Existence: Single or Double?

Abstract

Presumably most people distinguish between real (or de re) existence and ideal (or de dicto) existence. For instance, we normally distinguish roads from road maps. This distinction is so fundamental, that those who fail to draw it are diagnosed as schizophrenics in daily life, and as logicians in academia. In fact, a logical imperialist, such as Tarski or Quine, claims that there is a single existence concept, valid in physics as well as in mathematics, namely, the existential quantifier. Who is right in this case: commonsense or the sophisticated mathematical logicians? Let us see.