330 On Injxnltesl 



what has been heretofore termed infinite space, as existed 

 in the mind of Mr. Locke; and indeed, as it seems impos- 

 sible should not exist in every mind that has turned itself to 

 the subject, and is capable of taking a single step in the 

 course of an argument. If there is any use in a circumlo- 

 cution, there can be no objections to calh'ng it, the infinite 

 potentiality of admitting existence; or it may be called 

 nonentity, though a mere child in philosophy would be sure 

 that it is infinite nonentity. Besides, it seems too much like 

 dooming the term nonentity to penance for its past deficien- 

 cy, and decreeing, that whereas it has heretofore conveyed 

 from mind to mind tbe idea of a nothing of no extent, 

 it shall hereafter convey the idea of an infinite nothing. 



Mr. Locke remarks, that by repeated additions of the 

 idea of finite space we come at the idea of infinity of space, 

 but not at the idea of spice infinite. This indeed looks a 

 little like supposing that infinite space has a substratum. 



Dormitat aliquando etiam bonus Homerus. The human 

 mind usually in its first steps towards the idea of infinite 

 space, annexes finite to finite space several times successively; 

 but it does not appear certain that this is always the case. 

 However far the idea of specific finite space h carried, the 

 mere perception that there is space beyond it, by no means 

 implies the perception of infinite space, for the limits of 

 finite space are in all cases also beyond it. This process 

 appears to be merely opening the eyes of the intellect. The 

 ultimate process is to set up an imaginary limit without any 

 feference at all to the position or inter\ening distance, and 

 to substitute it for all supposable limits whatever ; a-nd the 

 mind then perceives with instant intuition that all such limits 

 are wholly an absurdity/ 



The error with recjard to mathematical infinity and infi- 

 nitesimals, exists principally in those minds which are not 

 eccustomcd to look beyoud the steps of a dem >nstration, as 

 they are laid down before them. President Day in his ex* 

 ceilent system of algebra has given the following definition 

 of infinites and of infiaitesimals. *^ Infinite in the highest 

 and most proper sense, is that which is so great that nothing 

 can be added, or supposed to be added. A mathematical 

 quantity is said to be infinite, when it is supposed to be in- 

 creased beyond any determinate limits. When a quantity 

 is diminished till it becomes less than any determinate 



