Do you know what hyperreal numbers are? They’re a concept in number theory, a sort of number, like integers, real numbers, imaginary numbers, etc. I myself have only a passing familiarity with hyperreals; I know that they’re represented by infinite sequences of finite integers, that you can perform arithmetical operations on them (though these are quite different from operations on everyday numbers), and… that’s all. I don’t know *how* one would operate on hyperreals; one thing I certainly don’t know—not an inkling—is how one would go about multiplying two hyperreal numbers together.

Imagine that I’m placed in a locked room. People outside the room pass pieces of paper to me through a slot, and on these papers are symbols; perhaps alphanumeric characters, perhaps ones and zeros, perhaps strange squiggles I’ve never seen before. They don’t seem to be in any sort of pattern, at least not one I can discern.

Along with the pieces of paper with the (apparently) meaningless symbols on them, I also get a set of instructions, these in a language I can understand—English, Russian, C++, whatever. The instructions tell me how to rearrange and manipulate the symbols I receive. “If you get such and such a symbol,” the instructions might say, “write down this other symbol and pass it back to us through the slot. And if you get these three symbols in this order, write down these other two and pass them back.”

The instructions shed no light whatsoever on the meaning of the symbols, or the significance of these purely mechanistic operations which I’m instructed to perform on them. Nonetheless I follow the instructions, I take in papers with symbols on them and pass back papers with other symbols, as instructed. I perform the manipulations perfectly, being a diligent and meticulous sort of person.

I do not have any clue about what it is that I’m really doing. Of course, as I am a student of philosophy, this all seems eerily familiar to me; I begin to suspect that perhaps the symbols represent Chinese, and that I am taking part in the famous thought experiment…

It turns out that I’m dead wrong. The symbols do not represent Chinese characters, or at least they aren’t intended to; they *are*, however, intended to represent, unbeknownst to me, hyperreal numbers. And the instructions are an algorithmic procedure for multiplying two hyperreal numbers together.

So, from the standpoint of a person outside the room, what takes place is this: he selects two hyperreal numbers, writes them down according to the selected encoding, passes them into the room, and out comes the product of the two hyperreals. The result of the calculation is correct, every time, without fail (and why wouldn’t it be?). Clearly, the room is multiplying hyperreals.

Now what is John Searle to say to this? Let’s be quite clear on this: *I*, the homunculus in the room, do *not* know how to multiply hyperreals. Were I to diligently manipulate the symbols for a thousand years, I wouldn’t learn how to multiply hyperreals. Even if I internalize the storage (the papers) and the computation (the instructions) and do it all in my head, I still wouldn’t know how to multiply hyperreals.

I don’t even know *that* I am doing any multiplication, or any mathematics; all I know is that I am manipulating meaningless (to me) symbols according to a meaningless (to me) set of instructions. Do we conclude that the room is *not* really multiplying hyperreal numbers? But what can we mean by this? In go two hyperreals; out comes the product. The result is mathematically correct.[1]

But what goes on in the hyperreal room seems to be just the same sort of thing as what goes on in the Chinese room. What basis, then, do we have for claiming that one room is “really” doing the thing it seems to be doing, and the other room isn’t? What fundamental, qualitative difference is there? I can see none. In any case, the burden of proof appears to be on Searle to show that this is not a reductio of his thesis, as it truly seems to be.

Now Searle has three options here, as I see them. One, of course, is to admit that the Chinese room does indeed speak Chinese. Another is to demonstrate some key difference between the Chinese room and the hyperreal room such that our conclusions about one do not apply to the other. The third is to insist that the hyperreal room does not really multiply hyperreals, as the Chinese room does not really speak Chinese.

Of course, should he select the third option, Searle will be unable to lean so heavily on intuition as he does in his original argument about the Chinese room. For in the case of the hyperreal room, intuition stands against him.

***

[1] Indeed, if we have a function *f* such that for all *x*,*y*, *f*(*x*,*y*) = *x* · *y*, then *f* simply *is* multiplication. The hyperreal room is such a function for all hyperreal *x*,*y*.

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