There are a number of connected reasons why this won’t work. Here are the main characteristics of the relativistic logic (RL) I have defended here.
- In RL there are two forms of negation for singular sentences. There is a narrow form ‘nonF(a)’, which is true when a exists and it is not the case that Fa, i.e. a is a nonF; and a wide form, which is true when either nonF(a), or when a does not exist. Excluded middle applies only to the wide form, naturally. By contrast, MPL has no such feature.
- In RL, a sentence of the form ‘An S is P’ has a narrow existential sense: it is convertible with ‘An S-P exists’. There is no distinction between a wide sense conveyed by ‘some’, and the narrow sense conveyed by ‘exist’. RL is not Meinongian. By contrast, it is open to MPL to invent an existence predicate ‘E()’, which may satisfied by some members of the domain, but not by others.
- As a direct consequence, in RL, the wide negation ‘it is not the case that Fa’ never implies the existential form ‘some x is non-F’. By contrast, in MPL a singular sentence is existential, at least in the wide sense: ‘~Fa’ implies ‘Ex ~Fx’.
- A further difference, though probably not relevant here, is that some relational statements in RL are not existential. ‘aRb’ does not always imply ‘Ex aRx’, namely in the case where ‘R’ is not logically transitive. This is how RL avoids the problem of intentionality without invoking Meinongian non-existent objects.
Another argument: how can we even say in MPL that Vulcan does not exist? The sentence ‘~Ex x=v’ will not do, for it asserts of something in the domain that it is not in the domain; ‘~E(v)’ will do, where ‘E’ means ‘exists’, but this comes at the price of Meinong’s junkyard. For ‘~E(v)’ implies ‘Ex ~E(x)’, which is precisely Meinongianism. Or it can be denied that ‘OM(v)’ means anything at all, which is strong Direct Reference of the familiar variety. There is no escape. Either we adopt a radically different semantics and inference schemata, on the lines of RL above, or we are left with Direct Reference.