[EM] Clarification on Bart's Pij definition

[MIKE OSSIPOFF]

The surest interpretation of the "given..." clause, based on its
position, is that it's a modifier for "probability", and that it
specifies the conditions under which the probability is defined.

One other thing:

When I spoke of the absurd contradiction of saying that my statement
#3 isn't true, I assumed that we accept the contrafactual claim
that Blake says is accepted by mathematicians. If we don't accept that,
then of course, if Richard wanted to object to statement #3, it would
have to be by saying that, though he agrees that if i & j are
frontrunners, then if there's a tie, it's between them, he denies
that if it's true that i & j are frontrunners, then it's true that
if there's a tie then they're in it.

That's at least as absurd.

Maybe Blake's claim is based on the idea that a statement should
always be true unless shown false. But why that instead of saying
that a statement is false unless shown true. It seems that Blake
is giving mathematicians an unreasonable amount of authority to
establish what's true on EM. If there's no tie, the the most accurate
thing that could be said about the statement "If there is now a tie,
it's between i & j", is that it's untrue & unfalse, because, without
a tie, it isn't saying anything about whether the tie is between i & j.

Mike Ossipoff

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