24 January 2009

Linguistic Factoid No. 5: Logic and Language

I suppose almost everyone here has heard of formal logic. Maybe in a past life, sometime in undergrad, we have taken a course on logic. You know, those propositional logic operators of and, or, if...then, if and only if, and so on. There also is modal logic, which involves possibility and necessity. And there is also first order predicate logic, which concerns predicates and arguments.

Now the thing is, many logicians and semanticists have tried to relate logic and language. The thing is, logic is a type of language, albeit a formal one, not a natural one. The language one uses to represent these different types of logic has a syntax, which tells us how the terms combine with, and a semantics, which tells us what the terms are supposed to represent.

Modeling natural language, however, is not easy, if one attempts to model it using formal language. One of the reasons have something to do with the fact that formal languages were created so that there are no ambiguities. Natural language on the other hand have plenty of ambiguities. Natural language also do not follow some of the rules that formal languages assume. Let me illustrate it with an example.

Formal languages have a concept called transitivity. So, observe the following example.

A. If it snows this morning, I will be late for school.
B. If I am late for school, I will be reprimanded by my teacher.

From the above two premises, one can conclude the following:

C. If it snows this morning, I will be reprimanded by my teacher.

That is fine and dandy, but natural languages have more uses than the ones simply specified by formal language. Consider this example, courtesy of Philip Johnson-Laird:

A. If you need any money, there's a pound note in your wallet.
B. If there's a pound note in your wallet, then you don't need any money.

Now can we conclude the following?

C. If you need any money, then you don't need any money.

Obviously not. The tools that formal language gives us say we can, however, the way we use language is not the same.

It is indeed a good venture that one tries to model natural language using formal language, but one must always keep in mind that formal language isn't always sufficient given the wide range of uses that natural language has.

(African American Memorial, from my Mount Vernon Series)


  1. That is definitely not something for me...I am very bad at logic !

  2. Sidney,

    Hehe. It actually proves a point regarding psychological reality. The fact that most people are not aware of logical proofs suggest that we do not do logic in our heads when we reason, but something else. But that is for another post.