s. The order of the number-series is not governed by an external
relation but by an internal relation. The same is true of the series of
propositions 'aRb', '(d: c): aRx. 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 feature 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. For every
variable represents a constant form that all its values possess, and
this can be regarded as a formal property of those values.

4.1272 Thus the variable name 'x' is the proper sign for the
pseudo-concept object. Wherever the word 'object' ('thing', etc.) is
correctly used, it is expressed in conceptual notation by a variable
name. For example, in the proposition, 'There are 2 objects which.. .',
it is expressed by ' (dx,y)... '. Wherever it is used in a different
way, that is as a proper concept-word, nonsensical pseudo-propositions
are the result. So one cannot say, for example, 'There are objects', as
one might say, 'There are books'. And it is just as impossible to
say, 'There are 100 objects', or, 'There are!0 objects'. And it is
nonsensical to speak of the total number of objects. The same applies to
the words 'complex', 'fact', 'function', 'number', etc. They all
signify formal concepts, and are rep