A formal language is a set of strings of meaningless symbols. If the number of terms in the language is countable, and if each sentence is of finite length, then the number of “sentences”, that is, strings of meaningless symbols in the formal language is countable: they can be put into one-to-one correspondence with the integers.
- Lakoff (1987), a pag.233

A formal “language” is made up of uninterpreted symbols. The use of this formal language is characterized in terms of symbol manipulation procedures, for example, procedures for proving theorems. “Understanding” a formal “language” is characterized in terms of knowing what it is, knowing how to use it, i.e., knowing how to perform symbolic manipulations such as deductions, and knowing what sentences follow from what other sentences via manipulations such as proof procedures. On this account, one can know a language and understand how to use it, and even know what sentences entail what other sentences-without the language meaning anything at all! “Meaning” is the study of how one can provide interpretations for a “language” in this technical sense.
- Lakoff (1987), a pag.255