Quine's Philosophy of Logic, chapter 5 "The Scope of Logic" distinguishes logic from set theory in that logic gives no ontology and set theory gives one. He even says logic can "simulate" ontology by using schematic variables which look as if they took classes as values, but they actually do not. In contrast "When we take on set theory forthrightly and without simulation, we take on both vocabulary and ontology." That is page 72 but the thought recurs in slight variants throughout the chapter. The essay on Whitehead does not give this thought anywhere that I can recognize, nor do I find it concisely stated in the book Set Theory and its Logic.

Quine's Philosophy of Logic, chapter 5 "The Scope of Logic" distinguishes logic from set theory in that logic gives no ontology and set theory gives one. He even says logic can "simulate" ontology by using schematic variables which look as if they took classes as values, but they actually do not. In contrast "When we take on set theory forthrightly and without simulation, we take on both vocabulary and ontology." That is page 72 but the thought recurs in slight variants throughout the chapter.

The essay on Whitehead discusses the logical issues at length, but so far as I can see it does not specify that the difference between logic and set theory is that set theory has an ontology. Albeit numerous web sites claim Quine in this essay calls second order logic "set theory in disguise," the essay does not seem to discuss second order logic at all and does not seem to contain the word "disguise." I suspect that a reasonable interpretation of what Quine is saying, somehow morphed over time into a factitious quote.

The logical issues are discussed again in Quine's book Set Theory and its Logic but I do not find concise quotable expression of the philosophic claim that this is difference between logic and set theory .