SECTION 16.-DEFINITE, EXACT, AND MATHEMATICAL PROCEDURE. 129 



or definition. 1 Such an attitude is manifestly erroneous. Rather 

 should there be from the very first the most determined resolve 

 to define terms as accurately as possible, to ensure that the 

 term is comprehensive in meaning, and to remodel the defini- 

 tions incessantly according to need. The indeterminateness of 

 language constitutes one of the weightiest reasons for pressing 

 an enquiry to the furthest limits practicable in order to obtain 

 the maximum of clearness and definiteness, and this indeter- 

 minateness presents also the heaviest indictment against a loose 

 or undefined use of terms in science. Ideally speaking, there- 

 fore, individual investigations pertaining to a new science should 

 extend to a life-time, should be pursued with eyes ever vigilant 

 to detect new facts and new relations, and should restlessly aim 

 at an increasingly exact, exhaustive, durable, and convenient 

 terminology. A science, then, commences in perplexing indefi- 

 niteness, and tends to terminate in dogmatic definiteness. It 

 is even indispensable that there should be a clear consciousness 

 of the inappropriateness of attempting, at the beginning of a 

 new investigation, to cast the results achieved into a mathemati- 

 cal mould, just as it should be an ambition and aspiration from 

 the first to attain to progressively greater exactitude and, even- 

 tually, to mathematical formulation. 



53. (C) PRECISION IN STATEMENTS If precision in the 

 use of terms is the pre-requisite of accurate scientific activity, 

 precision in general statements is its crowning glory. A vague 

 terminology bewilders the inquirer and gravely impedes advance, 

 and the circumstances are only slightly less disastrous when 

 instead of cautiously framed definitions, we are faced by an 

 interminable series of more or less nebulous generalisations.. 

 The methodological ideal is evidently that the material results 

 of an enquiry should be presented (as by Spinoza) in a chain 

 of definitions, accompanied by pithy explanations and a few apt 

 illustrations, because just as in the attempt to define terms 

 exactly, the maximum of error is eliminated, the endeavour 

 precisely to define general truths leads to a degree of reliability 

 in results otherwise scarcely ever attained. Any attempt at 

 consistent definition very speedily reveals that it is one thing 

 to formulate a general statement, and another to shape this 

 statement so faithfully that it should resist critical and minute 

 scrutiny. It is, therefore, essential for the scientific worker to 

 be aiming at definitions from the commencement to the con- 

 summation of the enquiry, both because it will clarify and con- 

 centrate his thought, and because it will place him in a posi- 

 tion to proceed deductively with increased assurance. Indeed, 

 deduction can only be pursued with full confidence and with 

 tolerable success when the scientific worker has been throughout 



1 The advantages are dubious of substituting one series of terms for 

 another virtually equivalent in meaning, as when thinking, feeling, and 

 willing become cognition, affection, and conation. 



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