Set theory and digital souls

There's considered to exist a classical, long lasting, philosophical conflict between two points of view, called dualism and materialism.

Dualism claims that some aspects of reality are genuinely mysterious. Not only inaccessible to science, but fundamentally mysterious and spiritual. Dualism is more or less religious, and the human soul is seen as an example of spiritual mystery.

Materialism claims, in opposition against dualism, that consciousness arises somehow as an effect of physical, chemical, electrical processes in the brain. We can today calmly conclude that consciousness is hard to understand, but according to materialism, it shouldn't be completely impossible.

I'm now about to overthrow these familiar perspectives, something that I started doing about 25 years ago.

But first a few more words about materialism:
There's a clever argument for materialism. The spirit world, if it exists, must somehow interact with the material body, if it's going to have any influence on how a living person behaves. Somewhere inside a living body there must be a place where the spirit intervenes and to some extent replaces the laws of physics. Such a "spiritual user interface" has never been found. The molecules of a living body would seem to obey the same laws as all other molecules do.

Materialism is a bit bleak, according to many, and some consider it totally unacceptable, whether it's right or wrong. If the soul is utterly dependent on the brain, then religios hopes for an afterlife, in all forms, will shatter against an austere wall of logic. Since any life lived will be forgotten when the brain decays, there can be no (individual) meaning to be won. (Ok, I think that concludes the worst part of this text. The rest will be easier, if somewhat harder to understand.)

A drastic version of materialism is called artificial intelligence, AI for short. Some mild variations on AI are restrained and cautious, but I write here about AI as the idea that a conventional digital computer could be equipped with consciousness, at least in theory. A longer life could then be won by moving one's soul over to a computer, but that's not quite the point I'm trying to make.

A short introduction to what I'm about to say can be found here:
http://www.flexitrack.se/nyplaton/indexE.html

The introduction is cautious and child friendly, as far as possible, and it avoids the most burning theological questions. I'm being more forthright here.

Ah, now, where was I? Oh, yes, I'd like to continue with a few remarkable logical consequences of AI. I'm no friend of loose assumptions, but assumptions can be mathematically respectable, if they are openly declared, and later, remembered. I assume, for now, that AI is correct. I'm not trying to convince anyone that AI is true, and I certainly haven't proven it, yet the assumption must here be made for the continued argument´s sake.

The contents of a conventional digital computer, at a specific point of time, can be completely described by a sufficiently long array of binary bits, zeros and ones. Since the computer's time is also digitally clocked (discrete), every computation performed by the computer can be expressed as one sufficiently long array of bits. To accomplish this, it would be enough to examine the computer at every discrete point of time and simply concatenate all the bit patterns together. An awkwardly uneconomical way to describe computation, pointless but very general, and good enough for the theoretical purposes here.

All computer computations, absolutely all, both actual, conceivable, possible and almost impossible, can be exactly described by bit patterns. It's easy to define the mathematical set of all bit patterns, and it's essentially identical to the set of all integers. Most realistic computations would correspond not to one, two or three, but to very large integers. The set of integers is of course well known. It's an infinite set of (transfinite) cardinal number aleph zero, which is to say the countable order of infinity. There's a starting point for more about cardinal numbers on wikipedia:
http://en.wikipedia.org/wiki/Cardinal_number

Is the set of integers something that really exists? "Of course not, it's only math and no real screwdriver?" But if the set utterly doesn't exist, how can we know anything specific about it? It can be explored into its finest details, and different researchers can reach similar results, independently of each other. It can hardly be the simple truth that the set of integers doesn't exist, at all.

The set of all computer computations is a subset of the set of integers. It might appear as a tiny subset, but it would in fact also have the countable order of infinity. Also this subset would exist, to some extent, although maybe not as materially evident as the archeological prison dungeons of the ancient heretics. And, at last, we have arrived at an interesting and challenging statement:

If AI is correct then the set of all subjective conscious experiences is a subset of the set of all computer computations. A horse in motion insane or just tranquil logic? I would myself prefer to consider the conclusion as quietly logical. All conceivable conscious experiences exist.

Having had some time to get used to the idea, it may start to appear more reasonable. If the impressions of the soul are possible to describe in any systematic way, then it should be possible to define the set of all such sequences. If the set is possible to explore, how could anyone claim that it doesn't exist?

But souls are alive, in time, whereas mathematics only contains a static description? True, but there are no details lacking from the mathematical description, according to the conditions that we have assumed! All non mysterious aspects have been accounted for. Time isn't a problem in principle here. We could ask Albert Einstein himself about that, or at least infer it from his work. The course of time is part of the description. There are no obstacles for consciousness in a mathematical set, if consciousness is understandable in terms of nuts and bolts.

But we immediately stumble upon a serious paradox. I'm sitting here writing, at my computer, and there seems to be a continuation of my life where I sit writing a while yet. But! There are, according to logic, an infinite number of continuations of my life where I am Kermit the Frog, and there are infinitely many continuations where I experience peculiarities I've never heard or dreamed of. I think, therefore I am suddenly Mickey Mouse. Why, why is my surrounding world so constant, if everything, literally everything, is possible??? (To avoid accusations of insanity, I should perhaps make clear that nothing of this has happened before my eyes. I'm merely using whatever logic I have available to reason about this.)

In the field of mathematics, if making an assumption, and later finding logical consequences that are unreasonable, then the original assumption is wrong. But I don't believe that I have proven with certainty that AI is wrong. Another possibility could be that the material universe we live in is configured in such a way that it "wins the combinatorial race" against other possible continuations of our subjective experiences. This might be in line with what has been suggested by the american physicist Hugh Everett. Also the more recent quantum computer researchers have been entertaining similar thoughts, to some extent in opposition against Niels Bohr and the Copenhagen school.
http://en.wikipedia.org/wiki/Hugh_Everett
http://en.wikipedia.org/wiki/Niels_Bohr
http://en.wikipedia.org/wiki/Quantum_computer
I'm now about to end this mail, and apparently without much of a punchline, awaiting further research.
/Bengt

Hello again
In my mail "Set Theory and Digital Souls" I mentioned the Copenhagen school and Niels Bohr. I don't know if the mail I'm writing now is directed first of all to you, but my last letter gives me a reason to write a few more lines.

Is the Copenhagen school backwards, prejudiced and lacking in fantasy? Before the verdict falls, I could as a lunatic-honest defense lawyer of the enemy perhaps mention verifiability and falsifiability.

The kind of logically reasoning science that I do in my former mail could perhaps be said to lie close to the classical ideals of Aristotle. That may sound very impressive, but at least within physics, Aristotle has lost some of his authority to Galileo Galileo, who represents a more experimental approach. (I'm not writing anything here about Galilei and the cardinals Bellarmine and Barberini, the later elected pope Urban the eighth.)

Galileis reliance on direct observation raises questions about a world view containing a very large number of different universes. We can't, in an evidently simple way, allow someone to travel to a different universe, perform experiments there and then return back here to publish the results. Nor will it be easy to send someone else to the same other universe to repeat the experiments, then return to compare the results. Points to the Copenhagen school, for its reluctance to accept Everett's branching multiverse.

But we do consider ourselves to have some logical, scientific knowledge, which isn't verifiable or falsifiable by experiment. An example is the division of the circumference of a perfect circle by its diameter, the number Pi, approximately equal to 3.14159265358979. We believe, on good grounds, that we know that the decimals continue in an irregular pattern, but we can never (?) perform an experiment showing that to be really so, or not.

Pi is a member of a simple world. The only details present, apart from the many decimals, is a circle, its circumference and its diameter. Any other details to keep track of there are not, in Pi's own universe. This carries some meaning, as logical reasoning is only correct when all relevant details are included, and non-identical details are considered separately.

Our own universe, that we by birth and natural habit interpret as the obvious reality, contains an astronomical amount of detail. Logic with a claim to know it all then becomes more treacherous. If logic suffers any defeat in its quest on reality, it'd be because of this, I'd presume. Logic is hardly wrong, otherwise.

And in the end, I dare not be the one to loosely dismiss Galileo Galilei and his experimental method, the foundation for lasting values in modern physics. Should I then take everything back, that I wrote about the mathematical set of all conscious experiences? I wouldn't want to completely take it all back. I feel I may be near the edge of my authority here, on one side of that edge, or on the other.

I mentioned the cardinal numbers of set theory because the set of normal continuations in the known universe could have a higher cardinal number than the set of peculiar continuations. That might suggest some kind of explanation why we don't constantly soar away.
/Bengt