On the Fundamental Principles of Mathematics. 339 



rest by two planes without border, must be regarded as nothing- 

 in comparison with the so-called half of all space; though in the 

 space so separated there would be room for all the visible creation, 

 could its form be adapted to the dimensions of that space in those 

 respects in which the dimensions are finite : or the two planes might 

 themselves be supposed to be situated outside of all that we can 

 discover by the best optical aid ; and the conclusion still be the 

 same ; viz., that the whole space separated by them must be re- 

 garded as nothing in comparison with all space ; which is itself 

 absolutely infinite. 



In the space thus separated, might also exist all the specifically 



infinite quantities described in (19.) 



f 



vides that line into two halves ; and the plane without border in 

 like manner divides all space, so (19.) the instantaneous present 

 divides the Eternity Past from the Eternity Future. It does 

 so (in so far as can be discerned) in all worlds at once ; as the 

 same plane in the figure cuts all the three straight lines which 

 penetrate it, and which are to be regarded as interminable in both 

 irections from the dividing plane. The present thus divides 

 those two Eternities now. So, also, it was, in so far as can be 

 discerned, after the first moment of the existence of the first 

 created befng or thing, and thus it shall be, after the present sys- 

 tem of things, like a worn out " garment," is, as it were, "folded 

 up" and laid aside. 



Through the limit thus ever present the current of time passes, 

 in a metaphorical sense ; and, moment by moment, the Eternity 

 Future is transferred to the Eternity Past. [We seem to recog- 

 nize this even in our ordiuary language. Thus we say, when to- 

 morrow comes (viz., to us) and not when we come into to-mor- 

 row.] As, moreover, in the case of the analogous quantities in 

 space, so, in this case, the transfer, whether of a single day, or of 



ft I m • ^ 1 ^ f* 



countless ages, trom the one .htermt) 

 to leave each of those Eternities in 

 absolute infinite of duration. Hence 



effect 



being thus actually indeterminate, may exist, m m far as it exists at all, any where 

 in this line. 



The like may be said of all space, which ha* no borders, Or — with reference to 

 its boundlessness on all rides — that its centre ifl any where. 



A line interminable in one direction may, as already intimated, be regarded m the 

 half he line interminable in both directions; — but it does not seem to be possible 

 o obtain in the same form any quantity which could be lied the or third, or the 

 one fourth, 6 , of the whole, let if an interminable curve l>e sunpo d to exist of 

 such a form that h might throughout meet the interminable straight line, and. any 

 and every where along it, I found finite portions of tl am, ♦ aeh equivah 1£ 



or 1|, i: C times tl- responding fraction of the straight line, a fraction such u i or 

 i of the in tinabh tr. it line would <■ m toex combined with the whol aid 

 ^11 expressed t r by the intern We car . It would seem to be so; but any 



such conclusion should be received with caution. 



