resented in conceptual notation by
variables, not by functions or classes (as Frege and Russell believed).
'1 is a number', 'There is only one zero', and all similar expressions
are nonsensical. (It is just as nonsensical to say, 'There is only one
1', as it would be to say, '2 + 2 at 3 o'clock equals 4'.)

4.12721 A formal concept is given immediately any object falling under
it is given. It is not possible, therefore, to introduce as primitive
ideas objects belonging to a formal concept and the formal concept
itself. So it is impossible, for example, to introduce as primitive
ideas both the concept of a function and specific functions, as Russell
does; or the concept of a number and particular numbers.

4.1273 If we want to express in conceptual notation the general
proposition, 'b is a successor of a', then we require an expression for
the general term of the series of forms 'aRb', '(d: c): aRx. xRb', '(d
x,y) : aRx. xRy. yRb',..., In order to express the general term of a
series of forms, we must use a variable, because the concept 'term
of that series of forms' is a formal concept. (This is what Frege and
Russell overlooked: consequently the way in which they want to express
general propositions like the one above is incorrect; it contains a
vicious circle.) We can determine the general term of a series of forms
by giving its first term and the general form of the operation that
produces the next term out of the proposition that precedes it.

4.1274 To ask whether a formal concept exists is nonsensical. For no
proposition can be the answer to such a question. (So, for example,
the question, 'Are there unanalysable subject-predicate propositions?'
cannot be asked.)

4.128 Logical forms are without number. Hence there are no pre-eminent
numbers in logic, and hence there is no possibility of philosophical
monism or dualism, etc.

4.2 The sense of a proposition is its agreement and disagreement with
possibilities of existence and non-existence of states of affairs. 4.21
The simplest kind of proposition, an elementary proposition, asserts the
existence of a state of affairs.

4.211 It is a sign of a proposition's being elementary that there can be
no elementary proposition contradicting it.

4.22 An elementary proposition consists of names. It is a nexus, a
concatenation, of names.

4.221 It is obvious that the analysis of propositions must bring us to
elementary propositions which consist of na