Instead of proceeding as originally intended, having read your additional posting during my ‘absence’, what constitutes science seems more important for facilitating this discussion.
Per your post Mon, 20 Jul 15 12:43 AM states “Whereas science is defined by … sequence - provisional hypotheses founded atop supportive observations and where measurement is possible, mathematics, followed by attempted disproofs and/or the discovery of environmental limitations, leading to fresh hypotheses.” This is well composed but as a comprehensive statement describing the sciences it is inadequate. Actually this description is, in practical terms, only true for the physical sciences and then only true in a way often not related to reality.
In my own work, which is not atypical in the physical sciences, there are no instruments capable of directly measuring the particles of interest. Instead various instruments are use, none of which are adequate for measurements, from which we infer what is being measured and upon comparing the various outcomes we further make judgment based conclusions.
In the traditional scientific method approach, the researcher isolates what is to be investigated to simplify the situation. This means eliminating as much of reality as possible so that the entire contents of the black box is known and one can therefore assume that all causes and effects are related to the subject experiment. Young people might assume that the conclusions hold true when brought back into the real world – they would be wrong.
So, in my work, I can’t measure what I want to characterize and I can’t observe what is operative and instead I can only formulate a model, an explanation of behavior, and from that model make decisions that can sometimes leads to progress in predictability. Very often, years later, I find that the breakthroughs that were obtained are not properly explained by the models that were adopted at the time (termed 'tracking the wrong variable'). Our work is highly uncertain. It does not bother me that I can’t see what I think is the operative factor that makes things happen.
What I was taught was to forget the “scientific method” since it is too simplistic (not related to reality because most of the real environment is eliminated in highly controlled experimentation). Instead, formulate a model and from this model make a projection about outcomes that could be expected from this or that set of conditions. Then sequentially assume each of all of the possible outcomes in a thought experiment. From this analysis see if there is one or more trials that could be conducted that would indicate if the model is close to reality. Do not test the hypothesis, instead, extrapolate further out and again do the thought experiment for each set of assumed outcomes. Now seek to identify a trial that would indicate if the assumptions are somewhat true or blatantly false. This approach avoids the simplicity of the false world of controlled, highly purified, experimentation and keeps the entire effort grounded in reality. The traditional scientific method will eventually arrive at the same result but will takes several generations longer to get there.
The soft sciences (economics, psychology and others) do not admit to controlled, purified, experimentation or even any experimentation. Measurements are largely impossible to conduct. How does one measure love or emotional stress or even craziness? Yet the fields of investigation are still termed science and accepted as such.
In the sciences, my opinion, the key to progress is ‘observation that discerns significance’. It is not enough to observe. One must observe in a way that significance is realized and consolidated into a hypothesis. Everyone can see the stars or the moon moving at night. Few can see that some motions have significance to certain questions. Once the motions of significance to a particular question are observed one can then hypothesize a model even if what is hypothesized cannot be seen or measured. The validity of the model comes from its ability to be correctly predictive.