What is proof?

[madnak]

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I guess I am questioning what level of precision the nature of this subject admits?

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It's sad that no real "proof" can be had where empirical disciplines are concerned. After all, logic can only derive conclusions from initial premises - in math, these initial premises (axioms) are both "obvious" and well-defined. Theoretically, it is possible to establish an empirical discipline as "perfect" as mathematics, but you would have to have a rigorous set of logical assumptions about the world that everyone agrees with (probably impossible). The issue of limited information in the real world also implies that definite conclusions will always be probabilistic conclusions (ie never "this is true" but always "this is n% likely to be true"), and that some conclusions can never be definite (due to a potentially infinite range of possibilities in many cases). Intuition is a much better approach in the real world.

I'm not interested enough in this particular case to study everything, but based on your summary the evidence seems damning. The behavior of the alleged cheaters is very unusual (and thus unlikely to be coincidental). This behavior is also consistent with cheating - I can't think of any other hypothesis that would explain it. From the look of things, there are no other plausible explanations being presented. Furthermore, the circumstantial evidence supports the cheating explanation. Finally, there is no way for the situation to be engineered (to frame the cheaters, for instance) - the information itself seems reliable.

To get at your original question - other than an outright admission of cheating, what more evidence could there possibly be in a case like this? As a rule of thumb, if the information we have represents the highest standard of evidence that we can realistically apply (given our technological means), that generally indicates a "very high" level of precision relative to the subject. All the bases appear to be covered in this case.

[BTirish]

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I guess I am questioning what level of precision the nature of this subject admits?

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It's sad that no real "proof" can be had where empirical disciplines are concerned.

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Why is it sad? Why should everything demand the kind of certainty had in mathematics?

[madnak]

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Why is it sad? Why should everything demand the kind of certainty had in mathematics?

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For one thing, I think technology would move along at a much faster pace. But I'm just talking about the lack of simplicity, and my own discomfort with uncertainty.

Edit - fixed nesting problem.

[tame_deuces]

You have uncertainty in almost anything except abstracted knowledges (like math), a little uncertainty goes along way - guessing is actually an incredibly effective way of handling data, if you can give your little guesswork a probabilistic nudge then all for the better. Good guessing is extremely efficient.

[madnak]

Sure, but if proof were available it'd be better.