I just discovered a text that I wrote somewhere around 1991. I hope it has a good combination of sense and humor to be amusing. It was an answer to a part of somebody's post on comp.ai.philosophy:

... "There are infinitely many theories interpreting a given finite set of experimental data"...

There seems to be just one object that is unique for a given set of data, and it is the CLASS of all theories that explain it. Just a few related ideas:

• Additional data can narrow the class, but not 'refute' it.
• A class of theories for a combination of two sets of data is an intersection of their two classes.
• "Minimized class" : Class stripped of the member theories that are supersets of other member theories (get rid of irrelevant pieces and unnecessary complexity).
• "Independent phenomena": sets of data whose minimized classes of theories don't intersect.
• "Acceptable explanation": any part of the class which has a non-empty intersection with My Current Understanding of The Subject (an arbitrary subset of the Class of theories explaining previously observed data).
• "An open mind (class)": one that excludes a situation when the only acceptable theory for new data is the "Wrong data" theory.
• "Useless/redundant data": any set of experimental data whose class of theories includes the class we already have.
• "Useless experiment": one that can yield nothing but useless data.
• "A simple theory": one that doesn't stick out too much after its projection on the existing class of theories.
• "The Ultimate Wisdom": the projection of the SuperClass of theories on the SuperSet of data = intersection of all classes of theories for all [potentially] observable data. Can be a pretty rich class of theories, if the [potentially observable] world as a whole allows alternative explanations; can be The Only One True Theory (?). I suspect that it might be The Wrong Data Theory. ;-)
• "Sufficient data": a set of data whose class of theories = The Ultimate Wisdom. Probably a lot smaller than The Whole World, in which case the rest of the world is unnecessary. Which might mean that the whole thing was not designed by a perfect being - or was intended for observers with a larger field af accessible data.

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All this stuff can be formally defined in terms of sets of theories, functional operators in semantic space, projections, factorizations, or some other form, and probably even should (or maybe it was?).