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Old 22nd August 2011, 12:24 AM   #106
stevea
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Join Date: Aug 2007
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Originally Posted by Dave Rogers View Post
Agreed. Until the hypotheses are tested under these newer conditions, we cannot determine in advance which will fail, so at the earlier stage of knowledge we cannot select between them other than by some arbitrary criterion.
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.

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The problem with that suggestion is that there must be an infinite number of potentially accurate hypotheses, and we cannot maintain all of them. If we maintain less than an infinite number, it seems a waste of effort to maintain more than one.
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.

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As will any other criterion that isn't based on knowledge that we do not have. So we can't consider the set of all supported hypotheses, because it's a task of infinite complexity.
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.

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OK, let's talk about cost. It may, indeed, be a costly blunder to accept the simplest hypothesis rather than considering all supported hypotheses. However, it must inevitably be a costly blunder to consider all supported hypotheses, for two reasons: firstly, some of them will at a later time be falsified, leading to your retrospective conclusion that any use of them was a blunder even if it didn't lead to any significantly inaccurate predictions of phenomena; and secondly, without the choice imposed by Occam's Razor, every phenomenon requires not a single, but an infinite set of explanations, and every calculation an infinite set of iterations. Without some selection criterion, no progress will ever be possible, because no calculation can ever be completed.
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..

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Yes, it's possible. Do you have any better suggestions than using the theory that combines being the simplest to use with being always correct as far as we know?
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.

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It really doesn't matter whether one is considered a greater presupposition than the other.

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.

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What matters is that, if calculations of motion had been carried out using the full Lorentz form, enormous amounts of extra work would have been required, resulting in no benefit whatsoever. We are trying to reduce the complexity of tasks, not enhance it.
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.

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Perhaps, alternatively, we should carry on doing what we do at the moment, which is to take note of more complex hypotheses that explain phenomena correctly, to put them aside until their applicability can be determined in the light of new data, and in the meantime to use the simplest hypothesis that accurately predicts all the existing data. That way, we make our lives easier, rather than gratuitously, and potentially infinitely, more difficult, while retaining the potential benefit of more complex hypotheses as and when they're needed.

Dave
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.
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