I believe the following five things.
(1) Barcelona will not win the Champions League.
(2) Manchester U will not win the Champions League.
(3) Chelsea will not win the Champions League.
(4) Liverpool will not win the Champions League.
(5) I falsely believe one of the statements (1), (2), (3) and (4).
This seems to me like a reasonable counterexample to Wittgenstein's doctrine.
topynate: It was only for reasons of space that I listed five events with probability 0.8 each, rather than 1000 events with probability 0.999 each; the modification is obvious.
Eliezer: Point taken.
I think Wittgenstein's point was that you're using 'believe' in a strange way. I have no idea what you meant by the above comment; you're effectively claiming to believe and not believe the same statement simultaneously.
If you're using paraconsitent logic, you should really specify that before making a point, so the rest of us can more efficiently disregard it.
I judge each of the four teams to have probability 0.2 of winning the Champions League. Their victories are mutually exclusive. Hence I judge each of statements (1)-(5) to have probability 0.8.
I believe the following five things.
(1) Barcelona will not win the Champions League.
(2) Manchester U will not win the Champions League.
(3) Chelsea will not win the Champions League.
(4) Liverpool will not win the Champions League.
(5) I falsely believe one of the statements (1), (2), (3) and (4).
This seems to me like a reasonable counterexample to Wittgenstein's doctrine.
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Hold on, Johnicholas, isn´t there a slip in the calculation concerning the third reader, case 4? You say
...but shouldn't this produce the answer (3:8) rather than (6:1)? The conclusion seems to be that as long as either the score is tied or "down" leads by one, readers will keep on voting according to their judgement, while as soon as either "up" leads by one or "down" leads by one, the next reader and all the following will ignore their judgements and follow suit.
Slightly more complicated, but still a great example!