and this eternity is now investigated. "The plainest form of an incontrovertible idea of eternity is the piling up of numbers unlimitedly in arithmetical progression. Just as we can give a complete unity to each number without the possibility of repetition, so at every stage of its being it progresses still further and eternity consists in the unlimited manifestation of this condition. This sufficiently conceived eternity has but one single beginning with one single direction. Although it is not material to our concept to imagine a direction opposite to that in which the progression piles up, this notion of a backward moving eternity is only a hasty picture drawn by the imagination. Since it must necessarily run in a contrary direction, it would have behind it in each instance an endless succession of numbers. But this would be inadmissible as constituting the contradiction of a calculated infinity of numbers, and so it seems absurd to imagine a second direction of eternity."
The first conclusion to be drawn from this conception of eternity is that the chain of cause and effect in the universe must once have had a beginning: an endless number of causes which have followed one another endlessly is therefore unthinkable, "because innumerability is thus considered as enumerated," therefore a final cause is proved.
The second conclusion is "the law of the definite number: the accumulation of identical independent objects of an actual species is only thinkable as being made up of a definite number of these individual objects." Not only must the actual number of the heavenly bodies be definite at a given time, but the total number of all existent objects, the smallest independent particles of matter. This last necessity constitutes the real reason why no composite body is thinkable except as made up of atoms. All
