xRb', '(d x,y) : aRx . xRy . yRb', and
so forth. (If b stands in one of these relations to a, I call b a successor
of a.)
4.126 We can now talk about formal concepts, in the same sense that we
speak of formal properties. (I introduce this expression in order to
exhibit the source of the confusion between formal concepts and concepts
proper, which pervades the whole of traditional logic.) When something
falls under a formal concept as one of its objects, this cannot be
expressed by means of a proposition. Instead it is shown in the very sign
for this object. (A name shows that it signifies an object, a sign for a
number that it signifies a number, etc.) Formal concepts cannot, in fact,
be represented by means of a function, as concepts proper can. For their
characteristics, formal properties, are not expressed by means of
functions. The expression for a formal property is a feature of certain
symbols. So the sign for the characteristics of a formal concept is a
distinctive feature of all symbols whose meanings fall under the concept.
So the expression for a formal concept is a propositional variable in which
this distinctive f
eature alone is constant.
4.127 The propositional variable signifies the formal concept, and its
values signify the objects that fall under the concept.
4.1271 Every variable is the sign for a formal concept.
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