 :Philogo, the reason that the definition of (formal) language does not include rules of syntax is that formal language theory is concerned with means of describing languages!  It studies, for example, whether particular types of syntactic rules are more expressive, or less expressive, than other types of syntactic rules.  It studies whether for particular types of syntactic rules we can automatically determine whether a particular sequence of symbols is valid according to those rules (it turns out that it's very easy to define types of rules for which this is not the case).  Etc. Etc.  Therefore, in formal language theory we strictly separate  languages themselves (i.e. that which can be described) from formalisms to describe languages.   