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In this lecture Hilary Putnam says the following:

  • Mind-body Functionalism is true. In fact not only is it true, but it makes ontological questions of philosophy of mind mostly irrelevant.
  • The laws of physics mean that human brains/minds can be simulated by Turing machines to an arbitrary level of precision.

And yet he also says that is it his opinion that:

  • AI is impossible, given the fact that AI programs are always problem specific and are not capable of general problem solving or of thinking outside of the context of their original design, whereas humans are capable of solving problems that have nothing to do with the original evolutionary purposes that their minds were designed to solve.

Isn't he contradicting himself in this lecture?

If mind-body functionalism holds and Turing machines can simulate human minds with arbitrary precision, then it follows directly from those two facts that a computer can do anything a human mind can do in principle, regardless of the current state of AI programming.

What am I missing? How can Putnam's statements ("Functionalism + Turing reducibility of the mind" and "General AI is impossible") be reconciled?

  • 1
    related: philosophy.stackexchange.com/questions/14026/… – Dave Jun 3 '16 at 21:41
  • Something exists that has nothing to do with the original evolutionary purposes that our minds were 'designed' to solve? What might that be? What is objectively unrelated to surviving in competition with other minds of equal quality to one's own? Once strategy and physics are both part of life, you have technology. At that point, any and every question is relevant to survival. – jobermark Jun 5 '16 at 4:24
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In defense of Putnam against a charge of contradicting himself, it might be said that he was trying to avoid doing so when he made a distinction between psychological states and Turing states according to the following characteristics:

  • Unlike psychological states, Turing states are independent of learning and memory.
  • Together with learning and memory, Turing states are deterministic with respect to subsequent states.

He asserts the following in regard to these differences:

"These characteristics establish that no psychological state in any customary sense can be a Turing machine state."

In addition to that, what may appear as a contradiction may be an indication of his doubts as to whether our current approach to artificial intelligence can ever be adequate for explaining mental life in humans. To some extent, we may all have unreconciled inconsistencies in our thinking with which we maintain hopes of eventually resolving. Putnam expresses such a hope by pointing out that our current approach to functionalism is unlikely to provide computers with the means to solve the types of problems which humans are able to solve:

"The notion of functional organization became clear to us through systems with a very restricted, very specific functional organization. So the temptation is present to assume that we must have that restricted and specific kind of functional organization."

At another point he says:

"We have no serious reason to believe that general intelligence is simply the accumulation of a large number of programs which have such restrictive solution statements."

Even so, I believe that the problems which are the cause of his doubts go beyond merely our approach to functionalism. That is to say that no new approach to functionalism can adequately address the problems that are evident in his arguments. To begin with, it might be helpful to recall Putnam's definition of functional isomorphism:

"Two systems are functionally isomorphic if there is a correspondence between the states of one and the states of the other that preserves functional relations'."

Supposedly, this concept of isomorphism should serve to clarify the reasons why he believes that ontological considerations are irrelevant to the question. However, Putnam himself brings up a point which may prove to be one of the greatest threats to his theory, namely, that the discrete structure of matter calls into question the possibility of any true continuity. He begins his response with the following:

"One [problem with this argument] is that there are continuities even in quantum mechanics, as well as discontinuities."

This first response is kind of trivial, because not all continuities are adequate for the tasks at hand. A magnetic field, for example, most likely lacks the necessary articulation which would be required to serve as a information medium. Putnam's second argument is more interesting:

"The other problem is that if that were a good argument, it would be an argument against the utilizability of the model of air as a continuous liquid, which is the model on which aeroplane wings are constructed, at least if they are to fly at anything less than supersonic speeds."

This argument is actually fallacious, because nobody is arguing that all discrete substances are unsuited for all purposes. Therefore, Putnam has to overgeneralize it to reach the conclusion he wants, i.e. he has to make a fallacious induction from a particular to a universal. Even so, the question that he brings to our attention is worth considering. He emphasizes that the discontinuity of a system is irrelevant if it approximates continuty. We might formalize that as follows:

  • Fxy = x and y are functionally isomorphic with respect to each other
  • Rxyz = x is functionally related to y in system z
  • Cx = x is continuous
  • Dxy = x approaches the continuity of y, but is discontinuous

    1. ∀x[∀y[Fxy ↔ ∀t[∀v[Rtvx ↔ Rtvy]]]]
    2. ∀x[∀y[(Cx & Dyx) → Fxy]]

That essentially amounts to saying that if a discontinuous system approaches the continuity of a corresponding system, they are functionally isomorphic; and being as such, all their functional relations should be functionally sound.

Now, to refute this claim, all that is necessary is a counter example. The first thing that came to mind was a childhood memory of my mother checking a string of Christmas lights for a burnt-out bulb. When one burns out, they're all out. The discontinuity of the string approximates the continuity of a string with all good bulbs. Furthermore, the two string exhibit distinct functional properties; namely, one lights up and the other doesn't: Rpbc & ~Rpbd (p = plugged in; b = blinking; c = continuous string; d = discontinuous). From that, it's straightforward to prove that there are some systems whose discontinuity approximates a continuous system, and yet they are not functionally isomorphic:

  1. Ǝx[Ǝy[Cx & Dxy & ~Fxy)]]

An important difference between my counter example and Putnam's airplane example is that mine is more closely related to the idea of communication, which makes it more relevant for the sort of functionality that is necessary for information systems. Like a string of Christmas lights, it's often the case that a single break in a line of communication can render it useless.

In addition to that, the distinction between discrete systems and continuous systems may also hold the key as to why computers are void of any semantical content. When you think about it, content for a computer amounts to nothing more than scalar values, and, even then, it's only scalar values that don't exceed the value of 1. Every bit in a computer is epistemically isolated from the rest of the system because they operate according to a causal chain of events. It's a one-way flow of communication in which each bit of information is disconnected from whatever preceded it. Computers simply lack the physical conditions to provide the sort of unity that is characteristic of mental life.

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Saying that:

[general] AI is impossible, given the fact that AI programs are always problem specific and are not capable of general problem solving

It is not really a contradiction to the claim that a TM can in principle simulate a human being.

By "AI programs" Putnam refers to programs that we create in practice. By a TM simulating a human being, Putnam is refers to a program that exists in principle.

These are clearly different things.

It is possible in principle to compute the representation of Pi with 10^1000000 digits, but it impossible for humans for compute it in practice.

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