  When we enumerate numbers up to some specific value, or, even if we do not
specify the number, we know at the same time that there are much greater
numbers which should be reachable by the same enumeration, but indeed we also
congnize them without practical enumeration. Namely, if we deem enumeration to
be a way of reaching a number without any "jump", there is a "jump'' in our way
of cognition of such greater numbers. In this article, making use of a set
theoretical framework by Vop\v{e}nka (1979) (alternative set theory) which
describes such structure, we attempt to shed light on an analogous sturucture
in human and social phenomenon. As an example, we examine a problem of common
knowledge in electronic mail game presented by Rubinstein (1989). We show an
event comes to common knowledge by a "cognitive jump".
