ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



477 



I shall be asked whether, when the intensive proposition is thus reduced to its skeleton 

 form, as a relation between wholes, I do not abandon the distinction of mathematical and 

 metaphysical, as designative of the two sides of logic. Is not the idea of a whole including a 

 smaller whole as mathematical as that of a part contained in a larger part ? Certainly 

 it is, but nevertheless I do not abandon the nomenclature, which loses none of its truth and 

 none of its utility : but the names must be held designative of a subsequent distinction. The 

 proposition of extent remains mathematical to the end ; the proposition of intent becomes 

 metaphysical in application. Even when man and brute are clothed with all their qualificative 

 concepts, they make up animal just as the items of a tradesman's bill make up the total 

 of goods furnished. The individuals are plain counters in the formal enunciation, and painted 

 counters in the material : but never anything except counters. But when, in the proposition 

 of intent, the whole is recognized by its separating attribute, that attribute coalesces with 

 others in each individual by a process of which we hide our ignorance when we call it 

 bntological or metaphysical. The whole rational contains the whole man; the attribute 

 rational goes to the composition of the attribute human: but, in spite of the logician, there is 

 more than summing up in this second process. Extensive quantity has partes extra partes, 

 as they once said, and some will admit no other kind of quantity: de essentia quantitatis est 

 habere partes extra partes, says Smiglecius (Diep. ix, qu. 5). But extensive quantity has 

 this quality objectively, permanently, and de essentia : intensive quantity has it only 

 subjectively, pro re nata, as an accident of the thoughts. We can separate the rational 

 in man from the animal in man, for the mind, by an act of the mind : we cannot but separate 

 this man from that, save only when we think of the class as a unit, a process as subjective as 

 that of separating the individual into concepts. First intentions give individuals which are 

 compounds not yet decomposed, and aggregants not yet aggregated. Second intentions 

 exhibit component attributes, and aggregate classes. The basis' of these oppositions is seen 

 in X))Y under the forms 'X and all its parts are parts of Y' — 'T and all its wholes are 

 wholes of X.' 



• Mr Mansel (iv. p. 117—119) has some remarks on exten- 

 sion and intension, hinting opposition to Hamilton's doctrine, 

 and recognising the change of the quantities in passage from 

 one to the other. With him '-some A is all B" gives all the 

 attributes of B as^someof thoseof A ; while "all A is someB" 

 classes A under B. This mode of enunciation is very con- 

 fusing: and from it follows that I owe Mr Mansel reparation 

 for all but absolute misrepresentation in my article Logic (col. 

 344, note) in the English Cyclopcedia; an inattentive reader 

 would suppose I malte him merely change the pl.xes of Hamil- 

 ton's forms, whereas he does more. Mr Mansel suys (p. 119) — 

 " The problem which we wish to see satisfactorily solved by 

 the advocates of Sir W. Hamilton's doctrine may be stated as 

 follows : To construct a synthetical proposition containitig an 

 equation or identification of subject and predicate in any other 

 respect than that of the objects thought under the compared 

 concepts." My position is, either that this question is now 

 solved, or that the given problem is net the one which should 

 have been given. 



Mr Mansel criticises Bishop Thomson for not taking suf- 

 ficient account of constitutive attributes as distinguished from 

 •imple oharacteristicf : I hold that Di Thomson — and others. 



including the author of my second paper — had taken too much 

 account of this extralogical distinction ; extralogical, so far as 

 entrance into enunciation is concerned. For a term is held to 

 be divided from its contrary before enunciation : while, in tlie 

 proposition, an attribute is of the same import whether it be 

 constitutive, or only characteristic. Hamilton, from whom I 

 seldom differ in principle as to what is and is not logic — though 

 in application we sometimes so widely disagree that, like a 

 professor I have mentioned elsewhere, I do not grant him that 

 the whole is greater than its part until I see what use he wants 

 to make of it — replies as follows : — " ...In reference to Breadth 

 and Depth, there is no difference whatever between 'constitu- 

 tive' and 'attributive', between necessary and contingent, be- 

 tween peculiar and common. It is of no consequence, what has 

 antecedently been known, what is newly discovered. These 

 are merely material affections. We have only to consider what 

 it is we formally think," (vi. 643"). With reference to the 

 quantities, Mr Mansel is answered by (f;44*, note) — "As 

 others, besides Mr De Morgan, have misunderstood this mat- 

 ter " followed by a clear and dogmatical exposition of 



Hamilton's doctrine of breadth and depth, never till then 

 given, and placing his enoi of quantity in broad daylight. 



