On Infinites, 327 



jre frequent, part comraon, and part perhaps unlversaL 

 It is not intended to say absolutely, that they are wholly, 

 or even partially erroneous; but to place the arguments 

 that bear against them in such a light, as to give them, if 

 possible, their full efficiency. The opinions alluded to are 



the foliovving. 



We cannot comprehend infinity: our ideas about it are 

 merely negative : we can tell what it is not, but we cannot 

 tell what it is. Mathematical infinites and infinitesimals, 

 although extremely great or extremely small, are still in all 

 cases measurable by a finite mind. Numericn] infinity is 

 nnposslble; for any collection of units, however great, is 

 With intuitive certainty numerable. The universe must be 

 unite m extent, because its parts are finite, and finite parts 

 cannot constitute infinity. The work of creation cannot 

 have been eternal for the same reason, that it would imply 

 an mfinite series of units, or of finife parts, which is im- 

 possible. Matter and finite spirits cannot have been eter- 

 nal, either in a combined or elementary state, because their 

 eternity necessarily implies their independent existence, and 

 precludes the need of a Deity, All sysiexnsy therefore, 

 that assert or admit the eternity of matter, are atheisticaL 



VVhen it is said that we cannot comprehend infinity, it 

 feems difficult to ieW what is meant by the assertion. If it 

 |s meant that we cannot encompass it in thouglit, or number 

 »ts parts, there can be no doubt in the case; for from the 

 nature of infinity and o( the human mind, this is of cour>e 

 'tnpossible. And if it is meant that we cannot know all 

 ^^^ tenth respecting it, this may be readily granted, for it is 

 ^he case with regard to almost evevy subject of investigation 

 ^^'ith which we are acquainted. That we can know^ some- 

 thing about it is seldom disputed; and with infinity, as with 

 pther subjects, we may go patiently to work, and exam- 

 '^3 it as far as the utmost limit to which our minds can 

 penetrate. 



Mr, Locke says, ^' We have no idea of infinite space ;" 

 and afterwards, -^We have no positive idea of infinite space, 

 duration or number," It appears that he attempted to prove 

 the less, because he was apprehensive that the arguments 

 vvhich he had adduced respecting the greater would not be 

 satisfactory to all. 3Jr. Locke huih wi^W on bis own foun- 

 dation, or rather the foundation which had stood for agef 



