Shannon's information theory and foundations of mathematics

[Vaughan Pratt]

Recently Rohit Parikh suggested to me that disinformation was not
information.  As I've always considered disinformation about any given
proposition to be less likely that the conventional wisdom about it, it
seemed to me that with Shannon's information theory, a less likely message
contains more information than a more likely one.  Hence in particular
disinformation should convey more information than the conventional wisdom.

Is there a foundational way of approaching these seemingly conflicting
notions of information that isn't too wildly ad hoc?

Vaughan Pratt
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