But, on the other hand, I can remember how to say "Wo yao yi ping Pijiu."
Da ping.
The occasion for all of this is that a poor school here in Georgia is
making Mandarin mandatory. Why? Because China is offering instructors for about half what they'd have to pay an instructor in any other language: $16,000 a year.
Now, how useful will this be to the students? Well, in theory it could be quite useful: Chinese is one of the most different languages from English, in structure, in terms of being tonal, and in terms of having a character-based writing system. Studying it even a bit will help you see that many things you take for granted about how thoughts should be formed and ordered is not, in fact, logically necessary but a mere consequence of the language in which you learned to think.
That is also true, by the way, of artificial languages.
Bertrand Russell and others hoped to eliminate this tendency to confuse logic with grammar in part by instituting formalized ways of writing. The problem turns out to be that you just introduce new errors of grammar, but now believe that you have said something logically necessary because you are writing in "the formal language of logic."
For example, I recently mentioned D. M. Armstrong's
What is a Law of Nature? He makes a great deal -- by which I mean that he goes on for many pages -- out of a "paradox" that he believes is a serious problem. It's really just a case of mistaking grammar for logic. The problem arises here:
(∀x)(Fx⊃Gx)
Fx: "x is a raven"
Gx: "x is black"
Now, what that says in plain language is, "All ravens are black." But what it says literally is more like "For every x,
if x is a raven
then x is black." The material conditional -- "⊃" -- is a logical function. It has a truth table so that you can determine when a given proposition is true.
For the material conditional, which links two terms, the truth table says that it is true any time the antecedent is false ("this is not a raven") or the consequent is true ("it is black"). Thus, if a given raven is black, the statement is true; if we find a white raven it is false. If we find something that isn't a raven, the statement is satisfied because this is only a rule about ravens.
Dr. Armstrong was greatly concerned by the fact that things that are not ravens have to be taken as helping to prove the rule that all ravens are black. (Nor is he
the only one to treat this as if it were a serious problem.) He wasn't so concerned about cases of not-black things, because they seem to help reinforce the idea of a link between the categories of "raven" and "black." But what about black things that are not ravens? That seems to trouble him quite a bit.
In fact, though, this is just a convention of language. What we really have here is a rule about ravens: "All ravens are black." It's only the form of the logical language that requires us to express it as a universal truth about all things ("For
every x"). We aren't talking about all things. We're talking about ravens.
What the formal language forces us to do is to say something purely formal and empty: "Every not-raven either is or is not black." In any natural language we would omit this formality because it's entirely irrelevant. Those logicians who take this as a serious problem -- something that might, for example, seriously inform our understanding about the laws of nature -- have fooled themselves. They don't realize that they're doing the very thing that they set up this system to avoid doing.