The Indeterminacy of the Physical

Bill Vallicella has another argument against materialism here.  He summarises as follows:
P1. All thoughts have determinate objects.
P2. No purely material representation has a determinate object.
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C. No thought is a purely material representation.
To justify P2 Bill asks us to consider a picture of our mother and an exact copy of said picture.  Does the latter represent our mother or the original picture of her?  This is the indeterminacy of material representations:  we can't tell from the physical stuff what it is a representation of, just as we can't tell from hearing spoken or seeing printed my name that it refers to me.  There is nothing in the physical entity that fixes the reference.

This is right as far as it goes, but it ignores the fact that such representations are embedded in larger systems that make use of them.  Imagine a robot consisting of a computer equipped with a TV camera 'eye' and a mechanical arm with a table bearing objects placed in front of it.  The computer can be programmed to analyse the pictures coming from the camera, identify the objects before it, calculate the coordinates of said objects relative to itself, and, on instruction, point to or even pick up with its arm particular objects.  This is well within the reach of present-day robotics, I'm sure.   In what sense are the representations of the objects on the table, as images or data structures in the computer's memory, insufficiently determinate?   True, the representations in our robot's computer memory could be bit-for-bit identical to those in the robot sitting at the neighbouring table, provided its objects were exactly like ours and arrayed likewise.  But our robot points to objects on its own table when asked, and likewise its neighbour.  And if we remove the objects on our robot's table then its own representations vanish, not its neighbour's.

But Bill will surely say that I am making the 'causal connection' objection and vanquish me with Hilary Putnam.   He quotes from Renewing Philosophy, p23, where Putnam discusses his uttering the word 'cat' on seeing a cat:
One cannot simply say that the word "cat" refers to cats because the word is causally connected to cats, for the word "cat," or rather my way of using the word "cat," is causally connected to many things. It is true that I wouldn't be using "cat" as I do if many other things were different. My present use of the word "cat" has a great many causes, not just one. The use of the word "cat" is causally connected to cats, but it is also causally connected to the behavior of Anglo-Saxon tribes, for example. Just mentioning "causal connection" does not explain how one thing can be a representation of another thing, as Kant was already aware.
Let's translate this passage to our robot example, supposing we have asked the robot to point to the book on the table:
One cannot simply say that the pointing to the book refers to the book because the pointing is causally connected to the book, for the pointing to the book is causally connected to many things. It is true that the robot would not be pointing as it does if many other things were different.  The robot's present pointing has a great many causes, not just one. The pointing to the book is causally connected to the book, but it is also causally connected to the behavior of robot makers, for example. Just mentioning "causal connection" does not explain how one thing can be a representation of another thing, as Kant was already aware.
Again, true, but we are doing a little more than merely mentioning 'causal connection' here.  We are saying that the robot's makers have established a causal nexus in which the book's representation in the robot supervenes on aspects of the book, and the motion of the robot's arm supervenes on the representation, in such a way that the arm continuously points to the book, regardless of changes elsewhere on the table-top.  What greater determinacy can we possibly ask of a representation?

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