Okay. I admit it. *Don’t hurt me.* I don’t own a copy of Wittgenstein’s Philosophical Investigations. Yesterday I decided it was time to remedy that. I have now come to the conclusion that no one owns it. The cheapest copy I could find at Barnes and Noble was $40. How absurd is that? It consists of 100 aphorisms. That isn’t even 100 pages. And it was paperback.
Well, enough of my ranting. Needless to say, I still don’t own a copy of it (and neither does the entire public library system in my district…what is this world coming to?). At least I found a wonderful website to keep me occupied until I find a copy here.
Some comments are necessary. I always seem to forget about the first half of this text. Everyone remembers the “language is everything, ” but I seem to forget the evolution of language and meaning as function parts. So Wittgenstein rejects the old view that language is stagnant and made up of words that have fixed meanings (look in a dictionary). He talks about how it is sort of living in that things get added, meanings change, etc. It evolves.
Why is this important to me? Well, mathematics is a language. Here is a plug for the position I’ve advocated several times in the past on this blog. Since math is a language it is not fixed or set in stone! People don’t seem to get that. Maybe the more natural definition to work with is monoid and not group. Maybe the more natural construction is category and not set. Mathematicians seem to forget that this is okay.
Also, meaning as function should be addressed. I don’t know of anyone who has interpreted this to a the language of mathematics. This definitely fascinates me. Definitions of terms in math are very rigorous. We tend to think of the meaning of terms as set in stone regardless of how they function in a proof or sentence. I think this is very much not the case as Lakoff and Nunez argue in their book. Sometimes we can use the same term in the same proof in two different ways if we are interpreting the metaphor in two different ways.
Just quick thoughts after rereading that wonderful work. I’ll post a follow-up tomorrow to see if I still feel that way.