After reading both of your posts I didn't know what you meant by induction nor what you were arguing against.

In my response I didn't explicitly urge you to stop using the terms "induction" and "subjective interpretation" (in an attempt to Replace the Symbol with the Substance through the game of Taboo Your Words). But I mentioned that we might find we agree on every important point after stripping away the purely definitional disputes. JoshuaZ and endoself made similar points here, though again they didn't explicitly tell you how to clear up the confusion. I'm asking you now to please find a new way of expressing yourself.

Until then I won't know if this next part actually affects your argument, but it seems worth saying anyway: your mathematical lemma does not deal with the sort of logical implications that scientists care about. If people frequently made statements such as, 'The Standard Model holds OR we won't find the Higgs Boson on the 23rd of July 2011,' then your lemma might seem like a perfectly natural and intuitive description of rational degrees of belief. In other words, your intuition may have misled you just because intuition often fails when it comes to mathematical statements that we can't interpret using our life experience to date.