AND ON LOGIC IN GENERAL. 179 



before she settled whether writs should run in the name of the King de facto or of the Pre- 

 tender. 



A little consideration will shew us that every inference which is anything more than pure 

 symbolic representation of inference is due to the presence of something material : even a derived 

 or compound symbol, representing inference, shews the presence of something material. Here 

 are two purely formal propositions, in which P, Q, R, S, represent individual objects of 

 thought, and —A— indicates a relation A : — 



P -A- Q R -B- S 



P stands in A-relation to Q and R in B-relation to S. What are we to infer ? Now rub out 

 R, and for it write Q. This is material : it is now seen to be of the matter of our system that 

 the second subject is the first predicate. And now we have P -A- Q, and Q -B- S. 

 Can we infer anything ? With the form of combination of relations in our thoughts, we may 

 symbolise it, and say P -AB- S. Now make the relations material : let -A- and -B- 

 each be ' is :' then we have a material inference ; P is Q, Q is S, therefore P is S. In common 

 logic, the objects of inference, being terms expressed in general symbols, are void of matter ; 

 the relations between them, and the modes of inference, are material: I speak of logic as it 

 is. Many relations have a common form : the logician cannot yet see that when many cases, 

 no matter what, proceed upon a common principle, his concern is with that principle. It is 

 his business to apprehend the principle and to shew, as to the modus operandi of the mind, 

 how containing cases severally contain it, and apply it. 



I am charged with maintaining that thought is a branch of algebra, instead of algebra 

 a branch of thought. The answer is easy enough. Logic considers, not thought, but the 

 form of thought, the law of action of its machinery. Psychology herself does not know what 

 thought is : and the odds are that if she did she would not feel bound to tell logic. Thought, 

 the genus, has parts of its machinery, usually under cover, which work by daylight in 

 algebra, the species, to every one who has meditated on the principles of algebra. He who 

 makes me confound all other thought with algebra, because I call attention to what is more 

 visible in algebra than in other thought, though it exists in all thought, must make his own 

 logic responsible for the inference, not mine. He may hire a soldier to cook his victuals, 

 because both soldier and cook cut flesh with steel : but neither Mr Boole, the greater culprit, 

 nor I, the lesser* one, have done anything to deserve an invitation to the feast. 



I might with much more justice charge the logician with affirming all thought a branch 

 of geometry, instead of geometry a branch of thought. By processes nearly resembling those 

 which led Des Cartes to affirm that space is all the essence of matter, he reduces all thought 

 of comparison to the assertion or denial of containing and contained. These are originally 

 terms of space-relation : and his only syllogism, his universal includent of all argument, can 

 be fully symbolised by areas : a practice which many logicians dislike, and with reason, for 

 it tells tales. I have pointed out, in my second paper, the syllogism in which the copulse may 

 be any relations whatever. The copula of cause and effect, of motive and action, of all in 

 which post hoc is of the form and propter hoc (perhaps) of the matter, will one day be carefully 



• Not meant for extenuation : I wish I were the greater one. 



23 — 2 



