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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 iti ]j will get 
    [the reward hej works for ]i 
If iti is intended to be co-referential with the reward hej works for, and hej is intended to be co-referential with the student who deserves iti , 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)

LIT. Bach, E. (1970)
May, Robert (1985)