4 NOTION AND DEFINITION OF NUMBER. 



their utterance. We arrive thus at natural number-words. For ex- 

 ample, utterances like, 



oh, oh-oh, oh-oh-oh, oh-oh-oh-oh, oh-oh-oh-oh-oh, 

 are natural number-words for the numbers from one to five. Num- 

 ber-words of this description are not now to be found in any known 

 language. And yet we hear such natural number- words constantly, 

 every day and night of our lives ; the only difference being that the 

 speakers are not human beings but machines namely, the striking- 

 apparatus of our clocks. 



Word-forms of the kind described are too inconvenient, how- 

 ever, for use in language, not only for the speaker, on account of 

 their ultimate length, but also for the hearer, who must be constantly 

 on the qui vive lest he misunderstand a numeral word so formed. It 

 has thus come about that the languages of men from time imme- 

 morial have possessed numeral words which exhibit no trace of the 

 original idea of single association. But if we should always select 

 for every new numeral word some new and special verbal root, we 

 should find ourselves in possession of an inordinately large number 

 of roots, and too severely tax our powers of memory. Accordingly, 

 the languages of both civilised and uncivilised peoples always con- 

 struct their words for larger numbers from words for smaller num- 

 bers. What number we shall begin with in the formation of com 

 pound numeral words is quite indifferent, so far as the idea of num- 

 ber itself is concerned. Yet we find, nevertheless, in nearly all 

 languages one and the same number taken as the first station in the 

 formation of compound numeral words, and this number is ten. 

 Chinese and Latins, Fins and Malays, that is, peoples who have no 

 linguistic relationship, all display in the formation of numeral words 

 the similarity of beginning with the number ten the formation of 

 compound numerals. No other reason can be found for this striking 

 agreement than the fact that all the forefathers of these nations pos- 

 sessed ten fingers. 



Granting it were impossible to prove in any other way that 

 people originally used their fingers in reckoning, the conclusion 

 could be inferred with sufficient certainty solely from this agreement 

 with regard to the first resting-point in the formation of compound 



