Originally Posted by Dave Rogers
That statement is not supportable. Just because we haven't demonstrated any improved basis for selection among hypotheses does not mean that such a selection criteria does not exist. It also ignores my objection that Occam's Razor(OR) criteria is not easy to define in practice.
Yes there are an infinite number, but I disagree that we can't maintain them all. Isn't this exactly what we do when we keep an open mind where evidence hasn't accrued ? Since this method avoids selection of a single likely-falsifiable hypothesis then it is not a waste of effort - it's potentially a great savings.
No, it's not an infinite task. It's just a matter of directly representing our lack of knowledge within the scientific model rather than making a presumptive guess about the OR hypothesis.
You are viewing my suggestion incorrectly. I did not say that we should should tentatively accept each individual hypothesis that matches current knowledge. I suggested that we tentatively accept the entire class as a whole. That we embrace and quantify the lack of knowledge. So there is no "costly blunder" coming down the road.
Occam's Razor does select a single simple hypothesis among the set, and therefore it typically selects a falsifiable (wrong) hypothesis. Any explanation based on this may be wrong as a result. You are assuming that an arbitrary simple guess at a hypothesis has more explanatory power then considering the full set of possibilities and the factual limitations of the observations..
My point is not to present some new scientific method full-blown, and it's not reasonable for you to (repeatedly now) demand that.. I am primarily arguing that the single hypothesis, Occam's Razor(OR) selection criteria is a very weak point in the 'standard model' and that there may well be better ways to represent observational knowledge.
What I am suggesting is that in addition to accumulating the simplest OR hypothesis that we also incorporate the limitations of the observations and conclusions directly in the model. We want the error bounds and we want the limited experimental conditions reflected in the model.
Perhaps you didn't recognize the language, but OR, and the parsimony principle is said to select the hypothesis with the least number of presuppositions
. So yes it matters greatly wrt to the the 'scientific method' which hypothesis has the least presuppositions, since that determines which hypothesis is selected for inclusion.
Aside: So Lorentz eqn has no benefit whatsoever over the Newtonian model ? That's not a statement I can support.
You are making another strawman argument against my suggestions. I never said that we should carry out calculations on the entire infinite class of hypotheses. Further the series expansion in this case has a closed form and is not hard to calculate.
You seem obsessed with the amount of computation involved, or with the theoretical complexity involved in considering a class of hypotheses but that is not really a great issue in practice. What I am suggesting is that there is no reason to promote one OR compliant hypothesis and exclude others in the model. There is no reason to allow extrapolation without a clear disclaimer. We can instead tentatively accept all compliant hypotheses.
Newton might study kinetic energy vs velocity & mass under a restricted range of velocities and mass and with some limited accuracy, and after some polynomial fitting might still conclude that KE = (1/2)*m*v^2 ,but ... A: under the range of the experiment, B: within some calculated error bounds, and C: other higher velocity terms are zero to within the accuracy of the experimental method. This form of hypothesis would incorporate the limitations of the hypothesis within the model. This form of conclusion does not contradict the relativistic calculation of KE. All this does is explicitly include the limitations in the model.
No - we should always try to improve over the status quo - even at the cost of some complexity.
Instead of tentatively accepted a single simple and likely wrong OR hypothesis we can incorporate the limitations of that conclusion directly into a model system. This prevents exclusion of other compatible hypotheses. It does not prevent any theorist from creating unjustifiable assumptions and extrapolations. The calculations are still the same except you must acknowledge the error bounds, the extrapolations and non-compliant conditions.
It's a little surprising that we haven't already created a formal model system for the scientific method. Modern computation is up to the task. I recall reading papers related to this as early as the late 1970s.