I had read that some tribe in the Amazonian region speaks a language that lacks any number. So they would use "many" to describe more than say, 2 or 3 things. Hence for them, I suppose, 99 is the same as 100 essentially. There is no obvious way for their minds to distinguish between big quantities, since there is no obvious way to explain it in words. I would tend to think that their language isn't "Turing complete" in the sense that it cannot describe anything that is describable.

If we take English or any other language other than Russian, I had read that it is essentially impossible to translate Russian in the sense that the "true meaning" of what is being said, cannot be translated into English words. Hence, I would tend to think, English is also "Turing incomplete". The same holds true for any other languages, of course.

Does this mean that we are limited in our thoughts due to our languages? Can we change/improve our thoughts by creating new words and expressions and possibly grammatical rules?

  • >If we take English or any other language other than Russian, I had read that it is essentially impossible to translate Russian in the sense that the "true meaning" of what is being said, cannot be translated into English words. - man, I've read this four times and couldn't get much sense out of it... – tum_ Oct 31 '19 at 20:41
  • @tum_ Let's take a concrete and simple example. Dostoyevsky wrote a sentence which cannot keep its meaning when translated into English. There is no way, using the English language, to translate the Russian sentence without modifying its meaning. – AccidentalBismuthTransform Nov 1 '19 at 13:10
  • The question is closed, anyway. Unless you give a strict definition of what the "true meaning" is - this conversation is moot. – tum_ Nov 1 '19 at 13:17

First, you should know that the exotic claims about Pirahã are viewed with skepticism in the profession. However, there are many languages that do not have a lexical item meaning 10^20. In fact, most dialects of English does not have a lexical item for 100,000 (Indian English has lakh). English lacks a lexical item for "all-white reindeer" (a word of North Saami – gabba). Still, we have a means of getting the point across.

I don't know exactly what you mean by "Turing completeness" as applied to language (languages are usually thought of as sets of strings, whereas Turing completeness is about systems of computational rules), but let's say you mean that a language is Turing Complete iff any state of affairs can be described. Any language has that property. Sometimes a state of affairs is encapsulated in a single word, sometimes it requires a sequence of words.

  • I am reminded of Jim McCawley's remark that the relation between having a language and a set of strings was not unlike the relation between having a car and a set of trips to the supermarket. – jlawler Oct 30 '19 at 23:18

No, it doesn't imply anything about thought as it receives and processes information. Our subject of study is mainly the output.

We are limited by our language insofar we learn from communication, so that any difficulty to explain something can have various consequences, including none.

Whether its useful to describe language or the language faculty as a TM, it is certainly a good model of computation, and as string morphism equally mighty as simply typed lambda calculus. Any language that can describe a turing machine or mediate its progressive process would be just as mighty.

Memory capacity is one factor in IQ-tests, and 7 items is an oft repeated mark; 3 is only one standard deviation away, it's the 1%; That's not a terribly significan't figure; In principle, we in turn only count to nine (... eight, nine, many, one many, too many, many three).

Tempo-spatial reasoning and pattern-recognition are another test and if speakers are naturally assumed to perform such tasks on a reasonable level, there would maybe be no need for them to talk about it. Also, speaking about "money" is taboo in many cultures for various more reasons.

While a TM is practically memory bound, programms are not all decidable and thus might blow the stack--that's a stack overflow!

Therefore it's reasonable to limit the language, or "theory" as logicians call it; to have strictly computable functions is useful, but necessarily a kind of heuristic approach.

But, to concure with your hypothesis, lacking counting ability would severely limit syntax, so we can at least observe the correlation.

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