106 Wisconsin Academy of Sciences, Arts, and Letters. 



such rank may be given to a simultaneous factor as well as to any other 

 factor of a thought. 



Of grouping little must be said, as the subject is broad enough and 

 deep enough for a special thesis. I merely note in the first place that, 

 in "Six and four are ten,*' "and" historically means "in addition to'" 

 or "added to." Among the possible methods of thought structure the 

 following is perhaps more plausible than others. Consciously intend- 

 ing "six"' as a partial subject, the speaker can however present the 

 same, according to observed linguistic methods, only as if it were his 

 whole subject. The same is true of "four." He can, however, indicate 

 that these subjects are to be taken concomitantly or cumulatively; and, 

 in so doing, he might either indicate that the two are to be taken to- 

 gether, or that one is to be taken with the other. As the latter 

 method is psychologically somewhat easier, it is more natural to suppose 

 it to have been elected, as words like "and" date back to extremely 

 early stages of mental development. Again the speaker, within the lim- 

 its of this method, may elect to add either the first group-element to the 

 second or the second to the first. Here again, it seems more natural to 

 suppose the latter alternative. To add the first to a not yet men- 

 tioned second, requires a greater mental effort, both in exposition and 

 in comprehension, than to add the second to an already mentioned first. 

 I accordingly assume, without attempting proof, that in "Six and four'* 

 I mean that "four" is added to "six." Accordingly my thought is as 

 follows: "Six" is partial subject of "are ten;" "four" is also partial 

 subject of "are ten." Between "four" and "six" there further holds 

 the relation algebraically expressible by "plus," linguistically expressi- 

 ble by "in addition to" or by "with" or by "and." But this relation 

 reads backward and not forward. That is, "four" is in addition to 

 "six" (not "six" to "four"), as indicated by the arrow in 



^ <r 



"six and four." 



"Six" being now a common factor in this last expression and "Six are 

 ten," I may indicate its function in "Six and four" by a relative word. 

 In so doing I elect the word for group-suggestion most tolerant of a 

 relative, namely, "with," obtaining "Six, wherewith (is) four, is ten."^ 

 That is, the relative clause and the conjunctive phrase are quite equiv- 

 alent.^ 



Further, in all my effort to show you that "four" is taken with "six" 

 in the formation of my subject, I do not forget that the very aim and 



^In such phrases Grammar has distinctly missed the really conjunctive word. 

 "And" or "in addition to" or "with" is merely an indispensable element of the 

 idea-trio (thought) expressed by "Six and four." As it advances "Six" and 

 "four" to a new thought-membership it may be said in a sense to join them. 

 But such joining, as indicated, is not distinctive of any thought element, being 

 conceivable of each. The true joiner is "Six ;" for it is at the same time a full 

 factor of "Six and four," and a partial factor with "are ten." 



