Lewis's principle of 'precisification' shows that for any vague predicate, there exist multiple equally legitimate sharp extensions, all corresponding to precise worldly properties.

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Equally legitimate(as used in epistemology): Having the same level of validity or justification; one is not better supported than the other.
Lewis(philosopher who created the similarity metric being discussed): David Lewis was a famous American philosopher who developed influential theories about possible worlds—alternative ways reality could have been.
Sharp extensions(as the possible precise meanings of vague words): The precise, boundary-free meanings you get when you fully specify a vague word. If you decide exactly where 'tall' begins and ends, that's a sharp extension of the vague word 'tall.'
Worldly properties(as what the bridge principle should map onto): Actual characteristics or qualities that exist in the real world outside our minds, like the redness of an apple or the hardness of a stone.

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