Gregory Todd Williams

More and more I’m agreeing with Shuli that any page on the internet that is not comment-enabled seems fundamentally broken. Maybe that’s just me, though.

I had a quick comment on Language Log’s recent “A smart person with a stupid idea,” but have since re-read the article only to find that my comment isn’t all that relevant.

The article is interesting, though, so I’ll just plug it instead. Mark Liberman discusses Leibniz’ lingua generalis:

The key ideas were a characteristica universalis that assigns a different prime number to each primitive concept (we’re guaranteed never to run out of primes), and a calculus ratiocinator that creates complex concepts by multiplication (since the prime factorization theorem guarantees a unique decomposition into primitives) and evaluates predication by division (are the factors of the predicate among the factors of the subject?).

He follows by asking,

Suppose that A and B are propositions — whether atomic or complex doesn’t matter — and we’ve assigned 27 to the concept “implies” — what about “A implies B” vs. “B implies A”? And what about more elaborate formulae where order matters? I can imagine various procedures for encoding string order or formula structure as products of primes, but did Leibniz have a story to tell about this?

I can also think of ways of encoding formula structure, and it rapidly becomes such a fantastically complex system that I could get lost in a contented daze just thinking about it.