128 PART II.-SOME IMPORTANT METHODOLOGICAL TERMS. 



determinate, merely severed from any axioms of natural philo- 

 sophy; and these are two, Geometry and Arithmetic; the one 

 handling quantity continued, and the other dissevered. Mixed 

 hath for subject some axioms or parts of natural philosophy, 

 and considereth quantity determined, as it is auxiliary and 

 incident unto them. 



"For many parts of nature can neither be invented with 

 sufficient subtilty, nor demonstrated with sufficient perspicuity, 

 nor accommodated unto use with sufficient dexterity, without 

 the aid and the intervening of the mathematics ; of which sort 

 are perspective, music, astronomy, cosmography, architecture, 

 enginery, and divers others. 



"In the mathematics I can report no deficience, except it be 

 that men do not sufficiently understand the excellent use of 

 the pure mathematics, in that they do remedy and cure many 

 defects in the wit and faculties intellectual. For, if the wit be 

 dull, they sharpen it; if too wandering, they fix it; if too 

 inherent in the sense, they abstract it. So that as tennis is 

 a game of no use in itself, but of great use in respect it maketh 

 a quick eye, and a body ready to put itself into all postures; 

 so in the mathematics, that use which is collateral and inter- 

 venient, is no less worthy than that which is principal and 

 intended." (Advancement of Learning.) 



52. (B) DEFINITION OF TERMS. However, a bridge 

 exists connecting mathematical rigidity with commonsense flui- 

 dity. This bridge comes into being so soon as a science com- 

 mences to define its terms with fair precision, and makes itself 

 thus independent of a fluctuating terminology. 



Where the conceptions are, as in physics, of severe simplicity, 

 it is frequently practicable to define them, though not without 

 having to allow for the ambiguities incidental to the complexity 

 of objects and to the readjustments necessitated by new dis- 

 coveries. Every science must thus aim at evolving a termino- 

 logy of its own where each term is unequivocally defined, 

 and a science is therefore progressing indifferently when it is 

 without a terminology which is being fashioned more and more 

 to assume the form of a series of unvarying and universally 

 accepted definitions, as in the nomenclature of chemistry and 

 the terminology of botany. It is patent that we cannot satis- 

 factorily define what we are acquainted with only imperfectly, 

 and that if knowledge can only be acquired by degrees, a defini- 

 tion cannot be flawless all at once, but must grow in exactitude. 

 For this reason, the least advanced sciences are in a sorry 

 predicament. This is particularly noticeable where the termino- 

 logy of a science is bodily transferred from the every-day 

 terminology; and the evil reaches the highwater mark when 

 the tacit assumption prevails, as in psychology and ethics, that 

 the terminology of the market place is substantially satisfactory, 

 and that there is consequently no need for its improvement 



