On Infinites. 327 



are frequent, part common, and part perhaps universal. 

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

 or even partially erroneous; but to place the arguments 

 that bear against them iu such a ligSit, as to give them, if 

 possible, their full efficiency. The opinions alluded to are 

 the following. 



We cannot comprehend infinity: our ideas about it are 

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

 tell what it is. Mathematical infinites and infinitesimals, 

 although extremely great or extremely small, are still in .'ill 

 cases measurable by a finite mind. Numerical infinity is 

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

 with intuitive certainty numerable. The universe must be 

 finite in 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 infinite series of units, or of finite 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 systems, thereibre, 

 that assert or admit the eternity of matter, are atheistical. 



When it is said that we cannot comprehend infinity, it 

 seems difficult to tell what is meant by the assertion. If it 

 is meant that we cannot encompass it in thought, or number 

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

 nature of infinity and of the human mind, this is of course 

 impossible. And if it is meant that we cannot know all 

 the truth respecting it. this may be readily granted, for it is 

 the case with regard to almost every subject of investigation 

 with which we are acquainted. That we can know some- 

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

 other subj :cts, we may go patiently to work, and exam- 

 ine 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, becaur^e he v.'as apprehensive that the arguments 

 which he had adduced respecting the greater would not be 

 satisfactory to all. Mr. Locke built well on his own foun- 

 dation, or rather the foundation which had stood for ages 



