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An Application of the Theory

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 tex2html_wrap_inline458 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.gif 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:

tex2html_wrap632

tex2html_wrap633

tex2html_wrap_inline652

The indicating situation, tex2html_wrap_inline458 , is

tex2html_wrap_inline656

where a is the x-ray and t' the time. We assume that tex2html_wrap_inline458 is factual, that is that tex2html_wrap634 . Now let f be any anchor defined on x and t (at least) such that

displaymath646

(Thus, tex2html_wrap_inline666 and tex2html_wrap_inline668 .) Then P = the proposition that

displaymath647

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:

tex2html_wrap_inline684

where T, the indicating type is as before. T', the indicated type is

tex2html_wrap635

and T'', the connecting type is:

tex2html_wrap636

As before, tex2html_wrap_inline458 is:

tex2html_wrap_inline656

Again, we assume that tex2html_wrap_inline458 is factual. Further, we assume that the connecting state of affairs, tex2html_wrap_inline698 is factual. Where b is Jackie, tex2html_wrap_inline698 is

tex2html_wrap_inline704 .

Any anchor f, such that tex2html_wrap637 , 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 tex2html_wrap_inline458 relative to tex2html_wrap_inline594 and tex2html_wrap_inline524 is the proposition that

tex2html_wrap638 .

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.


next up previous
Next: The Flow of Information Up: Information Previous: Information

John Perry
Sat Nov 16 22:19:34 PST 1996