"I am going to argue that we ought not to adopt 
the Brouwerian axiom (or B); it is not true of 
the metaphysical modality that applies to 
existence.  B is p … †‡p; that if something is 
the case then it is necessarily possibly the 
case.  I will do this by introducing a trilemma: 
that the conjunction of actualism, the B, and the 
belief that some objects exist contingently is 
impossible.  I will consider Alvin Plantinga’s 
attempt to resolve this trilemma through his 
applied semantics of individual essences and argue 
that they bury the problem rather than resolve it. 
I will argue that if we really are committed to 
actualism and to the belief that there are contingent 
beings, then we ought to endorse a modal logic that 
does not include B, such as S4.  My overarching 
target throughout this paper is Plantinga’s S5 
valid ontological argument."