AND ON LOGIC IN GENERAL. 



177 



III. Logic bears on its modern banner, The form of thought, the whole form, and 

 nothing but the form. It has been excellently well said that whatever is operative in thought 

 must be taken into account, and consequently be overtly expressible, in logic: for logic must 

 be, as to be it professes, an unexclusive reflex of thought, and not merely an arbitrary selec- 

 tion, — a series of elegant extracts, — out of the forms of thinking. Whether the form that it 

 exhibits be stronger or weaker, be more or less frequently applied, that, as a material and 

 contingent consideration, is beyond its purview. Nevertheless, so soon as a form of thought 

 is exhibited which does not come within the arbitrary selection, the series of elegant extracts, 

 it is forthwith pronounced material : — 



St. Aristotle ! what wild notions ! 



Serve a ne exeat regno on him ! 

 The proper reply to every accusation of introducing the material where all should be formal, 

 is as follows. You say this thought or process is material : now every material thinking has 

 its form : therefore this thought has its form. Logic is to consider the whole form of thought : 

 your logic either contains tlie form of this thought, or it does not. If it contain* the form of 

 this thought, shew it : if not, introduce it. I shall now state three instances of the objection. 

 In my last paper, as in my work on Formal Logic, I separated form from matter in the 

 copula of the common syllogism. The copula performs certain functions ; it is competent to 

 those functions; it is competent because it has certain properties, which are sufficient to vali- 

 date its use, and, all cases considered, not more than sufficient. The word 'is,' which identifies, 

 does not do its work because it identifies, except-}- in so far as identification is a transitive and 

 convertible notion: 'A is that which is B' means 'A is B'; and ' A is B ' means ' B is A'. 

 Hence every transitive and convertible relation is as fit to validate the syllogism as the copula 

 'is,' and by the same proof in each case. Some forms are valid when the relation is only 

 transitive and not convertible ; as in 'give.' Thus if X — Y represent X and Y connected by 

 a transitive copula, Camestres in the second figure is valid, as in 



Every Z— Y, No X— Y, therefore No X_Z. 



♦ When I see a chapter in a book of logic headed On ma- 

 terial and formal consequence, distinguishing " A = B, B=C, 

 therefore ^ = C " as material from " A is B, B is C, therefore 

 A is C" as formal, I am at first inclined to think that the 

 distinction of formal and material is that of contained and not 

 contained — in Aristotle. But when the title-page shews me an 

 author whose mind is as free from the sway of that distinction 

 as my own, I am compelled to have recourse to the difference 

 between the ideas of form belonging to the mathematician and 

 to the logician. Is there any consequence without form ? Is 

 not consequence an action of the machinery ? Is not logic the 

 science of the action of this machinery ? Consequence is always 

 an act of the mind : on every consequence logic ought to ask, 

 What kind of act ? what is the act, as distinguished from the 

 acted on, and from any inessential concomitants of the action ? 

 For these are of the form, as distinguished from the matter. 

 What is the difference of the two syllogisms above? In 

 the first case the mind acts through its sense of the transi- 

 tiveness of 'equals :' in the second, through its sense of the 

 transltiveness of ' is.' Transitiveness is the common form : the 



Vol. X. Part I. 



difference between equality and identity is the difference of 

 matter. But the logician who hugs identity for its transitive- 

 ness, cannot hug transitiveness : let him learn abstraction. 



t I again call the reader's attention to the pure form of nut- 

 cracking, with which I began. The syllogism is the nut to be 

 cracked. I believe I have got to the pure form, which equally 

 applies to two levers, a screw forced into a receptacle, Nas- 

 myth's steam-hammer, the collision of a couple of planets, as 

 the case may be : the common form of all being pressure 

 enough applied to opposite sides of the nut. The logician in- 

 sists upon it that the pure form is a couple of metallic levers, 

 with friction-studs, if that be the proper name, to prevent the 

 nut from slipping aside, and such a hinge that, according to 

 the way we turn it, the levers give convenient entrance to a 

 common nut or a walnut. All his additions to the pure form 

 I admit to be usual and convenient : but I affirm and main- 

 tain that whatever can cn;ck a nut, and does crack a nut, is a 

 nut-cracker; and being a nut-cracker, must be considered as a 

 nut-cracker, and included among nut-crackers, in every trea- 

 tise on the whole form of nut-cracking. 



23 



