AND ON LOGIC IN GENERAL. 



203 



when the divisor does not exceed 10, would look down on a calculator, a user of pebbles on 

 all occasions, in spite of the manner in which the pebbles would assist fundamental explanations. 

 This is no proof of wisdom : but we may as well wedt to teach a boy his letters until he can 

 read his way to school by the corners of the streets as expect to teach the world on a basis 

 which requires it to have philosophical acuteness before it can make up its mind to want the 

 teaching. The mathematics made their modern way, not as the philosophy of space, time, and 

 number, but as the instrument of surveying, navigation, commerce, &c. : and in this day, more 

 than ever, they have a crowd* of followers who have no idea of any other use. Let logic be 

 taught so as to sharpen the intellect as well as to analyse its processes, and logic will thrive as 

 much as mathematics : while the abacus will become, as it ought to be, the starting-point of 

 little boys and girls, instead of being at the top of a column of psychology. 



XX. In the metaphysical words of relation we have seen that necessity is of the purely 

 logical form, as explained. But all reference to causation must be absolutely thrown away 

 from each relation. This is not merely a logical demand : even the material meaning of 

 the words ought to be independent of causation. Thus, health and intemperance are repug- 

 nant. We do not mean that intemperance is the cause of ill-health, or even one cause : we 

 may know this, but the proposition in hand does not state it ; and in fact, ill health frequently 

 leads to intemperance, not the converse. Another form is, temperance is an essential of health : 

 not a cause, there may be temperance without health ; ill health often leads to temperance. 

 Another equivalent is, health is dependent on temperance ; but not on temperance alone. 

 Lastly, ill health and temperance are alternatives, but not repugnant alternatives. This 

 branch of logic would help to drive out the idea of causation which lurks in that of connexion. 

 In the logical form, necessary and sufficient cause is dependent (in the form of thought) upon 

 its effect, as well as effect upon cause: effect is essential to cause, as well as cause to effect. 

 If the attributes gravity and weight be never separate either from the other, they are logico- 

 metaphysically identical, and each is an essential dependent of the other. When our reputed 

 cause and effect are not precedent and consequent, but strictly simultaneous, a question arises 

 whether these words be rightly applied. Their real sense may be of a much more subjective 

 character than physical philosophers take them in. Force and change of momentum are always 

 simultaneous: our predetermination to employ force is only in consciousness: we say that 

 change of momentum will follow ; but the two things go together, and in fact we change one 

 momentum in producing what we call the force which changes another momentum. Would 

 higher knowledge teach us to say that change of momentum evolves force, not vice versa? 



* There is a strong impression in the world of physical in- 

 quiry that a mathematician is almost bound, whatever his pur- 

 suit may be, to make his science the means of investigating 

 or registering some facts connected with the material world. 

 A teacher of mathematics for example, whose business it is to 

 study the mind and its discipline, that he may make his teach- 

 ing permanently useful to those who will not, in nineteen cases 

 out of twenty, ever have any need to apply it professionally, 

 would be thought quite in the right way if he- should take to 



investigating the force of steam, or the strength of beams, or the 

 orbits of binary stars : they would call him a practical man. 

 I should give him quite another name if he took up steam or 

 star for anything beyond relaxation, supposing his taste to turn 

 that way. The disposition to hold material application to be 

 always practical is one of the consequences of the want of psy- 

 chological thought, and will vanish before sound logical train- 

 ing, with other myopisms. 



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