updating same column as in the select query
ROOT CAUSE

Look at the following parts of your query

UPDATE table_name (&lt;&lt;-- table_name)
   SET quantity = 19
 WHERE  productID = 148357
               AND productCost IS NOT NULL
               AND exampleDate1 &gt;=
                      (SELECT min(exampleDate1)
                         FROM table_name (&lt;&lt; -- same table_name)
                        WHERE exampleDate1 &gt;=
                                 (SELECT min(exampleDate)
                                    FROM table_name2
                                   WHERE description LIKE "We are true"))


You cannot execute an UPDATE or DELETE query against a table that uses a subquery against that same table. I have discussed this before : 


Feb 22, 2011 : Problem with MySQL subquery
Jan 23, 2013 : Problem with nested UPDATE queries
Apr 30, 2013 : UPDATE table based on the same table


SUGGESTION

Rewrite it as two queries

#
# Retrieve Minimum Date into a Session Variable
#
SELECT min(exampleDate1) INTO @MininumDate
FROM table_name
WHERE exampleDate1 &gt;=
(
    SELECT min(exampleDate)
    FROM table_name2
    WHERE description LIKE "We are true"
);
#
# Use Session Variable in the WHERE clause of the UPDATE
#
UPDATE table_name
    SET quantity = 19
    WHERE  productID = 148357
    AND productCost IS NOT NULL
    AND exampleDate1 &gt;= @MininumDate
;


GIVE IT A TRY !!!