In this paper, the authors show that there is a reading of
St. Anselm's ontological argument in Proslogium II that is logically
valid (the premises entail the conclusion). This reading takes
Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language
and logic in which definite descriptions are genuine terms, and in
which the quantified sentence "there is an x such that..." does
not imply "x exists". Then, using an ordinary logic of
descriptions and a connected greater-than relation, God's existence
logically follows from the claims: (a) there is a conceivable thing
than which nothing greater is conceivable, and (b) if <em>x</em>
doesn't exist, something greater than x can be conceived. To
deny the conclusion, one must deny one of the premises. However, the
argument involves no modal inferences and, interestingly, Descartes'
ontological argument can be derived from it.