Metalanguage for actual, modal, and intentional contexts

[John F Sowa]

There has been some discussion about modal and intentional logics.  But it's possible to replace all such logics with ordinary first order logic just by using metalanguage.  The following diagram shows the kinds of relations that can be used to replace those logics with FOL.  The relation named 'possible' relates a diagram that describes the actual state to a diagram of the modal state.  The relation named 'intended' relates a diagram of an actual world and a person to a diagram of a state that person intended.

With ordinary FOL plus these two new relations, It's possible to define and use an open ended variety of ways of talking about and relating contexts.  New options may include contexts that are desired, feared, wanted, rejected, preferred, despised, foolish, or brilliant.  There is no limit to the number of ways  of thinking, talking,, and representing relations among contexts.

These options provide a much richer and more flexible range of options than a modal logic that only supports a two-way distinction of necessary or possible.   They show that metalanguage with ordinary FOL provides a much greater range of options than any kind of modal or intentional logic.  

Furthermore, it does not require any special kind of theorem prover.  Any system that can reason about physical things can be used to reason about the way people think and talk about anything --- including themselves.  It's simpler and more general than inventing a large number of special purpose logics.

John