So perhaps we could relax the definition a little, and take what “I know” to mean what “I think”
That is not exaclty possible for everyone. Because what you think at any one time is still less than the knowledge that you have. What you can do, though, is expand your knowledge by putting your knowledge in a different perspective to create new thoughts, and therewith new knowledge.
What I mean is that what you know can't be what you think, because everything you know influences what you think and the other way around.
But let’s maybe define language as a socially constructed system of signs that represents the objects of the world and structures the propositions via which we speak about those objects. I think the key here might be whether, when we think about an object, we really only think about that single object, or whether we only ever think about it in relation to other objects, the concatenation of which is the thought (the “logical picture of the world” in W’s words). Maybe directing consciousness towards the representation of a single object, just like the landscape, is not really a thought, because it is not really about anything at all, it is “just” a representation, like a mental replay of a sensory experience.
Maybe we do that through language. The heater and the cat are things/beings in the world grasped as objects in the mind through the signs (“cat”, “heater”) that we have at our disposal to represent not just each of them separately as mere mental representations, but how they interact with one another in a completely virtual way, by means of signs and through the linguistic apparatus that connects signs together – call it logic or grammar. Of course, when we “perform” such thinking, we are not constantly telling ourselves under our breaths that “this is a cat and he’s now jumping on the heater to have a nice long cozy sleep”. But it’s possible that we are implicitly operating from the very beginning, without realising it, with an understanding of the heater and the cat as signs (linguistic signs) that can interact with each other through the grammar that connects them. And if we can find a way to show that all objects, circles included, fall into that category of signs, and that only in that way does one articulate thoughts and string them with other thoughts, maybe W has a point.
I do believe that our minds have an inherent form of grammar that helps us communicate among our species (as in the fauna), only we have expanded our language to talk of things that are intangible, we gave them names. Not just mere displacement, or double articulation, or any other officially language-defining feature. (I mean the Role and Reference Grammar, based on Noam Chomsky's work on universal grammar.)
Coming from there, we have an established framework of innerspecies communication, which structures our thoughts so we are able to communicate them. But language is not only comprised of grammar, but also a lexicon, both which is different wherever you are on the globe, but we can still learn every other language. Therefore, judging by the way we are able to communicate through language barriers, there must be an inherent understanding of the other's mind's structure, which leads to the assumption that there is a UG. However, the thing that complicates things is that, while the base components can be superimposed over any present data, not all base components are present in all languages and also in different compositions.
This is how every language changes the way we think. But there is an underlying way of thinking by which we are enabled to communicate cross-culturally. Thus, there must also be an inherent structure of thought underneath the language-level. I think it may be more of a biological (or neurological) phenomenon.
I should add that to my mind, this understanding of the relationship between language and thought would in no way necessarily “blunt” creativity and original thinking. You could even suggest that the more numerous the objects that interact with one another in thought, and the more complex the grammar that provides the rules under which the interaction takes place, perhaps the more likely the thoughts strung together are to produce novel insights. Language does not limit thought as such, it only provides the boundaries beyond which a thought isn’t a thought, but a mere phantasm. But perhaps the phantasm can be objectified into a sign by means of language, and subsequently made to interact with other objects in thought, to produce a novel insight, perhaps even a new word. Here language really seems omnipresent and inseparable from the activity of thinking: the “voice of thought”, endlessly extending along with thought.
Language is a means of structuralisation, but as I already argued, it is merely superficial and does not impact that we think, but only what we think. There must be a source of thought, and we need to find it.
@Ren
Also some times a cat is just a cat. When you see an actual cat on an actual heater, it's not symbolic, it's a thing being itself. It might become a symbol when you recall it later as memory or knowledge, but I'd argue it's only trivially a symbol for the sole reason that your memory is not the actual cat.
This is a very language-like thought. A little like words, which are comprised of morphemes, an image may be disected into its constituent parts, which grow ever more smaller. I could have mentioned grammar here too, but morphology concerns itself with word-structure as well, and not only the arrangement of words. We could go ever more deeper, without ever reaching an answer that lies in structure.
What you haven't thought of,
@Ren, is that there must have been means of thought before there was communication, or words and signs to communicate with. Otherwise, we wouldn't have any means of communication now.