 A second objection against second-order logic can be traced back to Quine (Quine 1970). This objection states that the interpretation of full second-order logic is connected with set-theoretical questions. This is already indicated by the fact that most regimentations of second-order logic adopt a version of the axiom of choice as one of its axioms. But more worrisome is the fact that second-order logic is inextricably intertwined with deep problems in set theory, such as the continuum hypothesis. For theories such as arithmetic that intend to describe an infinite collection of objects, even a matter as elementary as the question of the cardinality of the range of the second-order quantifiers, is equivalent to the continuum problem. Also, it turns out that there exists a sentence which is a second-order logical truth if and only if the continuum hypothesis holds (Boolos 1975). We have seen that the continuum problem is independent of the currently accepted principles of set theory. And many researchers believe it to be absolutely truth-valueless. If this is so, then there is an inherent indeterminacy in the very notion of second-order infinite model. And many contemporary philosophers of mathematics take the latter not to have a determinate truth value. Thus, it is argued, the very notion of an (infinite) model of full second-order logic is inherently indeterminate.