Socrates is a man.
Modern logic goes further and characteristically separates form from content .
The idea of a formal logic is that it should be possible to evaluate the goodness of an argument by whether it conforms to a set of formal rules, independently of the specific meaning of the sentences involved. More precisely, it is unimportant what Socrates refers to, what man means and what mortal means to judge whether the above argument is good , while the use of all and of is remains fixed and in fact defines the form of the argument. Often, say in a mathematics book, a natural language is used for the comfort of the reader, but it is understood that its sentences stand for sentences of the formal language. Sentences in the natural language thus acquire new and more precise meanings. Translating between a formal language and a thus regimented natural language is simple for simple sentences, because the structure of simple sentences in formal languages is typically modelled on commonplace structures in natural languages, but gets more and more complex with more complex sentences, which may have a very different structure in the two languages.