>> What's more, whatever you like to call the transoforming of information into thinked information by definition can not be a (mathematical) function, because it would require all people to process the same information in the same way and this is plainly false
No this isn't the checkmate you think it is. It could still be a mathematical function. But every person transforming information into "thinked information" could have a different implementation of this function. Which would be expected as no person is made of the same code (DNA).
Not sure there aren't 10 other "lines of discussion/disagreement" on this, but the one I think might be most salient is Davidson's https://en.wikipedia.org/wiki/Anomalous_monism (Davidson was a student of Quine who people here might know more from his work in logic/kitchy programs-that-print-themselves games than as the bigtime analytic philosophy Word & Object, naturalized epistemology type work).
Note that using words like "function" and "mathematical" are more the biases of computer science/Penrose while philosophy of the mind & psychology has more typically used slightly different ideas of "attitudes" and "events" to guide the discussion. I don't think this really radically shifts many central disputes, except (which Penrose might view as a critical "except") for all the funny business quantum mechanics / quantum computation can potentially bring in and the (undisputed) physicality of our brains and (also undisputed) lack of understanding of many details of biological computation.
No this isn't the checkmate you think it is. It could still be a mathematical function. But every person transforming information into "thinked information" could have a different implementation of this function. Which would be expected as no person is made of the same code (DNA).