When a theory is as accurate as relativity or as accurate as quantum electro dynamics; one may wonder if this very accuracy may be a warning sign something is amiss.
One physicist has mentioned the Sherlock Holmes mystery; where the key clue was "the dog didn't bark". Why didn't the dog bark on the night of the crime? Because the trespasser was known to the dog! The physicist (Possibly F.W.Peat) considers the question: why do experiments agree so well (and not "bark" at) the theory? (say of QED)
Could it be that QED and Relativity are not being "barked at" (refuted by) experiment because these theories are 'ALREADY KNOWN and the same thing as the experiment' in a different language?
Like using a carpenter's level (water running downhill) to determine if water runs downhill?
(Though this creates a new subtlety: if the theories were not circular but agreed with experiment; would the descriptions not also necessarily be the same thing as the experiment? How tell difference between the circularity of accurate description (identity) and the circularity of reflection (tautology)?
Re: QED and Relativity and Classical Mechanics: Richard Stafford allegedly proves that the whole thing is circular and "true by definition". If QED and Relativity are very accurate, it may be the accuracy that comes with circularity, or tautology. And Dr. Stafford may have shown that. I reckon it is possible to show Stafford's results much more directly and simply if he's right; maybe I'll manage to do that.
Re: probability: in the book "The Uses Of Argument" philosophy professor Stephen Edelston Toulmin demolishes the pretensions of probability, mathematical version included.
When you look at it: ALL probability statements (linguistic or mathematical) reduce to either statements about "how much you are willing to bank on something", or just circular arguments (that is, the conclusion is contained in the premises and is just a re-wording). Saying there is 1 chance in 6 of getting a 4 with a dice-toss is just another way of saying that the 4 is one of the 6 items in the set.