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Can somebody let me know if this is a reasonable explanation for how the two theories are similar and different? This is not for homework, I'm just try to understand the difference, and my textbook doesn't highlight Chomsky hardly at all.

Sapir-Whorf basically says that human language has a direct impact on how we think by directly influencing other centers of cognition in the brain (highly interconnected centers of the brain) while Chomsky says that human language is quite a bit more separated from the brain, and is something far more innate and isolated from other centers of cognition.

I'm using the original theories, no new modifications or schools of thought.

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    "my textbook doesn't highlight Chomsky hardly at all" -- what an awful textbook! :-) – Ivan Kapitonov Oct 15 '15 at 6:26
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    Chomsky has written about a lot of things. It would help if you could be more specific about exactly which theory of his you're asking about. – curiousdannii Oct 15 '15 at 7:13
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Let's start at the end. It is impossible to talk about original theories in this context. There was actually no cohesive formulation of the Sapir-Whorf hypothesis. That is a label assigned later to a set of assumptions about language relativity formulated by Whorf who was inspired by his teacher Sapir.

Neither can you talk about Chomsky's original theory because in its first formulation in Syntactic Structures he did not focus on questions of universality. It is actually hard to exactly pin point what the 'current theory' is because so many aspects (and terminology) have changed over the years. The latest form, 'minimalism' is virtually unrecognizable from what we saw in the 1950s and 60s even if some of the assumptions about universality remain the same.

So what you really need to compare is claims of linguistic relativism and universal grammar (UG).

But it is really hard to directly compare the two because they study different domains of language. Universal grammar is largely concerned with "deep" syntax (agentive structures, co-reference, phrase structure, etc.). Whereas linguistic relativity is more concerned with meaning - most often at the lexical level but in its strongest formulation at the level of syntax, as well. In this, UG and relativism could actually quite happily coexist. Linguistic relativism, in particular, is not tied to any particular conception of language structure. In the old formulation of UG, there was a universal set of principles and each individual language set the parameters in how they were expressed. This is pretty inoffensive, so, in theory, you could just have a debate about what the principles and parameters are.

However, it is the other assumptions of the UG proponents that is the real crux of the controversy. The key is modularity - where UG assumes that language is a module (or several modules) in the mind (so not divorced from it) that interacts with other modules such as perception, cognition, etc. Linguistics relativists tend to see language as part of the general cognition and linguistic knowledge as just as type of any knowledge. And this then makes any discussion of where the boundary of the universal and particular lies completely non-sensical - the proponents do not talk about the same thing when they say language. If you read them in their 'native habitat' it does not even feel like they're in the same discipline. Which is why when they come into contact and debate each other, they generally talk at cross-purposes.

There are many other dimensions of the relativism debate that are much more fruitful. See for example, the recent debate between Mark Liberman and Lera Boroditsky.

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I think you've got it the other way round.

"Chomskyan" theory of UG is much more of a claim about "the brain", which (in humans) has specific machinery for language. The idea is that the language is probably not underpinned by the general cognitive mechanisms.

Whorfian stuff, by contrast, is psychological. He does not claim that brains of people speaking different languages are different -- rather, the difference lies in their picture of the world.

Your confusion might come from the terminology: cognitive science is more or less neuroscience, while cognition is more of a psychological notion.

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