Though the point Sewing-Machine made about NP-completeness is completely apt, one should not take NP-completeness as a sign to stop thinking; it’s too prevalent.
The original question implicitly gave an argument something like: Alicorn has (various enumerated) good reasons to believe that “ways to cook marshmallows” is within her expertise. A straightforward query yielded only one way, requiring an open fire. Therefore, she can conclude that it is difficult or infeasible to cook marshmallows without an open fire.
I vaguely recall a quote something like “If an expert believes a thing is possible, they are very likely correct. However, if an expert believes a thing is impossible, they are very likely mistaken.”
Possibly we can take this as a recipe for judging / weighing specific kinds of arguments. I think Douglas Walton calls this kind of argument “argument from position to know”, and we could add a checklist for judging argument of this sort, something like: Is the claim universal over a combinatorially large domain? Does the expert have a reason, other than their expertise, for their belief? If not, discount the expert’s belief as the expert is likely to be overconfident.
“When a distinguished and elderly scientist says something is possible, he is almost certainly correct; when he says something is impossible he is very probably wrong.”
Apparently he presented this as the first of three principles, the others being:
“The only way of discovering the limits of the possible is to venture a little past them.”
And the third is probably the most famous one:
“Any sufficiently advanced technology is indistinguishable from magic.”
Though the point Sewing-Machine made about NP-completeness is completely apt, one should not take NP-completeness as a sign to stop thinking; it’s too prevalent.
The original question implicitly gave an argument something like: Alicorn has (various enumerated) good reasons to believe that “ways to cook marshmallows” is within her expertise. A straightforward query yielded only one way, requiring an open fire. Therefore, she can conclude that it is difficult or infeasible to cook marshmallows without an open fire.
I vaguely recall a quote something like “If an expert believes a thing is possible, they are very likely correct. However, if an expert believes a thing is impossible, they are very likely mistaken.”
Possibly we can take this as a recipe for judging / weighing specific kinds of arguments. I think Douglas Walton calls this kind of argument “argument from position to know”, and we could add a checklist for judging argument of this sort, something like: Is the claim universal over a combinatorially large domain? Does the expert have a reason, other than their expertise, for their belief? If not, discount the expert’s belief as the expert is likely to be overconfident.
The quote is from Arthur C. Clark:
Apparently he presented this as the first of three principles, the others being:
And the third is probably the most famous one:
Thanks!
Thank you for making me look it up. I thought it was Isaac Asimov for some reason!