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Bach-Peters paradox

**SYNTAX: **paradox in the description of sentences such as (i), first noted by Emmon Bach and Stanley Peters.

(i) [the student who deserves it_{i }]_{j} will get
[the reward he_{j} works for ]_{i }

If* it*_{i } is intended to be co-referential with *the reward he*_{j} works for, and *he*_{j} is intended to be co-referential with * the student who deserves it*_{i } , and if the coreferring terms are equated in the description, we have the paradox that a term *a* which properly contains a term *b*, is equal to a term *b* which is properly contained in *a* (the paradox being that a term must be both equal and unequal to another term). In the case of (i) the paradox is avoided if the description is
something like (ii).
(ii) for all x, x:a student & for all y, y:a reward (if x
works for y & x deserves y, then x will get y)