THE AMBIGUOUS AND THE SINGULAR IN FREGE AND RUSSELL'S PUZZLES. THE PARADOX OF ANALYSIS

The controversy on how to deal with Frege's puzzle about Leibniz's Law (about whether the cognitive value of a = a becomes essentially equal to that of a = b, if a = b is true) is treated, starting from the analysis of the sentence proposed by Russell: "George IV wished to know whether Scott was the author of Waverley", and similar ones. It is emphasized how the logical formalization of an ambiguous expression of ordinary language, in no way has the capacity by itself to transform that ambiguity into a singular, more exact proposition. A precise awareness of the difference between the knowledge provided by an ambiguous expression and the extended information, in the form of conjectures, offered by the singular expressions issued from it, is necessary. By not taking this into account, indeterminate expressions, which are valid as a logical possibility, with the application of Leibniz's Law, inadvertently become considered as having a truth value that belongs exclusively to the singular propositions with which they are confused when appealing to additional information that these expressions do not provide independently, which generates the puzzle. To avoid this problem, a simple extension to the enunciation of Leibniz's Law is proposed.