Constants, Inconstants, and Higher Order Propositions

Peircers,

A question arising on the FOM List provides me
with an opportune excuse to broach the subject
of “higher order propositions”, which I think
afford a better way to handle the situations
of confusion, doubt, obscurity, uncertainty,
and vagueness that are often approached by
way of variations in the values assigned
to propositions.

Re: Irving Anellis
At: http://cs.nyu.edu/pipermail/fom/2012-November/016822.html

IA: 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.

Irving,

I like that usage.

If we start with a universe of discourse X and think of propositions
as being, or being represented by, functions of the form f : X -> B,
where B = {0, 1}, then what we are doing here is choosing suitable
names for higher order propositions of the form m : (X -> B) -> B.

The term "tautology" or "1-definite" is true of exactly
one f : X -> B, namely the constant function 1 : X -> B.

The term "contradiction" or "0-definite" is true of exactly
one f : X -> B, namely the constant function 0 : X -> B.

The term "contingent" or "indefinite" is true of all
the functions f : X -> B that 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.

http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Functional_Logic_:_Quantification_Theory#Higher_Order_Propositions_and_Logical_Operators_.28n_.3D_1.29

I see I called the contingent propositions either "informed" or "non-uniform".

Regards,

Jon

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