A question arising on the Foundations Of Math List gives me an opportunity to introduce the subject of higher order propositions, which I think afford a better way to handle the situations of confusion, doubt, obscurity, uncertainty, and vagueness often approached by way of variations in the values assigned to propositions.
- My own preference for t-definite, t-indefinite or f-indefinite, and f-definite, as opposed to tautology, contingent, and contradiction lies in allowing application of those terms for truth as well as for validity, for semantic and syntactic uses.
If we start with a universe of discourse and think of propositions as being (or denoting) functions of the form where then what we are charged with is choosing suitable names for higher order propositions of the form
The term tautology or 1-definite is true of exactly one namely the constant function
The term contradiction or 0-definite is true of exactly one namely the constant function
The term contingent or indefinite is true of all the functions which are neither of the above.
Here is a place where I took the trouble to think up names for higher order propositions over a 1-dimensional universe.
I called the contingent propositions either informed or non-uniform.