As pointed out in the comments, in linguistics and science circles there is a name for view you advocate in your post: the Sapir-Whorf hypothesis. I don't think there is much evidence for the strongest forms of the hypothesis, but there is definitely some cool science around it. I will give my favourite example.
Physics does not have colour, it just has a continuous spectrum of wavelengths. Even when you look at the sensitivity of the 3 types of cones in the retina it is not discrete, but continuous. The categories of colours (i.e. "that's red", "that's blue") are produced by perception and these discrete-ish categories form the basis of colour qualia. Scientists can study these categories by asking participants if various stimuli 'feel' like the same colour. The arbitrary boundaries of the categories people draw between colours is language dependent (Regier & Kay, 2009).
Of course, the brain is a messy place, and there is no reason to expect that it will produce a clean well-ordered mind. Gilbert et al. (2006) showed that the Whorf hypothesis is supported in the right visual field but not the left. In other words, when I present colours in one part of your visual field, you experience them one way and when I present them to the other then you experience them in a fundamentally different way. The right visual field integrates with your linguistic processing and the other doesn't. As often is the case in science, the answer is messy and not what arm-chair reasoning might suggest.
The effects of language on perception (and thus the conscious experience) are not limited to colour. Unsurprisingly, you have a similar effect in phoneme perception: how the continuous variations in how the air shakes get mapped to discrete categories of "that's an a", "that's an o". Peltola et al. (2012) showed that this categorization is not only language-dependent, but in the case of bilingual speakers depends on if they are a balanced or dominant bilingual (see the paper for details). Yay, for relativity.
Does this mean you should draw conclusions about linguistic-relativity of higher level cognitive processes from this evidence? If you are a philosopher then maybe, if you are a scientist then of course not.
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