THE PHONE BOOTH PUZZLE
In 1997 paper Jennifer Saul adduces various examples of the simple sentences in which the substitution of one co-referential singular term for another appears to be invalid. The author addresses the question of whether anti-substitution is 'logically' justified by examining the validity and soundness of a substitution of the co-referential singular terms in three simple-sentence arguments each exhibiting a different logical structure. The result is twofold. First, all three arguments are valid, provided 'Leibniz's Law' is valid with respect to the simple sentences (something Saul herself does not doubt). Thus, as far as these arguments are concerned, there is no logical problem with a substitution in the simple sentences. Second, two of the arguments cannot be 'sound', because their respective sets of the premises are inconsistent. Thus, it would be logically irrational to commit oneself to all the premises of the respective arguments. To the extent that the origin of Saul's puzzles is in logic (rather than pragmatics, say), the author suggests , tentatively, that substitution may appear to be invalid because the issues of validity and soundness have not been kept separate. The author then considers in depth Saul's first sentence, 'Clark Kent enters a phone booth and Superman exits'. Obviously, two-way substitution is trivially valid, if the expressions are co-referential semantically (and not just grammatically) the proper names, the conclusion being but a rephrasing of the premise. However, the author argues that a non-trivial semantic analysis of this sentence should take account of the diachronicity of Clark Kent's entrance and Superman's exit while preserving the internal link between being Superman and being Clark Kent. The author proposes the following. 'Superman' and 'Clark Kent' refer to two distinct individual concepts. 'Superman is Clark Kent' then no longer expresses the self-identity of an individual bearing two names, but that two named concepts are held together by the requisite relation: wherever and whenever someone falls under the concept of Superman the same individual also falls under the Clark Kent concept, whereas there are exceptions to the converse. This semantic analysis always validates the substitution of 'Clark Kent' for 'Superman', but validates the substitution of 'Superman' for 'Clark Kent' only if the additional condition is met that somebody should fall under the Superman concept when Clark Kent enters. The analysis is accompanied by a device of extensionalisation from the individual concepts to the individuals and two rules of a predication.
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