Donnellan's introduction of referential use of definite descriptions serves as a necessary modification to Strawson's theory. The distinction between referential and attributive uses allows Russell's logical form of denotation to subsist while creating a format in which any ambiguity is resolved in the context surrounding the phrase. The example on p. 293 of the definite description denoting Mr. Goldwater provides a clear distinction between Russell's idea of referencing and that of Donnellan.
In his rejection of Strawson's limited theory, Donnellan provides an example of the old man with the walking stick/umbrella. In this definite description, an object is misidentified and yet is still understood by the interlocutor as the object being referenced. Donnellan reasons that this indicates that even though the presupposition fails, there is still a reference. This example seemingly provides a clear need for a separate use of definite descriptions (i.e. reference) to deny any sort of truth gap. However I am unconvinced that the presupposition necessarily includes whatever the man is carrying. Could it not be that the presupposition is that there is a man who is carrying something? Does this misidentification actually cause a failure in Strawson's model?
I find it interesting that Donnellan suggests reducing any ambiguity of a definite description to it's pragmatic usage. It seems that this may be evidenced in lawyers manipulation of testimony.
I agree with you that Donnellan's theory improves on Strawson's theory in eliminating ambiguity. I think you chose a good example from the text that does a good job of proving that Donnellan's theory is an improvement on Strawson's and shows how ambiguity is resolved through context. I also think you raise an interesting point when you connect lawyers' manipulation of testimony
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