### Theorem

Branden Fitelson recently brought the following result to my attention.

Theorem:At least one of the following claims is false.

Qualitative Law of Likelihood:$E$ favors $H_1$ over $H_2$ if and only if $\Pr(E|H_1)>\Pr(E|H_2)$.Likelihood-Ratio Measure of Confirmation:The degree to which $E$ confirms $H$ is $\Pr(E|H)/\Pr(E|\sim H)$.Favoring-to-Confirmation Bridge Principle:If $E$ favors $H_1$ over $H_2$, then it confirms $H_1$ more than $H_2$.