Some American philosopher exists = Some philosopher is AmericanIf we take the right hand, we range over every philosopher and test whether they are American. E.g., we ask whether Quine is American. This test does not explicitly test for 'existence'. But if we take the left hand, we range over every American philosopher, and test for existence. This test explicitly invokes the concept of existence. E.g. we have to ask whether Quine exists. Therefore the definition above is circular. Even though 'exist' isn't explicitly invoked on the right hand side, it is implicitly and irreducibly part of the sentence.
Against, consider the Latin translation of the definition above.
Quidam philosophus Americanus est = Quidam philosophus est AmericanusThe only difference is word order. Latin is flexible about word order, as its semantics are given by inflection, unlike in English. So we can either put the copula 'est' at the end of the sentence, as on the left, or we can interpose it between 'philosophus' and 'Americanus', as on the right. The semantics, indeed the syntax of the two sentences is identical. What becomes of our argument? Well, it is invalid because it involves a mistake about logical form. We can only descend via the subject of a subject-predicate sentence, if all such sentences really have the logical form subject-copula-predicate. We obviously can't pretend that the subject and predicate are really a single subject, and that the copula 'is' is really a predicate. That was the whole point of Aristotle's remark about 'is' being used as a 'second element', which I discussed here. Therefore we cannot descend to singulars by ranging over individuals which satisfy subject and predicate together, and the 'descent' argument is invalid.
Against that. In reply, the Phoenician may object that a sentence like 'Quine exists' (or 'Quine is', if you like) is certainly meaningful. Then either (a) the proper name 'Quine' embeds a hidden subject and predicate Qa-Qb, just like 'American philosopher', and so 'Quine exists' really means 'Qa is Qb'. But that seems implausible. Or (b) the verb 'is' is genuinely a predicate, in which case the descent to singulars argument is valid.
PS today I drive to Rushmoor in Surrey, hoping to locate the place where Russell began work on Principia Mathematica, and where he wrote the letter to Frege that I discuss here. If this is successful, I may return with photographs.