This is not unsound in the usual sense of "logical soundness" (which applies to logical systems such as first-order logic, rather than specific theories in the

This is not unsound in the usual sense of "logical soundness" (which applies to logical systems such as first-order logic, rather than specific theories in the system such as ZFC). This is unsound in that it runs counter to certain philosophical commitments, namely that there should be some tangible, physical realization of all the natural numbers (although if you really go far in that direction you end up with ultrafinitism, which most set theorists would find unpalatable, so the philosophical implications of all this are rather tricky).