Daniel Chew, currently studying at WSC, recently wrote a paper on science. http://puritanreformed.blogspot.com/2011/05/paper-science-as-paradigmatic-critical.html
He offered some additional comments not in his paper in this post: http://puritanreformed.blogspot.com/2011/05/science-and-fallacy-of-induction.html
It’s straightforward, lucid, and worth sharing a taste:
In Fig. 3, we once again see our proposed equation in black, and the alternate equation in red. Now however, we have a competing equation of the form y=3x-1+ 1/(1000-100x). Now, it can be seen that no matter how much data we have from 0<x<9 thereabouts, there is simply no way to differentiate between the two equations. If all our data points are within that range of x values, then we simply have no way to choose between them.
What does this tell us about science therefore? Science is limited. Science cannot give us the truth of anything. What science does is to give us a working description of reality (which is of course immensely practical in application), but it does not explain it. And the working description of scientifically derived laws are circumscribed by the limitations of the experiments, but we can cannot go beyond it. As I am sure it is still taught in classes on scientific methodology, scientists are not allowed to extrapolate their equations beyond the range of their data. For instance, in the initial data set of 3 points given, nothing should be said of anything with an x value of 4 or 5. If the data set has a highest x value of 7, nothing should be said of what the case would be if x=9.
This has implications especially for what is called ‘historical science’, which is the investigation of the past using scientific methodology. Since scientists are not and cannot be in the past, all of such historical science investigations are inherently fallacious. Most of them of course are done within the framework of naturalistic uniformitarianism, which as a philosophy is not science and is not testable. Translated into data interpretation, it is a hopelessly naive methodology which assumes that the simplest interpretation of existing data points must hold true in the past too. Thus, if we have the data set above, uniformitarianism simply assumes that the equation must be a linear one. If another data set seems to follow a quadratic or simple logarithmic equation, then that must be the right type of equation.