What is the importance of vocabulary on human knowledge?

We’re talking about several different things here. The “bells and whistles” do not do much to how a person thinks; a Spanish speaker doesn’t care that a bridge is “masculine”. Some grammatical obligatory features more fundamentally require the speaker to develop a certain kind of specialized awareness, such as the absolute-direction languages.

But you seem more interested in “vocabulary” – and “access” to that differs as much from speaker to speaker of the same language as it does from one language to the next. Sure, there are ideas which one language has a word for and another doesn’t – “wabi sabi” in Japanese, etc., etc. – and these do usually reflect the importance some idea has for one culture. But the vocabulary doesn’t shape the mind, except at the margins.

Certainly, “complexity” has little to do with any of this. It is difficult to measure “complexity”, and one language is usually complex in some ways and not others, while the next language is complex, too, but in different ways.

There are sometimes (debatably) a few ways that complexity can be measured overall, and “creolization” (to put it in an oversimplified way, parents having to use a second language to speak to each other, and their children speaking the result as a first language) will simplify a lot of things pretty consistently (English is more creolized than other Germanic languages except for Afrikaans, e.g.). “Indigenous” languages, spoke by relatively few people, will thus tend to retain the most “complexity”, in many ways. But I doubt you would contend that German speakers have more access to complex thought than English speakers, and Navajo speakers more than Germans.

What do you mean by the “vocabulary” of a language? The sum total – lexicon – of all words used by all its speakers? Spoken, or written? Which dialects do you include? How much technical vocabulary do you include? How do you define any one person’s “access” to some defined portion of the total potential lexicon? This may be a useful exercise for some reason or another, but not, I’m almost sure, for better predicting how a person’s mind works, or what they are capable of thinking, or even what they are likely to think (except to the trivially obvious extent that a language’s culture and geographic setting, and the things it has words for, will show much correlation for certain kinds of words.)

Or, to put it more succinctly, the OP commits a fallacy of the excluded middle. The thought-ways available to anyone are largely channelled (though not strictly limited) by their “culture”; and, portions of any language’s lexicon (roughly, “vocabulary”) will reflect things particular to one or more of the “cultures” with speakers of that language; but the lexicon does not have much to do with channelling the thought-ways.

One (of many) reasons why not: Languages evolve through time, and there is no way to define precisely the moment when a language becomes a different one. The English lexicon, for maybe 96% of any speaker’s utterances, is an Anglo-Saxon base with a Norman French grafting, plus some learnéd Latin filligree. Are English speakers, then, restricted to the mindsets of 8th-century Saxons, or 12th-century Normans, or 3rd-century Romans? Of course not.

Well put!

Vocabulary is not important. Some things are important, some are not. Important things are different from unimportant things because they are not the same. The important things are important. Things that are not important are not important. It is easy to tell what is important and what is not important because all important things are important. Vocabulary can’t be important because it’s not important. Does that explain it?

Probably not. Shakespeare used just over 30,000 different words in his works. Presumably he knew a lot more; up to 66,500, according to a paper writen in the '70s. Here’s a link to the first page of a 1976, here’sa breakdown of what was within. Even if it wasn’t quite that high, you can assume he knew plenty of words not in his works.

But beyond that, there’s no point in comparing Shakespeare to a modern college-trained English-speaking person. Think about how many words you know that relate to cars, or driving, or fuel. Or computers, the internet, the stock market, prices of IPOs. And on and on.

Jub jub? Jub! Jub jub jub jubjub jubjub jub! Jub Jubjubjub jub jub jub jub Jubjub.

In jub, jub.

Jub. jub jubjubjub JUB jub jub, jub jub jub jub. Jub, jubjubjub! jub.

It good!

still close then. remember, we’re comparing shakespeare with the average joe.

I’ve heard the later theory on and off for the past 25 years, but haven’t found anything which has convinced me. Do you have any good cites for evidence of language making a difference in math? I see the difference on the amount of time spent drilling arithmetic, the amount of homework given and such, but most of the research I’ve seen seems flawed to me.

Vocabulary is a result, not a cause.

The conditions that produce a specific vocabulary in large societies differ from one to another, so we can end up with a horrid meaningless mash of haphazard words as in English, compared to very sophisticated word structure (not grammar or syntax) like in German, Russian or Greek, but even then, vocabulary is a result, not a cause.

On an individual level, which I think where your question is aimed at, the more educated a person is the more that person “knows”, whatever that means, so in that case then vocabulary can shape that a person can know because it gives a way to formulate abstract ideas in a more concrete way that can be later examined and analyzed.