Look at http://www.science20.com/the_hammock_physicist/falsifiability_and_the_integrity_of_physics-151714 and then consider my point of view.
There is
triple truth requirement in science. First the models used must be among the atlas
that cover the reality with well understood demarcation lines between different
theories. That is math in the theory must be correct.
Second the measurement
model used with physical model must be consistent and the limitations on measurement
model must be respected. You should decide right math with right devices you
use for measurement. Understand your devices.
Now you
have two models physical model and measurement model. But it is not enough. You
have to have model for gathering information and making predictions and
inference. You need mixed model of experimental results and analysing
statistical model, for instance Bayesian inference method.
As a result
you can have only approximation of the true value you are looking in
experiments.
This
interaction of tree theories is a loop or a proses. Form some argument you can
improve the result, the theory and the devices and methods of experiment.
The
subjective truth is in what you believe you have find. You can be sure, but the
others try to confess that you are not right yet.
The truth
as we understand it may not lie on lose ground. This is our forth model we have
to use. The logic is a theory and some of them are incomplete and we have some
unknown reason to believe to unprovable truths.
Science
want to limit it methods to provable logics that are independent about the
observer who proved. That is a challenge.
