I thought I would jump in here as I am quite disappointed with level of the discussion on a rather simple subject. First, you are all talking about opinions and not facts and there is no recognition of that fact to speak of. As I have commented elsewhere, dictionaries can not be used to learn the meanings of words in a language as the meanings of the words used in the definition of a word must be known before the definition can be used to understand the word. We actually learn what words mean by guessing their meaning from usage and, for that reason, every language extant is vague and imprecise when examined carefully. (Which is also true of what I am saying here by the way, and does much to explain Goldwater's famous gaff, "listen to what I mean, not what I say!")
As an aside, the fact that all languages are vague and imprecise plays a very important role in the advancement of human thought because it allows misunderstanding and misunderstanding can lead to new perspectives which might better explain things than what was intended by the source of the explanation. If our perspective on reality never changed, we would still be living in caves. (An opinion by the way and not put forth as an argument.)
And Pyrotex, your comments are perhaps the best in the thread but you also are misrepresenting some important issues. (Again, an opinion only
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Originally Posted by Pyrotex
Going to the dictionary to (re-) define what someone else means in their argument is fraught with peril.
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Dictionaries are a stabilizing factor in communications and your comment smacks of Goldwater's gaff.
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Originally Posted by Pyrotex
Algebra is a language. There is no word for 'shit' in algebra. What the HELL?!?!  Why not? It's a 'language' isn't it? We can translate French into English ('shit') so why can't we translate French into Algebra? |
No one said all languages are equal and this can often lead to communication problems. The fact that we "walk in space" is due to exactly such a problem. The Russians were the first to do it and when they announced their accomplishment they used a word which does not exist in English. In Russian they have two different words for "to go", one to go in a vehicle and the other to go without a vehicle. When translated into English "to go without a vehicle" is commonly translated as walk, but it could just as reasonably be translated as swim or fly or slide for that matter. I also understand Chinese has no word for "freedom" and is translated to a word meaning something closer to "out of control". (Of course, as you said, meanings change and evolve and the meaning of that word might very well be different to the next generation of Chinese.)
Languages evolve to handle the subjects of interest to the users of that language and there exist many differences between many languages. I very much doubt the Pirahă have a word for snow. The important concept here is that "languages" are used to communicate and that includes communication with ourselves (it is common knowledge that it is very difficult to consciously think about things you have no words for).
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Originally Posted by Pyrotex
And how about 'add', 'subtract', and the other operators. Are they arbitrary? Have these processes changed over the centuries with custom and tradition? No. Not in the same sense as the pronunciation, spelling and common usage for 'shit' or 'merde'. Don't go there.
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Here you are confusing concepts with the symbols used for the concepts. In mathematics, particular care has been made to assure that the total collection of concepts are internally consistent thus impeding misunderstanding and slowing any evolution of the referenced concepts. "+" means "to add" and "to add" is a rather universally well understood and useful concept (except, it seems, in the Pirahă language). Now the verb "to add" in English has evolved to include things such as attractiveness or health (very imprecisely defined concepts) because they want to talk about these issues. The verb "to add" in mathematics has also evolved to include things like modular addition but the concept is quite precisely defined (otherwise it wouldn't be in mathematics).
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Originally Posted by Pyrotex
These are just a few of dozens of differences we could point out between Algebra and French. And they are a different KIND of difference than you find between English and French. You cannot go to Paris and find someone in the bookstore who 'speaks Algebra' and carry on a conversation about your children and pets in Algebra, no matter how good you are at factoring quadratic equations.
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They are not a different KIND at all; they all have to do with concerns of the people who developed the language. You couldn't carry on a conversation about your children and pets in "Algebra" anywhere because these issues are insufficiently well defined to be included in "Algebra"; no more than you could have a discussion about snow in Pirahănese. Notice that I invented that word! The rules of English are sufficiently imprecise that such invention can take place under the "looks like a usage I have seen before so he'll probably guess what I mean correctly" rule. You can't do that in mathematics; you must be very careful to assure the meaning is well understood before you can use a symbol "that's what we call what stands for "words" in mathematics".
Sorry about that, but I had just expected a little more precision in your thoughts than I found here.
Have fun – Dick
