Let's now apply the theory more formally and fully to our example involving Jackie's leg and the x-ray. We can consider this as a case of pure information or of incremental information.
In both cases, the indicating fact
is the x-ray's being of a
certain type at t. When we consider the pure information, we have in
mind the following simple constraint: whenever there is a state of
affairs consisting of some x-ray's having such and such a pattern at
some time t, then there is a state of affairs involving a dog's
leg having been the object of that x-ray and that leg's being broken
at t.
So the indicated
proposition is that there is a dog of which this is the x-ray, and it
has a broken leg. The pure information is about the x-ray, but not
about Jackie, or her leg.
Using the resources of situation theory, we represent the simple constraint as follows:
The indicating situation,
, is
where a is the x-ray and t' the time. We assume that
is
factual, that is that
. Now let f
be any anchor defined on x and t (at least) such that
(Thus,
and
.) Then P = the proposition that
Thus P is the proposition that the state of affairs which consists of some dog being the object of a, the x-ray in question (at t', the time in question) and that dog's having a broken leg (at the time in question) is factual. Or, more simply, it is the proposition that there is some dog whose leg is depicted by a at t' and whose leg is broken at t'.
When we consider this as a case of incremental information, we have in mind the relative constraint that if an x-ray is of this type, and it is the x-ray of a dog, then that dog had a broken leg at the time the x-ray was taken. The fact that the x-ray was of Jackie is the connecting fact, and the incremental informational content is the proposition that Jackie has a broken leg. This proposition is about Jackie, but not about the x-ray.
The relevant relative constraint is:
where T, the indicating type is as before. T', the indicated type is
and T'', the connecting type is:
As before,
is:
Again, we assume that
is factual. Further, we assume that
the connecting state of affairs,
is factual. Where b
is Jackie,
is
.
Any anchor f, such that
, must be defined on the parameter y
of the connecting type, in particular, it must anchor y to
Jackie. Thus, for any such anchor f, the proposition carried
incrementally by
relative to
and
is
the proposition that
.
This is a singular proposition about Jackie, and not at all about the x-ray. And it is, after all, Jackie that we're concerned about.