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mvp9 comments on Superintelligence Reading Group - Section 1: Past Developments and Present Capabilities - Less Wrong
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A different (non-technical) way to argue for their reducibility is through analysis of the role of language in human thought. The logic being that language by its very nature extends into all aspects of cognition (little human though of interest takes place outside its reach), and so one cannot do one without the other. I believe that's the rationale behind the Turing test.
It's interesting that you mention machine translation though. I wouldn't equate that with language understanding. Modern translation programs are getting very good, and may in time be "perfect" (indistinguishable from competent native speakers), but they do this through pattern recognition and leveraging a massive corpus of translation data - not through understanding it.
I think that "the role of language in human thought" is one of the ways that AI could be very different from us. There is research into the way that different languages affect cognitive abilities (e.g. -- https://psych.stanford.edu/~lera/papers/sci-am-2011.pdf). One of the examples given is that, as a native English-speaker, I may have more difficulty learning the base-10 structure in numbers than a Mandarin speaker because of the difference in the number words used in these languages. Language can also affect memory, emotion, etc.
I'm guessing that an AI's cognitive ability wouldn't change no matter what human language it's using, but I'd be interested to know what people doing AI research think about this.
Lera Boroditsky is one of the premier researchers on this topic. They've also done some excellent work on comparing spatial/time metaphors in English and Mandarin (?), showing that the dominant idioms in each language affect how people cognitively process motion.
But the question is more broad -- whether some form of natural language is required (natural, roughly meaning used by a group in day to day life, is key here)? Differences between major natural languages are for the most part relatively superficial and translatable because their speakers are generally dealing with a similar reality.
I think that is one of my questions; i.e., is some form of natural language required? Or maybe what I'm wondering is what intelligence would look like if it weren't constrained by language -- if that's even possible. I need to read/learn more on this topic. I find it really interesting.