What is the difference between linguistics and philosophy of language? Often when posting on one of them or thinking about one of them, I get confused as to if I really know the difference. Here I will try to sort out what I think the difference is.

Taking a purely academia perspective at first, if you look at degree requirements for philosophy of language you get readings like Frege, Wittgenstein, Carnap, Quine, Strawson, Searle, Kripke, and Putnam. If you look at degree requirements, well, I’m mostly finding classes, so sociolinguistics, phonology, psycholinguistics, language acquisition, semantics, and syntax. So there is a lot of overlap, but let’s try to pull some of it apart.

From the list it seems that phil lang is concerned with questions of foundations. Is language fundamental, or do we interpret through language? It seems intimately tied to philosophy of mind. What is a concept? Can we think in conceptual terms and bypass language? How do we attribute meaning to language? These types of things. Linguistics seems to be more interested in the language itself. What are the origins of this word? Is their a father language that all others come from? How do sounds differ between cultures? What are allowable constructions in a language? Can these be modeled mechanically, as in computer translators? These types of things. So there does in fact seem to be a difference.

There is probably more similarity than people would guess, though. Clearly questions dealing with logic apply to both. Is a language a formal system? Also, the effect of language is in both. How do words affect brain chemistry? How does language affect how a social system interacts? Can we determine something about human nature by determining which words are culturally specific and which are universal?

Not sure why I posted this. Just something I was trying to sort out. Also, I know almost nothing about linguistics, so this could be way off. It is interesting that you can tell when I’m mathematically frustrated, because my posts become things like this for awhile. You can tell when I’m having a good math week, because my posts become essentially unreadable to people without a degree in math.

So I’ve pretty much given up on Syntactic Structures. It wasn’t really as great as I thought it was. There was some linguistics jargon that I didn’t feel like learning, also. Before I stopped there was some interesting, yet unsurprising, things (especially for its time).

Chomsky talked about modeling languages using what he called (I think, I’m not actually looking it up) “finite state markov processes.” Apparently this was how linguists thought at the time. According to today’s standards, I’m not entirely sure he wanted to use the phrase “Markov process” as that usually implies randomly switching from state to state. Clearly when people speak, it isn’t random streams of words that come out (although it may seem that way sometimes).

Nevertheless, I assume that in today’s jargon he wanted to use “nondeterministic finite state automata” to model language, at least that is what his description was of. Now from basic theory of computation we know that if we could model a language using one of these, then it would have to consist entirely of regular expressions. No language consists only of regular expressions, thus the myth of being able to model in this way is debunked.

Chomsky obviously did not have that tool at his disposal, since he went on for pages considering different cases and why they wouldn’t work to conclude (in a pretty non-rigorous way) that you can’t model a language using an NFA (or DFA for that matter). Not surprising, but noteworthy I’d say. It really was a paradigm shift to claim that there is no way to have a grammar that can’t be modeled. Too many people are still trying to figure out how to do it. Things like online translators, AI, and many others work from the assumption that it is possible to get really close to being able to do it.

Since this little gem was in there, I feel like quitting is depriving me from some other interesting little tidbit that I hadn’t thought about, but oh well.

I’ve decided to start reading Chomsky’s pivotal book Syntactic Structures, since I’m into the phil language thing and it was a really important work. This post is going to be sillyness, but it was something I couldn’t get out of my head while attempting to read past the first couple sentences.

“Each language has a finite number of phonemes (or letters in its alphabet) and each sentence is representable as a finite sequence of these phonemes (or letters), though there are infinitely many sentences.”

Now we encounter “free structures” all the time in math. It is perfectly legitimate to create something with an infinite number of elements from just stringing together a finite alphabet. In fact, you can impose lots of structure such as the free group on two generators. This “language” only has an alphabet of two, must satisfy group axioms, and ignores triviality (must be fully reduced), yet still achieves an infinite number of words (not even sentences, but words).

I must argue, though, that there are not “infinitely many sentences.” I don’t think it would be controversial to claim that there are a finite number of words in a language. Take English, for example. Use the good old OED plus maybe a slang dictionary and throw in a couple thousand for good measure as an upper bound on the number of words in the language.

This number of words is huge, though finite. When we generate sentences, if we do so in the “free” way, then we clearly get an infinite number. Now I’m not so concerned with “grammatically” correct sentences, as I am with imposing conditions on repetition. The sentence “the dog ran dog ran” is pointless. Due to repetition, I argue that there must then be some upper bound on the length of the longest sentence possible (to continue the group analogy, this is like the “free presentation” with restrictions like ).

To make this easier, let’s reduce our sentences to ones that are not conjunctions of two complete sentences (if former is finite, then so is the latter). Now a sentence can only be so long (non-conjunctively), say you use basically every word in the language a couple of times (which I find hard to believe that you would still have a “sentence” at that point). So now we have an upper bound of, I don’t know, a couple billion words in a sentence. This would give us on the order of a couple billion factorial number of sentences. This is absurdly large (and an absurdly overestimate in my opinion), but still finite.

Despite having zero relevance to your book Mr. Chomsky, I must respectfully disagree with your opening lines. What does everyone else think?

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.

Well, I’ve been thinking about that first uncertainty post a little throughout the day and here is what I came up with. Why does this only have to hold for the Tao? There are really two schools of though on philosophy of language dealing with the meaning of words. The one says that words are defined in terms of the system in which they are used, and the other is that words are defined in terms of other words.

Either way, words are a superposition of other things. We can almost take quantum mechanics now as a special case of Wittgenstein and Kripke. They say that everything is language. Without language nothing would exist, including consciousness. It is how we think. So maybe the uncertainty in a wavefunction of a particle is really due to the fact that their is uncertainty in the superposition of terms describing it. When we pinpoint the terms and collapse the wavefuntion, it is no longer uncertain. This is the case for every physical object. They exist and are concrete precisely because we have named them and collapsed the wavefunction.

Probably lots of holes with this since I haven’t thought about it much, but I think there might be something there.

Well, I’m pretty mad that I came up with this idea before reading about it, and then it turns out that other people have already thought about it. I haven’t quite found it in the formal way I would like to think about it, though. This assumes knowledge of Taoism and the Heisenberg Uncertainty Principle. It is also a good example of tying together philosophy of language, religion, and physics together.

Take the line from the Tao Te Ching: The Tao cannot be named. Why is this? Maby the uncertainty principle can shed some light on this. If you have a particle, then you cannot know both its position and momentum perfectly. Uncertainty is inherent in the system. We could say by definition. To know these perfectly, you must observe the system (make a measurement) and collapse the wavefunction.

Now, maybe the true definition is like the superposition of wavefunctions of the particle. Instead of wavefunctions, though we have terms. Tao is a superposition of all terms (or maybe just infinitely many or maybe just two). To precisely define what Tao is, you need “silent,” “unnameable,” “the way,” etc. When you give it a single name, such as Tao, you have collapsed the true Tao of superposition into a single state, which is a changed object. You no longer have the true Tao, but just one of the superimposed parts of the Tao. In order to keep all assets of the Tao, one must not name it and collapse its wavefunction. By definition it cannot be named without being changed.