If 'actually being on David's right' were a necessary property of Paul, counterpart theory would be unable to evaluate Paul's modal properties without trivializing all actual relational facts as necessary, an unacceptable result (Lewis, 'On the Plurality of Worlds', 1986).

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'On the Plurality of Worlds' (1986)(the specific work being referenced): A major book by David Lewis arguing that all possible worlds—including ones different from our own—actually exist in some real sense.
Counterpart theory(as used in metaphysics and modal logic): A way of thinking about possible worlds where instead of asking 'could I have been different?', you ask 'is there a version of me in another possible world that is different?' That other version is your 'counterpart.'
David Lewis(the philosopher who created this theory): An influential American philosopher (1941-2001) who developed Counterpart Theory as a way to understand how we talk about objects in different possible worlds.
modal properties(Discussion of what entities bear modal properties in the context of the modal argument): Properties such as being necessarily true, contingently true, necessarily false, or contingently false, and being true or false at a possible world.
necessary property: A property F of an object o such that the singular proposition [o is F] is true at every index (time and world)
trivializing(what happens to physical laws if inconsistent math isn't controlled): Making something seem unimportant or meaningless when it actually matters.

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