For a second, exit the realm of language and think about your grade school math days.
We start with counting, and quickly progress to adding and subtracting. In learning mathematics, we’re doing a lot of things similar to what we do when we learn language; most importantly, we’re learning to attach meaning to symbols, just as we do when we learn that what we perceive in our mind’s eye as a boat is represented by the word “boat.” This, of course, is also what happens when we learn how to read and write (keep in mind that language and writing systems are two separate things; I’ll have a post about that up soon).
After addition and subtraction, we make our first forays into multiplication and division. Through boxes and tables of numbers, we grasp the idea that 2 x 2 is 4, and that 4 x 4 is 16. Somewhere along the way, when exponents and the quadratic equation are still a long way off, we learn something crucial to higher levels of math: that, when multiplying, if we have two positives in a sequence, they make a positive; a positive and a negative give us a negative; and, finally, that two negatives, when multiplied together, give us a positive. With this knowledge (and more), we can confidently find our way in a world (or classroom) of algebra and trigonometry. But the inherent utility of knowing that two negatives make a positive begins and ends with mathematical thinking. It is not a natural rule of language, as many people believe.
Cross-linguistically, it is more common for languages to use two (or more) negatives to simply reinforce the negative meaning of a phrase. English (and at that, only some dialects of the language) is in the minority in that it is said that two negatives in an English sentence create a positive meaning. For example, in Spanish, one would say:
No veo nada.
meaning, “I don’t see anything,” but literally translating to, “I don’t see nothing.” This is the same for all Romance languages, and is also true of languages such as Welsh and Greek. Both systems–negative concord and systems where multiple negatives cancel each other out–are perfectly understandable and logical, as far as language is concerned. This elucidates the fact that language is not formal logic, nor mathematics. Language is a system all its own. Let’s check out another example.
In logic, as well as math, things only come once; there’s no utility in repeating items, and such repetition may in fact cause confusion or create different meanings. In language, on the other hand, repetition and reinforcement (“concord”) are all over the place. Think about the sentence below:
“He walks to school every day.”
Your first reaction may be to say that this sentence has only the elements it needs, and no others. But if you speak what’s known as a “pro-drop” language, where pronouns are optional in some circumstances, you might see it instinctively: the pronoun “he,” when given in context, would likely be unnecessary. Imagine you’re talking about your young son, and you explain how he gets up on his own, and eats all of his breakfast, and gets out the door on time. With all this information, and the topic of the conversation well-defined, the “he” in the sentence above is a doubling of the information already found in the context as well as in the sentence itself: when you say “walks,” you already know you’re talking about a he, she, or it that engages in ambulation on a regular basis, or as a matter of fact (this is given by what we call the “simple present” conjugation of the verb “to walk”); in addition, you’ve been talking about your son already, and so the he, she, or it aspect is disambiguated. “He” is just giving information given elsewhere already. Why does that make any sense?
The answer is because language is language, not logic or math or any other symbolic system. The logic of language is organic and communal–this is likely a part of the reason why constructed languages (e.g. Esperanto) don’t catch on, no matter how “logically perfect” they seem.
Natural languages cannot be replicated, and once a language is gone, it’s gone. This is why language revitalization is so important. And the unique logic of language–and the way it differs from one language to another–is an invitation to explore linguistic complexity, and to get outside of our own conception of what is “right” and “wrong” in a language and appreciate tongues for what they are: unique, meaning-dense expressions of ourselves, and of our humanity.