AND ON LOGIC IN GENERAL. 193 



Man is animal, and tried to make out whether it should be universal or particular, they 

 were dealing with the metaphysical form of speech, attribute predicated to be component of 

 attribute. Nor is this the only instance in which the metaphysical intruded itself within the 

 mathematical boundary. To me the old books read like a running fight between the two 

 modes of conception : not a pitched battle between regimented ranks under the banners of 

 quid and of quale; but a mob-scuffle in which there is neither front nor rear. It has been 

 said that logic ought to be the uncovered skeleton : this was said of the mathematical view. 

 The old logicians clothed the bones with a little metaphysical muscle : so that, instead of 

 presenting the examination of a skeleton in one compartment of a museum, and of muscular 

 fibre in another, logic looked like an inquest on a starved pauper in the workhouse. 



4. Contra-physical. This form is rarely in use. In human thought, the more fre- 

 quently one of two inverse forms occurs, the more rare is the other. But it is only in a result 

 to be expressed that this reading is a rarity. When the old metaphysician was hunting the 

 species in a genus by a differentia which was of the essence, he was engaged in a contra-phy- 

 sical process. 



All these words express distinctions which are purely formal. The logico-metaphysical is 

 only the form, law, mode of entrance, of the metaphysical notion, so long as humanity and 

 phenacostrepticisra are equally admissible as attributes of Newton and Leibnitz. I shall make 

 no other answer to the charge of materialism, except this, and a reference to what I have 

 already said. If all that precedes contain any matter, find the form of it, and either point it 

 out as existing, or introduce it. If the phrases savour too much of the material, either sub- 

 limate them into formalism by mental chemistry, or find better phrases. 



Even the words necessary and contingent must be allowed a formal sense, which has an 

 eye to the mode of action common to two kinds of matter. Real necessity only exists in the 

 laws of thought, applied to matter of which we form judgments a priori: popular necessity 

 exists where contingence has never shown two different kinds of result. Instead therefore of 

 widening the bounds of logic to introduce tiie consideration of true metaphysical necessity, it 

 is to be part of logic that the necessity which can be seen « priori or from a priori, the three 

 angles of a triangle make two right angles, is not of the same material as the necessity in- 

 ferred from uncontradicted contingency, man is biped, but that the two have a common form in 

 thought, or set the machinery in action in the same way. The same may be said of other notions 

 of pure metaphysics : the subjective and the objective are of one form of process in logic. 



XI. The only copula which logicians provide, for all the modes of reading, is the sub- 

 stantive verb 'is."" Nor is another wanted, so long as one relation only is used : but more must 

 now be found. To express in language all that is contained in thought, is to divide in lan- 

 guage all that is divided in thought. We must have definite ivords of relation, anaphorical 

 or schetical terms : and these I shall presently propose. But an ambiguity, to which I now 

 proceed, nipped the use of schetical words in the bud. 



Dichotomy, in mathematics, has an extreme case which is always included. If c = a + 6, 



the terminal instance c = a+0 is admitted and accounted for, or else excluded under the showing 



of the particular problem. Logical dichotomy, class into two classes, has the well-known 



quantitative division of all into two somes. The word some, in mathematical meaning, ranges 



Vol. X, Part I. 25 



