Classes of theories
Alexander Chislenko -
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
- "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
- "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.
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?).