5.451 If logic has primitive concepts then they must be independent of each other. If a primitive concept is introduced then it must be introduced in every combination in which it ever occurs. One cannot therefore introduce it for *one* combination first and then another time for another. E.g., if negation is introduced then we must now understand it in propositions of the form “~p” in just the same way as in propositions like “~(p v q,” “(Ex). ~fx” et al. We may not introduce it first for one class of cases and then for another, because it would then remain undecided whether its meaning [*Bedeutung*] in each case was the same, and there would be no available ground for using the same way of combining signs in both cases.

(Briefly, what Frege (*Grundgesetze der Arithmetik*) has said about the introduction of signs through definitions goes, mutatis mutandis, for the introduction of primitive signs.)

Agreeing with Frege and therefore disagreeing with Frege, then.

White (p. 89): “We understand the point of this paragraph best if we see its target as Russell and the way the primitive logical constants were introduced in *Principia Mathematica*.” Russell and Whitehead first introduced signs for ‘or’ and ‘it is not the case that’, using ‘~’ only where there were no quantifiers used. When they later introduced quantifiers they had to explain how these worked together with the negation sign. Then they define what these combinations of signs mean. White says that Wittgenstein objects to this piecemeal approach. “Either the negation sign means the same as it did when it was first introduced, in which case the significance of its combination with the quantifiers ought to follow from the way it was initially explained, or it means something different, in which case to use the same sign leads to confusion. Wittgenstein is claiming that this situation can only be avoided if we introduce all the primitive signs of logic, not in serial order, but all at one go.”

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