which perhaps was not within his meaning. The logician himself will substitute another 

 process : ' The colour of the rose is red colour ; red colour is pretty colour ; therefore the colour 

 of the rose is pretty colour : ' he thus reduces it to the equation of two terms by comparison 

 with a third ; when most probably the real form of thought (and logic professes to be the 

 study of existing forms) is nothing but the composition of relations. The rose is (in its 

 relation to one sense) red; red is (in the relation of the perceptions to the judgment) pretty; 

 therefore the rose is (to one sense that which is to the judgment) pretty. This distinction 

 of copulae is more nearly present to the mind than any one of the transformations by which the 

 technical form is arrived at : it is visible, more or less distinctly, that the first premise is matter 

 of fact, the second matter of taste ; here is a recognition of difference between is of the first 

 premise and is of the second ; which leads, with proportionate strength, to the recognition of 

 the composite character of is in the conclusion. Nor does the logician's form avoid it, except 

 by a pure assumption that the copulas are the same ; an assumption not true in fact. Nor can 

 an answer be given by saying that logic takes no cognizance of the matter, but only of the 

 form; for it is bound, by the laws of form, not to represent differences by agreements, except 

 when it is formally shown that the differences cannot affect the object to be gained. 



In one very material consideration, the logicians have evidenced the manner in which their 



commensurables. An editor who was not a mathematician, 

 seeing \6ym, which to him was only communication in its 

 most general sense, may have excogitated the absurdity above 

 alluded to, by help of <$>wvr\. Proclus has been used in a 

 similar way. Barocius makes him inform us that the prede- 

 cessors of Euclid had written on inexplicables (qua non ei/ili- 

 cari possuni) : Proclus says aXoycr, and means incommensu- 

 rables. 



But how can Xoyos be called discrete ? Before Euclid it 

 must have been so. Euclid's definition, which brings incom- 

 mensurable;; under the same law with commensurables, gives 

 the term ratio a title to continuity, which it had not before: 

 just as in modern times, the interminable decimal, when ad- 

 mitted as a distinct conception of arithmetic, gives continuity 

 to number. 



