e minute. Accordingly there are different types
of extrinsic character of convergence which lead to the approximation to
different types of intrinsic characters as limits.

We now pass to the investigation of possible connexions between
abstractive sets. One set may 'cover' another. I define 'covering' as
follows: An abstractive set p covers an abstractive set q when every
member of p contains as its parts some members of q. It is evident
that if any event e contains as a part any member of the set q, then
owing to the transitive property of extension every succeeding member of
the small end of q is part of e. In such a case I will say that the
abstractive set q 'inheres in' the event e. Thus when an abstractive
set p covers an abstractive set q, the abstractive set q inheres
in every member of p.

Two abstractive sets may each cover the other. When this is the case I
shall call the two sets 'equal in abstractive force.' When there is no
danger of misunderstanding I shall shorten this phrase by simply saying
that the two abstractive sets are 'equal.' The possibility of this
equality of abstractive sets arises from the fact that both sets, p
and q, are infinite series towards their small ends. Thus the equality
means, that given any event x belonging to p, we can always by
proceeding far enough towards the small end of q find an event y
which is part of x, and that then by proceeding far enough towards the
small end of p we can find an event z which is part of y, and so
on indefinitely.

The importance of the equality of abstractive sets arises from the
assumption that the intrinsic characters of the two sets are identical.
If this were not the case exact observation would be at an end.

It is evident that any two abstractive sets which are equal to a third
abstractive set are equal to each other. An 'abstractive element' is the
whole group of abstractive sets which are equal to any one of
themselves. Thus all abstractive sets belonging to the same element are
equal and converge to the same intrinsic character. Thus an abstractive
element is the group of routes of approximation to a definite intrinsic
character of ideal simplicity to be found as a limit among natural
facts.

If an abstractive set p covers an abstractive set q, then any
abstractive set belonging to the abstractive element of which p is a
member will cover any abstractive set belonging to the element of which
q is a member. Accordingly it is useful t