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>'' |
| − | |||
===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)'' |
| − | |||
===Link=== | ===Link=== | ||
| − | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma= | + | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Bach-Peters+paradox&lemmacode=812 Utrecht Lexicon of Linguistics] |
===References=== | ===References=== | ||
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.
