create trigger trigger_course
after insert on course_course for each row
begin
    declare sid varchar(8);
    declare sname varchar(20);
    select logic_id into sid from course_selectcourse where id=new.course;
    select name into sname from course_selectcourse where id=new.course;
    update course_course
    set sub_logic_id=sid, sub_name=sname
    where id=new.id;
end;

22:28:06 create trigger trigger_course after insert on course_course for each row begin declare sid varchar(8) Error Code: 1064. You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near '' at line 4 0.000 sec

一方面是已采纳的老哥说的那个问题，另一方面是update循环触发触发器也有问题。
记录一下正确写法：

drop trigger if exists trigger_course;
delimiter $$
create trigger trigger_course
before insert on course_course for each row
begin
    declare sid varchar(8);
    declare sname varchar(20);
    select logic_id into sid from subject_subject where id=new.subject_id;
    select name into sname from subject_subject where id=new.subject_id;
    set new.sub_logic_id=sid, new.sub_name=sname;
end;
$$