I have been rather busy recently, but I replied to Joseph's comments privately. I now post my responses to the list. Joseph's remarks were of course first published there.
Cheers,
John
Hi Joseph,
Sorry to take so long to reply, but I have been pretty busy. I finally got my South African taxes together, and when I submitted them they immediately said they were auditing me. So I had to put together all my documentation and send it in. As a lot of it was in Durban this was not easy.
At 05:50 PM 2012/11/26, you wrote:
John,
Have you seen this note? I don't know when Pedro will get around to circulating it.
It is your comment that I would welcome most.
Cheers,
Joseph
----- Original Message -----
From: Joseph Brenner
To: John Collier ; fis
Sent: Friday, November 23, 2012 10:13 AM
Subject: John Collier's "Large Correction". And Information?
Dear John, Dear Colleagues,
In his detailed note of November 19, John made a series of points which, taken together, add up to a good foundation for a non-computationalist view of real processes. I have identified my glosses by initials.
1. Specific reference is made to non-computable processes in biological development, with implications for evolution and phylogeny.
2. Reaction diffusion systems cannot be solved because dissipation is an essential part of their dynamics.
JEB: This opens the door to the existence of systems in which some process other than diffusion is also at work.
I am not quite sure what you mean here, but the result can be larger scale patterns or structures. For example, in development of animals the formation of the gastrula in the blastula (the gut from the round oocyte) is a reaction-diffusion process. This leads to differentiation that can lead to further differentiation, and so on.
3. Analytical models that are not synthetic are non-computable for infinite possible data.
JEB: I suggest also for transfinite data, data that are infinite to all intents and purposes. I agree that synthetic models may (or may not) be reducible to their data, but only if their mereology is classical, which it seems to be in Johns note. Rosens distinction is itself too classical.
I am not sure what you mean by classical here, Joseph. They are the only logically possible types of models if we take a model to be a logical structure. Synthetic models are reducible from their definition; analytical models are not. Behaviorist models are synthetic, for example. Of course they don't work in most cases (they do work in a restricted range of behaviors). Computational models of mind can have the same reducibility, but need not be if the computations are only partial recursive (which is equivalent to saying that they are not algorithms in the usual sense of Knuth -- that is always terminating).
If I am missing something here, please expand.
4. Irrationality is not a property of a machine, and as such would indeed be unimaginable and not understandable.
JEB: Irrationality in human behavior is complex but not "illogical" in my terms. We are all rational and irrational to different extents at different times.
That would be a consequence of partial recursive functions being an correct analytical model of the processes, I would think. There would be a range of predictability (and hence controllability) but it would be limited.
5. Again if my body is a machine; if the world is a quantum computer, but I (John) worry about decoherence.
JEB: The hedging and the restrictions placed by Lloyd and Tegmark on their theories of the universe amount to intellectual dishonesty. By the time they are applied, you have a computational model all right, but it is a caricature of the real world.
I think the problem arises because of the failure to recognize that decoherence is a form of entropy production, and to further recognize that this is part of the dynamical process that can involve the system working on itself, particularly on its boundary conditions (constraints). This is not a typically computational process (though it can fit the weaker notion of computation as a recursively enumerable process, but not necessarily recursive). Recursive functions are all computable. A recursive function is one whose values and their complements are both recursively enumerable, so you can tell of any value whether or not it is in the range of the function. It might seem that this approach ignores the possibility that some processes are many-many relations rather than many-one, but I think this would violate some basic conditions on causality that don't have any empirical counter-examples that I know about. I am willing to allow that there might be non-causal connection principles, but I would want empirical evidence of some sort for those as well.
6. To avoid reductionism in reality, as opposed to it in logic and mathematics, I think we need the additional condition of dissipation.
JEB: The point of my logic in reality is that it is non-reductionist. It gives, even in its current perhaps oversimplified form, a structure to the evolution of dissipative processes.
The implication I see for information follows: information for me is a set of (dissipative) information processes, and these can be, and are, in part non-computable. Any proper theory of information, and its appropriate non-standard logic, should take this into account.
I basically agree with that.
Best,
John
Professor John Collier colli...@ukzn.ac.za
Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South Africa
T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031
http ://web.ncf.ca/collier
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