abbreviatory


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See: compact, pithy
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13) Ernest Sosa has suggested to me that this use of "explains" as relating propositions, regardless of their truth-value, would connect with ordinary usage better if it were regarded as abbreviatory of "would explain".
But for Russell, a phrase of the form (lx)[phi] is not a genuine term; it is an abbreviatory device that permits (provably legitimate) shortcuts in the course of proofs, and the use of pseudo-formulae that are sometimes easier to grasp than the genuine formulae for which they go proxy.
When using their abbreviatory notation, Whitehead and Russell introduce a device for representing the scope of a description: they place a copy of it within square brackets appended to the front of the formula that constitutes its scope.
If Russell's theory predicts ambiguity where there actually is ambiguity in natural language, this is a virtue rather than a vice, and if there is any "problem" it concerns only the fact that the use of Russell's abbreviatory conventions may, on occasion, require the insertion of scope indicators in order to make it clear which of two (or more) unambiguous formulae in primitive notation a particular pseudo-formula is abbreviating.