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I've been re-reading the Wikipedia article on the Chinese Room argument and I'm... actually quite unimpressed by it. It seems to me to be largely a semantic issue involving the conflation of various meanings of the word "understand". Of course, since people have been arguing about it for 25 years, I doubt very much that I'm right. However... the argument can be thought of as consisting of several layers, each of which I can explain away (to myself, at least).

  • There is the assumption that being able to understand (interpret a sentence in) a language is a prerequisite to speaking in it.
    Let's say that I don't speak a word of Chinese, but I have access to a big dictionary and a grammar table. I could work out what each sentence means, answer it, and then translate that answer back into Chinese, all without speaking Chinese myself. Therefore, being able to interpret (parse) a language is not a prerequisite to speaking it.
    (Of course, by the theory of extended cognition I can interpret the language, but we can all agree that the books and lookup tables are simply a source of information and not an algorithm; I'm still the one using them.)
    Nevertheless, this task can be removed by a dumb natural language parser and a dictionary, converting Chinese to the set of concepts and relationships encoded in it and vice versa. There is no understanding involved at this stage.
  • There is the assumption that being able to understand (identify and maintain a train of thought about concepts in) a language is a prerequisite to speaking in it.
    We've already optimised away the language, to a set of concepts and relationships between concepts. Now all we need is another lookup table: a sort of verbose dictionary that maps concepts to other concepts and relationships between them. For example, one entry for "computer" might be "performs calculations" and another might be "allows people to play games". An entry for "person" might be "has opinions", and another might be "has possessions". Then an algorithm (yes, I'm introducing one now!) would complete a simple optimisation problem to find a relevant set of concepts and relationships between them, and turn "I like playing computer games" into "What is your favourite game to play on a computer?" or, if it had some entries on "computer games", "Which console do you own?".
    The only "understanding" here, apart from the dumb optimisation algorithm, is the knowledge bank. This could conceivably be parsed from Wikipedia, but for a good result it would probably be at least somewhat hand-crafted. Following this would fall down, because this process wouldn't be able to talk about itself.
  • There is the assumption that being able to understand ("know" how information in affects one's self) a language is a prerequisite to speaking in it.
    A set of "opinions" and such associated with the concept "self" could be implemented into the knowledge bank. All meta-cognition could be emulated by ensuring that the knowledge bank had information about cognition in it. However, this program would still just be a mapping from arbitrary inputs to outputs; even if the knowledge bank was mutable (so that it could retain the current topics from sentence to sentence and learn new information) it would still, for example, not react when a sentence is repeated to it verbatim 49 times.
  • There is the assumption that being able to have effective meta-cognition is a prerequisite to speaking in a language.
    Except... there's not. The program described would probably pass the Turing Test. It certainly fulfils the criteria of speaking Chinese. And yet it clearly doesn't think; it's a glorified search engine. It'd probably be able to solve maths problems, would be ignorant of algebra unless somebody taught it to it (in which case, with sufficient teaching, it'd be able to carry out algebraic formulae; Haskell's type system can do this without ever touching a numerical primitive!), and would probably be Turing-complete, and yet wouldn't think. And that's OK.

So why is the Chinese Room argument such a big deal? What have I misinterpreted? This program understands the Chinese language as much as a Python interpreter understands Python, but there is no conscious being to "understand". I don't see the philosophical problem with that.

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If you check the Wikipedia article on the argument that you linked, in the History section, you'll note the following statement:

Most of the discussion consists of attempts to refute it.

I think this directly answers the question,

Why is the Chinese Room argument such a big deal?

The Chinese Room Argument was a relatively early attempt in the intermingling of Philosophy and Computer Science to make as concrete an argument on the definition of a "mind", "understanding", and whether or not these can be created with a program. That is, it conjectures that a "mind" cannot.

It's famous in part because the concreteness of this argument means that a counter-argument can be made in kind. That is, the argument spawned a large quantity of refutations, attacking the argument from a large number of vectors, outlined later in the argument.

Put another way,

The Chinese Room Argument is such a big deal because of how many people in the field have found value in refuting it.

Incidentally, your post provides more evidence to this point.

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The Chinese room argument is such a big deal because it takes the concept of the Turing machine and Turing's conception of the electronic digital computer (so-called) as a practical version of the universal Turing machine, and shows that the resulting concept of machine computation does not allow the creation of an internal semantics (knowledge). Explaining why this is the case is is a bit of a fraught task, though.

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