On Wednesday, August 21, 2002, at 09:46  AM, Bruno Marchal wrote:

> Hi Tim, Hi All
> So I got indeed the Yetter's book. I promise to you, Tim, some
> commentaries. Here they are. It is for me an opportunity
> to write my last long post, before I try to write that english
> text as Wei gently insists I do. Yetter's book interests me for
> two related reasons, both linked to my thesis, and even to the most
> advanced part of it---in some sense you arrive, in the list, a
> little to early with your toposes! :-).

Many thanks for remembering my current main interest, but I still have a 
long, long way to go before I can understand your logic points. (I have 
several "advanced" books on logic, but mainly for inspiration and 
direction. Have recently picked up more introductory books by Tarski, 
Boolos, Smullyan, etc. My focus is more on the lattice/Heyting algebra 
side, so a lot of logic has not yet been needed.)

> About the mind I am a conservative sort of logician, and I am
> platonist about positive integers, so by mind I take first
> boolean arithmetical truth. Did not George Boole entitled his
> book "The Laws of Thought"?

Yes, but the conventional logic point of view has not proved to be 
especially useful for understanding mind and AI, as I'm sure you know 
very well. I actually used to be in the AI business, when I was still at 
Intel in the mid-80s, and I mostly lost interest in using logic and 
algorithmic reasoning in AI. Did a bit of work on the emerging neural 
net/connectionist approach, and also realized how lacking that was.

So while I think the IL/Brouwer/Heyting/topos stuff will _eventually_ be 
of use in epistemology and ontology aspects of AI, I'm not expecting 
quick progress.

As for mind-body issues, I've never understood what the big deal is.

> It is not a too big exaggeration to say that the work by Everett,
> Graham, Hartle, Zeh Joos, Kiefer (and others) gives an explanation
> of BITS from QUBITS. That is, how classical observers/worlds emerge
> from a quantum reality.

Quantum theory is of much more current interest to me. Hence the work of 
Chris Isham and others. (Ironically, as I may have mentioned, I took GR 
from Jim Hartle back in 1973. Then it was all stuff about Killing 
vectors and rotating black holes and all, and none of the math I was 
also taking in a seminar on analysis and topology was then recognized by 
me as being effective. (Though one seminar I was in was using the 
just-published Hawking and Ellis, "Large-Scale Structure of Spacetime" 
book. I wasn't mentally prepared, I assume, to see the connections I am 
now seeing, nearly 30 years later! The seminar leader was Terry 
Sejnowski, who later switched to connectionist AI and was the force 
behind the "Boltzmann Machine" in the early 80s, ironically enough.)

> And it is not at all an exaggeration to say my work is an attempt
> to explain QUBITS from BITS. Actually I show more and less:

This interests me a lot more than dealing with the mind-body 
problem...perhaps because I only think about things I can "sort of" 
grasp. The problem of mind is just too large a problem at this time, I 

>  -More: because my work provides a proof that, IF we take the
> comp hyp seriously enough, THEN qubits *must* follow from bits.
> This is basically done by the Universal Dovetailer Argument UDA (+
> the Movie Graph Argument if you don't like explicit reference to
> OCCAM razor).

I hope to spend more time looking at your LISP programs.

> [much logic elided]

> And more: It is natural to define S4Grz* (which correspond to
> G* as S4Grz correspond to G). But surprise: S4Grz = S4Grz*.
> The first person is his own guardian angel! Even Boolos remarks
> in his second 1993 book on provability that this phenomenon
> is "shades of the intuitionists' doctrine that mathematical
> truth is to be identified with provability.

And this point of view is also consistent with Greg Chaitin's notions of 
the provable truths being a tiny fraction of the "uncharted territory," 
with "experimental math" playing a more important role in the future 
(though it can be argued that nearly all of our math is motivated by 
either experimental or physics or other "sociological" considerations: 
mathematicians tend to work on problems linked to other problems or 
motivated by physics and other observations.

The "constructivist" motivation is not all that strange.

> Bruno
> So it is not exactly my last long post, but it is among them.
> Perhaps such more detailled explanations will help me in
> planning a longer paper. Thanks for your patience.

In my own way, I find that writing articles helps me to think through 
complex arguments.

BTW, the most exciting recent thread for me was the one about the 
"reversability of time" arguements, raised initially by Wei Dai and then 
argued by Hal Finney. Writing the "Professor Ludwig" piece, in which an 
1860 Prof. Ludwig (Boltzmann, obviously) predicts that the simplest 
time-reversed pocket of the universe means telescopes will likely see 
nothing but chaos outside the local region, helped me to clarify my 
thinking on anthropic arguments. And motivated me to finish reading Huw 
Price's book.

This is the real blessing of mailing lists like this one! I may now be 
motivated to understand the kinds of logic you discuss if only to try to 
refute you! (no offense intended)

--Tim May
(.sig for Everything list background)
Corralitos, CA. Born in 1951. Retired from Intel in 1986.
Current main interest: category and topos theory, math, quantum reality, 
Background: physics, Intel, crypto, Cypherpunks

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