Bach-Peters paradox

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Bach-Peters paradox refers to a 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)


Utrecht Lexicon of Linguistics


  • Bach, E. 1970. Problominalization. Linguistic Inquiry 1: 121.
  • May, Robert 1985. Logical form. MIT Press.