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The answer, I should think, is that B is not improbable with respect to that conjunction.
To apply the reduction test, we must ask whether B is improbable with respect to the conjunction of A with EBS−B.
Of course B itself might initially be a member of EBS, in which case it will certainly not be improbable with respect to it.
But defeat is not impossible; it sometimes happens that one does acquire a defeater for a belief B, by learning that B is improbable with respect to some proper subset of one's evidence base.
"Perhaps B (the proposed defeatee) is improbable or unlikely with respect to part of what I believe," she says, "but it is certainly not improbable with respect to the totality of what I believe, that totality including, of course, B itself".
Call the result of deleting B from S's evidence base 'EBS reduced with respect to B'EBS−BBS−B' for short.[11] And now the suggestion — call it 'the reduction test for defeat' — is that A is a defeater for B just if B is appropriately improbable with respect to the conjunction of A with EBS−B.
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Our question is whether A, the belief that Simon's theory is proper science (and that it entails the denial of B), is a defeater for B. Add A to S's evidence base; and now the right question, perhaps, is this: is B epistemically improbable or unlikely with respect to the conjunction of A with EBS?
Obviously, this is consistent with p remaining very improbable on balance with respect to a set of total evidence.
With respect to EByou−P, P is epistemically improbable; after all, you have the same evidence as the jury for ¬P, and the jury is quite properly (if mistakenly) convinced that you did the crime.
with respect to politics.
What stance with respect to the world?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com