# Bach-Peters paradox

**Bach-Peters paradox** refers to a paradox in the description of sentences such as (i), first noted by Emmon Bach and Stanley Peters.

### Example

*(i) [the student who deserves it _{i} ]_{j} will get [the reward he _{j} works for ]_{i}*

### Comments

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)*

### Link

Utrecht Lexicon of Linguistics

### References

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