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Can the Mind Be Modeled by Mathematics? Classic ID-related Paper Now Available Online

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I don’t know how long this has been available (I have looked before, but was unable to find it), but I just noticed that Douglas Robertson’s “Algorithmic information theory, free will, and the Turing test” is available online. This paper has been highly influential in ID circles, as can be attested by its citation list.

The main thrust of the paper is that, solely on the basis of mathematics, any mathematical physical theory is incapable of producing consciousness as we know it. The reason for this is that mathematics are incapable of producing mathematical axioms. Therefore, a mathematical physical theory is incapable of producing the mathematical axioms on which it is based.

The paper is a fantastic read, and anyone who is interested in ID or in the relationship of mind to matter should give it a read. It is definitely both readable and worthwhile.

Robertson’s conclusion is this:

The existence of free will and the associated ability of mathematicians to devise new axioms strongly suggest that the ability of both physics and mathematics to model the physical universe may be more sharply limited than anyone has believed since the time of Newton.

Now, I actually disagree with this, at least in a way. I think we will continue to advance in our models of the universe, but I think we will have to rethink the *types* of models we come up with. The models we have looked at so far are deterministic, past-determines-future models. I think we will need to be looking at non-deterministic, future-influences-present models in order to accurately model the universe as we find it.

For those interested in these kinds of topics, remember that there is a conference this summer covering these things and their practical applications – The Engineering and Metaphysics 2012 Conference. I hope to see you there!

Comments
Neil and Elizabeth: Just to be clear: A human mind created Hamlet. Human minds have generate new and unexpected scientific models of reality. Formal mathemathical systems cannot do that.gpuccio
January 16, 2012
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Neil: So, would you accept this form of the statement? "In other words, the quantity of information output from any formal mathematical operation or from any computer operation is always less than or equal to the quantity of information that was put in at the beginning or added at some other moment." I would accept it that way, and still argue that our mind does much more than that.gpuccio
January 16, 2012
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Yes, but that's beside the point. Any input from outside is information that was not there from the beginning. It makes no difference whether it comes from a free will agent, or from a sensor connected to the computer.Neil Rickert
January 16, 2012
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Or input from an random number generator?Elizabeth Liddle
January 16, 2012
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Neil: I have not the time at present to go into detail on this subject (busy on a couple of other fronts), but I just ask you: isn't my typing on the keyboard and my moving the mouse an input coming from an agent who is supposed to have free will? Just curious...gpuccio
January 16, 2012
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I said I would give some details of my disagreement with Roberson. So here they are. Honestly, Robertson's paper should never have made it past peer review.
Godel’s Gödel's work put an end to a half century or more of unsuccessful attempts to build a firm theoretical foundation for mathematics.
Many people, especially researchers in Foundations of Mathematics would disagree with that.
Chaitin’s development of Algorithmic Information Theory (AIT) has sharpened our understanding of the meaning and significance of Gödel’s theorem to the point that the theorem that was once considered extremely difficult to understand now seems rather simple and obvious.
Yet, in the Wikipedia entry for Chaitin we find: "Some philosophers and logicians strongly disagree with the philosophical conclusions that Chaitin has drawn from his theorems. The logician Torkel Franzén criticizes Chaitin’s interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin’s work represents." And note that Torkel Franzén was widely considered to be an expert on Gödel's work.
As Stewart put it [3]: “From Chaitin’s viewpoint, Gödel’s proof takes a very natural form: the theorems deducible from an axiom system cannot contain more information than the axioms themselves do.” This simple insight has fundamental consequences for both mathematics and philosophy, yet it is not widely known or appreciated.
Let's start with the quote attributed to Stewart. If we take the commonsense or intuitive meaning of "information", then the conclusion about theorems deducible from an axiom system was well known before Chaitin's time. It was probably already familiar to Hume, and perhaps even to Aristotle. That's not intended to criticize Chaitin. He introduced his Algorithmic Information Theory, which includes definitions of the quantity of information. So what Chaitin showed (or claimed to show) is that Gödel's work can be used to make that informal commonsense view of the limitations of logic quite formal and precise in terms of how Chaitin formalized algorithmic information. For what Robertson is using, it is the informal commonsense view of "information" that is needed. Robertson does not make any essential use of Chaitin's formalization. So when he says that this "is not widely known or appreciated" he is spouting nonsense.
Indeed, the failure to anticipate this idea has lead to a number of fundamental and even embarrassing conceptual errors, not the least by Hilbert and his distinguished colleagues in the early part of this century in their brilliant but ultimately futile effort to finish all of mathematics.
Really! Robertson accuses Hilbert of embarrassing conceptual errors? It is Robertson who should be embarrassed about having written that.
AIT and free will are deeply interrelated for a very simple reason: Information is itself central to the problem of free will.
Yes, information is central to free will. But Chaitin's AIT is an abstract theory of a highly idealized notion of "information." I'm doubtful that it has any relevance at all to the problem of free will, or to any other practical real world use of information.
Since the theorems of mathematics cannot contain more information than is contained in the axioms used to derive those theorems, it follows that no formal operation in mathematics (and equivalently, no operation performed by a computer) can create new information.
This is true.
In other words, the quantity of information output from any formal mathematical operation or from any computer operation is always less than or equal to the quantity of information that was put in at the beginning.
But this is false. If you are using a computer, then anything new that you type in at the keyboard, or any motion of your computer mouse, provides information that was not there at the beginning. Robertson's analysis of free will completely fails at that point. I could go on, criticizing the rest of the paper. But that seems pointless. It is already quite clear that Robertson is in way over his depth.Neil Rickert
January 16, 2012
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Elizabeth - I think you are misreading it. The purpose of the definition of free will is to be sure of what he is arguing for, since there are so many disagreements over what free will is. There are people (such as Nancey Murphy) who include in "free will" entirely deterministic processes. As such, Nancey Murphy argues *for* free will, but it is nothing like the free will most philosophers have discussed for centuries. The point of the math is the evidence for the free will. Namely, showing that, for any mathematical physics, that physics is not sufficient to create the axioms from which mathematics derives. In other words, physics can't be introspective. Thus, the ability of humans to derive mathematical axioms places human action beyond any purely mathematical physics. Note that this is essentially the point which Kurt Godel spent his life making. It is unclear whether Turing thought the same thing - I think he was an atheist, but he was not a materialist - at least when he wrote "Systems of Logic Based on Ordinals". A good lecture on this subject, and the relative contributions of Turing, Penrose, and Godel, is available herejohnnyb
January 16, 2012
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It seems to be a circular argument in which "free will" is defined in such a way as the argument must hold. Namely, that "free will" means that there is a disembodied "mind" or "will" that can act on matter, but is is uncaused by it. He says that all other kinds of free will are "illusions". If that's where you start, clearly that is where you will finish. You don't really need the math in between.Elizabeth Liddle
January 16, 2012
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Out of curiosity, are you the same Neil Rickert that wrote the Sendmail book?
Yes. However, to be clear, I did not write the book. I am listed as a co-author, because I made many contributions. The primary author was Bryan Costales.Neil Rickert
January 15, 2012
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Anything specific or just poisoning the well?
I'll go through some details tomorrow.Neil Rickert
January 15, 2012
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Out of curiosity, are you the same Neil Rickert that wrote the Sendmail book?johnnyb
January 15, 2012
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Anything specific or just poisoning the well?johnnyb
January 15, 2012
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I have downloaded the paper, and have read the first two pages. I'll try to read more over the next few days. I am already underwhelmed by those first two pages.Neil Rickert
January 15, 2012
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