Difference between revisions of "Bach-Peters paradox"

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===Example===
 
===Example===
''(i) [the student who deserves it <sub>i</sub> ]<sub>j</sub> will get  
+
''(i) [the student who deserves it <sub>i</sub> ]<sub>j</sub> will get [the reward he <sub>j</sub> works for ]<sub>i</sub>''  
    [the reward he <sub>j</sub> works for ]<sub>i</sub>''  
 
  
 
===Comments===
 
===Comments===
 
If ''it'' <sub>i</sub> is intended to be co-referential with the reward ''he'' <sub>j</sub> works for, and ''he'' <sub>j</sub> is intended to be co-referential with the ''student who deserves it'' <sub>i</sub>, 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).
 
If ''it'' <sub>i</sub> is intended to be co-referential with the reward ''he'' <sub>j</sub> works for, and ''he'' <sub>j</sub> is intended to be co-referential with the ''student who deserves it'' <sub>i</sub>, 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
+
''(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)''
    works for y & x deserves y, then x will get y)''
 
  
 
===Link===
 
===Link===

Latest revision as of 14:18, 3 March 2008

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.