The indefinables of logic must be independent of each other.
If an indefinable is introduced, it must be introduced in all
combinations in which it can occur.
We cannot therefore introduce it first for one combination, then for
another; e.g., if the form
x R y
has been introduced, it must henceforth be understood in propositions of
the form a R
b just in the same way as in propositions such as
(
∃x,y). x R y and
others.
We must not introduce it first for one class of cases, then for the
other; for it would remain doubtful if its meaning was the same in
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both cases, and there would be no ground for
using the same manner of combining symbols in both cases.
In short, for the introduction of indefinable symbols and combinations
of symbols the same holds, mutatis mutandis, that
Frege has said for the
introduction of symbols by definitions.