I just started to read a popular mathematics book and in the second paragraph it makes a claim which feels to me to be the mathematical equivalent of all those nonsense claims about "Language X has no word for Y". (Actually it's partially linguiistic as well because of how it's phrased.)

It says

quote:

We have it indeed on the authority of African Explorers that many Hottentot tribes do not have in their vocabulary the names for numbers larger than three. Ask a native down there how many sons he has or how many enemies he has slain, and if the number is more than three he will answer "many". Thus in the Hottentot country the art of counting firce warriors would be beaten by a child of kindergarten age who could boast the ability to count up to ten.

I have come across this claim before with respect to other so-called "primitive" peoples and it always strikes me as both mathematically and linguistically dubious. The implication, as with its solely linguistic equivalent, is that a) they have no word for it therefore b) they can have no concept of it. It's nonsense.
There must, in those languages, be the ability to express, at the very least, relative sizes. If not then, to extend the example above, a tribe of a thousand people would not dare to figth a tribe of three because they would be too evenly matched.
It's obvious nonsense.

As I say I've heard this kind of claim before but this time I thought I'd check it out.

But half an hour of googling various permutions of "have no number greater than" produced nothing relevent at all.

Anyone got any suggestions of how it would be possible to either verify or debunk this claim?

This is definitely a linguistic claim because it's about the words a language has. I hear it all the time about Pirahã. There's a paper entitled Numerical Cognition without Words. I think the author, Peter Gordon, assumes linguistic determinism - that the lack of numbers affects numerical cognition, when there could be other factors - but it does seem that the Pirahã don't have words for numbers and have trouble counting. But I have no doubt they can tell the difference between 3 and 1000.

From a brief glance it looks like an intereting paper. I shall read it properly later. Thamks for the links.

I have encountered the claim in less explicitely linguistic terms before and I have even seen it argued the other way - that the number system of 1,2,>2 came first and the language to describe it came later.

I don't believe the claim either in linguistic or mathematical terms and it would take a pretty powerful argument to convince me that a mother might leave one of her four kids behind because she can't tell the difference between three and four. I know it's a facetious example but if we are to believe that the counting system really only contains three possibilities then it's also a logical consequence. The fact that it's clearly untrue leads me to believe that the claim itself must be false.

Now it's perfectly possible that the language may lack specific lexical items for higher numnbers but that seems to me to be a slightly different issue.

I'll comment again when I've read the links.

I don't see the difference between the mathematical and the linguistic claim. That is I don't see a difference between saying "the counting system doesn't have numbers larger than three" and "the language doesn't have ways of expressing numbers larger than three".

You may be right.
And as I'm busy packing and leave tomorrow morning for a two week holiday away from my computer, I can't really get into much discussion on it.
But I'll leave you with this question, which is relevent.

Which came first, this


or this


"elephant"


and this




or this

"two"?

In each case which can exist without the other?
If an elephant can exist independently of a word to name it then surely a counting system can exist independently of words to describe it.

Or am I wrong?

I will check your views on the subject when I return on 2nd Feb.

Bob

This message has been edited. Last edited by: BobHale,

quote:

Originally posted by BobHale:
If an elephant can exist independently of a word to name it then surely a counting system can exist independently of words to describe it.

I don't know. A counting system isn't the same as an elephant. But I understand you when you say it's possible to tell the difference between 3 and 4 even if you don't have words for "3" and "4". But is it really possible? You gave the example of children, but there would be other factors there: you don't have to count the children, you can name them - and they're your *children*, why would you forget them?

I find it impossible to imagine what it would be like to speak a language with no numbers. According to the evidence from Pirahã, it would seem that there are cultures that don't count. But does that mean they can't tell the difference between 3 and 4 when it is really important?

I would have to say you are right, Bob. Each can exist independently without words to describe them. We have discussed that concept for years here on WC.