NUMERICAL RELATIONS OF SOCIAL FORMS 129 
the group. In that case the size immediately determines 
the form.! 
Definite correlations between characteristic sociologi- 
cal formations and arithmetically definable magnitudes 
appear only near the lower boundary of the numerical 
series. Higher up in the scale such a definite mathematical 
formulation is not possible, and the modifications must be 
formulated in terms of more or less. More precisely, how- 
ever, the situation is this. To every definite number of ele- 
ments there correspond, in accordance with the purpose 
and the spirit of their association, a specific sociological 
form, a characteristic organization, and a definite degree 
of firmness of texture. With every added or subtracted ele- 
ment these experience a modification, however small and 
indeterminable. There are, however, no special terms for 
these different sociological conditions, even in a case where 
the differences can be observed. This forces us to describe 
the situation as if it were a combination of two conditions 
with the one more, the other less conspicuous. 
The Monad 
The simplest structure which may be subsumed under 
the sociological category is the single individual, however 
paradoxical and essentially contradictory it may seem. 
The two phenomena, isolation and freedom, which appear 
in relation to the individual are distinctly of a sociological 
character. Not only are they characteristic of the relation 
between the individual and the group, but the amount of 
freedom and isolation which the group allows the individ- 
ual elements is immediately significant for the structure of 
the whole. 
The mere fact that an individual maintains no recip- 
rocal relationships with other individuals is. of course. not 
' Soz., p. 47.