This is a hard question to think about, or even to fully specify. It's particularly hard when one uses language to think about it.
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This doesn't mean it's impossible, though. Mathematicians have figured out powerful ways of reasoning about infinity, using purely finite processes of reasoning.
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Another analogy is to the way computer scientists have gradually developed more powerful ideas about programming languages: things like Lisp macros, lazy evaluation, higher-order functions, etc. These ideas were, in some sense, discovered, & can transcend earlier ideas.
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I have so many thoughts about this!! I wrote some here on the boundary between and beyond image and language: https://tinyletter.com/hypotext/letters/speculative-nonfiction-the-indescribable-image-the-unpicturable-sentence-1 …
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I suspect you will greatly enjoy Pavlenko's book "The Bilingual Mind: and what it tells us about language and thought" http://hypotext.co/resources/The_Bilingual_Mind__Aneta_Pavlenko.pdf …
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Do you believe there are forms of art which take us as far beyond language as language did beyond the communication of chimps? Examples? (I understand they may take quite some time to appreciate!)
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Many things await us. http://www.xenology.info/Xeno/25.2.2.htm Current language is a reflection of our ability to process information. Imagine being able to think in terms of 1 billion simultaneous scenarios. How might you communicate ideas at that scale? Way more detailed glyphs for one thing.
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Listening to a music track which has thousands of instruments layered in millions of patterns??
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You could look at shared cultural contexts as communication beyond language. Or at least making language more powerful than just the words. There is a lot wrapped up in "he's like Ceasar"
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this point is reminiscent of the languages vs. libraries debate in PL!
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