THE DEDUCTIVE METHOD. 



303 



in the case of physiological, to say 

 nothing of mental and social pheno- 

 mena,) the laws of number and exten- 

 sion are applicable, if at all, only on 

 that large scale on which precision of 

 details becomes unimportant. Al- 

 though these laws play a conspicuous 

 part in the most striking examples of 

 the investigation of nature by the 

 Deductive Method, as, for example, in 

 the Newtonian theory of the celestial 

 motions, they are by no means an 

 indispensable part of every such pro- 

 cess. All that is essential in it is 

 reasoning from a general law to a 

 particular case, that is, determining 

 by means of the particular circum- 

 stances of that case what result is 

 required in that instance to fulfil the 

 law. Thus in the Torricellian experi- 

 ment, if the fact that air has weight 

 had been previously known, it would 

 have been easy, without any nume- 

 rical data, to deduce from the general 

 law of equilibrium that the mercury 

 would stand in the tube at such a 

 height that the column of mercury 

 would exactly balance a column of 

 the atmosphere of equal diameter ; 

 because, otherwise, equilibrium would 

 not exist. 



By such ratiocinations from the 

 separate laws of the causes we may, 

 to a certain extent, succeed in answer- 

 ing either of the following questions : 

 Given a certain combination of causes, 

 what effect will follow ? and, What 

 combination of causes, if it existed, 

 would produce a given effect? In 

 the one case, we determine the effect 

 to be expected in any complex cir- 

 cumstances of which the different 

 elements are known : in the other 

 case we learn, according to what law 

 — under what antecedent conditions — 

 a given complex effect will occur. 



§ 3. But (it may here be asked) are 

 not the same arguments by which 

 the methods of direct observation and 

 experiment were set aside as illusory 

 when applied to the laws of complex 

 phenomena, applicable with equal 

 force against the Method of Deduc- 



tion ? When in every single instance 

 a multitude, often an unknown mul 

 titude, of agencies, are clashing and 

 combining, what security have we 

 that in our computation d priori we 

 have taken all these into our reckon- 

 ing ? How many must we not gene- 

 rally be ignorant of ? Among those 

 which we know, how probable that 

 some have been overlooked ; and, 

 even were all included, how vain the 

 pretence of summing up the effects 

 of many causes, unless we know ac- 

 curately the numerical law of each, 

 — a condition in most cases not to be 

 fulfilled ; and even when it is ful- 

 filled, to make the calculation trans- 

 cends, in any but very simple cases, 

 the utmost power of mathematical 

 science with all its moet modem im- 

 provements. 



These objections have real weight, 

 and would be altogether unanswer- 

 able, if there were no test by which, 

 when we employ the Deductive Me- 

 thod, we might judge whether an 

 error of any of the above descriptions 

 had been committed or not. Such a 

 test, however, there is ; and its appli- 

 cation forms, under the name of Veri- 

 fication, the third essential component 

 part of the Deductive Method, with- 

 out which all the results it can give 

 have little other value than that of 

 conjecture. To warrant reliance ou 

 the general conclusions arrived at by 

 deduction, these conclusions must be 

 found, on careful comparison, to ac- 

 cord with the results of direct obser- 

 vation wherever it can be had. If, 

 when we have experience to compare 

 with them, this experience confirms 

 them, we may safely trust to them in 

 othei cases of which our specific ex- 

 perience is yet to come. But if our 

 deductions have led to the conclusion 

 that from a particular combination of 

 causes a given effect would result, 

 then in all known cases where that 

 combination can be shown to have 

 existed, and where the effect has not 

 followed, we must be able to show (or 

 at least to make a probable surmise) 

 what frustrated it ; if we cannot, the 



