The Sapir-Whorf Hypothesis asserts that categories in particular human languages influence or even control our possible thoughts. You have most likely heard this presented in its most (in)famous example, about Eskimos having N different words for "snow". I thought this version was well taken-apart by Steven Pinker in The Language Instinct. Recently an Edge essay HOW DOES OUR LANGUAGE SHAPE THE WAY WE THINK? by Lera Boroditsky has made me reconsider.
Using the terminology of Lakoff and Johnson's Philosophy in the Flesh, Pinker's critique is classic first-generation Cognitive Science. Pinker says the brain is the equivalent of a computer or Turing Machine, processing abstract symbols. He asserts that thinking is done in "mentalese", not in a particular human language. Translation to human language is the last step before speaking, so it cannot influence the core of thought.
Lakoff and Johnson's second-generation Cognitive Science can be difficult to grasp, so I'll go slow. It is a big idea, and since you can't see where I'm going, it is easy for me to get too far ahead for you to follow. Simply stated: thinking is largely based on metaphor, and abstract thinking is based on metaphorical analogy to bodily operations in the physical world. Re-read the examples in the first two sentences: "difficult to grasp", "go slow", "big ideas", "see where I'm going", "get too far ahead", "follow". All of these are related to operations or relations in the physical world. Their use in the realm of ideas is much more vague and abstract. It is easy to agree on a measurement for the "bigness" of a tree, but how do you measure bigness for an idea? Works such as Feldman's From Molecule to Metaphor show how evolution started with simple minds able to interact with the physical world, and placed increasing layers of abstraction on top. But abstract thinking still bottoms out at the use of modules originally evolved for physical world manipulation.
So how does this relate to language and Sapir-Whorf? The studies cited by Boroditsky indicate different cultures use different physical-world metaphors for their abstract thinking:
"English speakers tend to talk about time using horizontal spatial metaphors (e.g., "The best is ahead of us," "The worst is behind us"), whereas Mandarin speakers have a vertical metaphor for time (e.g., the next month is the "down month" and the last month is the "up month")."
This is plausible. There is no inherent reason why time should be metaphorically mapped horizontally versus vertically. It can easily be culturally determined rather than hard-wired into the brain. And this puts an interesting new spin on Sapir-Whorf. Thought is not determined by language, but instead both thought and language are determined by culturally transmitted, culturally specific abstract metaphorical mappings. And how is culture transmitted? Primarily through language. So linguistic determinism or linguistic relativity is in a sense correct, but not for the reasons usually proposed.