From the back cover:

We speak of consciousness, or awareness, or the I, or my inner being, or sentience, or however to call it. It may reach to the deeper metaphysical levels of the universe, but what is its relation to the material world? What is this relation from the perspective of science? Science always builds carefully, slowly on what is more certain. It can start to have a somewhat mathematical character. Thought provoking observations appear, and issues. Some are these.

 

What is the material world? Does meaning/logic exist outside and independent of the human mind? What is meaning’s relation to time and space? Are there different I’s? Is the idea of death so simple? All this in the book is within a scientific perspective.

 

The book is valid hard-nosed science, philosophy, and logic. It is in the form of the developing thoughts of a person on a long walk through the desert and who meets a god that assists. The flight backwards in time is fiction, but we see generally accepted historical facts. Elsewhere, in a brain surgery hospital very far in the future, we see hypothesized observations about hard, universally valid, scientific logical going-on’s in a brain. At the book’s end, the flights through space are fictional, but not the judgments. The “all souls” theorem is not fiction but genuine scientific mathematical statement.

 

The author’s background includes, over time, going into works of philosophers from Wittgenstein to Spinoza. And from Pythagoras, Lao Tzu, and Heraclitus, to the forms of Plato and Aristotle. And Parmenides and Zeno to Lucretius. And Hegel to Gottlob Frege.

 

Earlier, the author obtained masters degrees and doctoral work in mathematical logic at the University of California at Berkeley, and in artificial intelligence at Stanford University, with specializations in machine theory, complexity theory, computer vision, automatic programming, and, always, logic.

 

(This February, 2008 book is the same as the July, 2005 edition except for the description above, covers, publishing information, and contact website.)

 

 

 

 

If I wrote the book today I would leave out most of the distracting Roman-numeral preface pages. The following are excerpts from Chapter 20, pages 183 to 197.

20 Devices to See Logic

Neurosurgery

It is centuries in the future. A door opens, whereupon a neurosurgery specialist beckons us into one of the rooms where a patient lies on an operating table. Thus starts the presentation and our visit. Looking close up at the opened human brain, we see naught but a bunch of gray slime. However, we should not be distracted by what our native perspective so emotionally pushes at us. Instead, we must somehow take our perspective on what we are natively blind to, the logic going on in this slime. That is everything; the slime is nothing more than its physical substrate.

But what is logic? Logic is the same sort of thing that meaning is. The going on of a logic in some region of the brain is the going on of meaning in that region. Indeed, even at a single nerve cell, neurobiologists speak of the encoding in the signals. This is the encoding of meaning in the signals – the encoding is the way in which the signals represent meaning. If we look at how the animal acts in different situations, if we look at how the creature may have come to have those actions through the process of evolution, and if we look at how all that comes to be going on in the creature, it is always the meaning that is encoded in the signals in the brain. It is not the signals themselves, it is not even the specific encodings, for they could be anything (as long as they are capable), but the meanings in the encodings, the meanings that are coming into the brain, and that are going out of the brain. The meanings are everything. The signals are just a way to carry the meanings, they are just a physical basis for carrying on the meanings. The different interactions between signals are really interactions of meaning.

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The Devices

Our surgery specialist of the future brings us over to a device to look into the gooey mess. The device can show so many perspectives which people back in the 21st century would never be able to see.

At first, the device displays nothing more that what our native perception shows, a slimy grayish mass. There is a button. We push it. Now the device shows multitudes of little greenly-lit strings flitting about all through the slime, in spaghetti-like tangles. These are the nerve signals, which our native vision is blind to. There are dials on the device to slow them down or speed them up. In their regular speed, they are way too fast for us to see. There are other dials to look closer in or farther away, or to move to this area or that of the brain. If we hit the button again, the little green strings disappear leaving only the gooey mess visible. The button shifts back and forth between the two perspectives. We push it again. Little green strings are back.

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Hours have passed. You are getting rather proficient with all the buttons, dials, and computer controls. You have discovered a variety of computer screens. On one of them one may set ranges of all kinds of controls and options. You have moved far beyond having the device show just little signals moving around.

You push a button. “Choose a logic,” the screen says. You press “help,” and the screen says, “There are currently 312,849 meaningfully, separable logics in this X954.2 region of this particular human brain (using the delta-5 separation scheme, version April, 2541, with usual values for major alpha divisional parameterizations).”

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Now as you use the device to see into the brain being operated on, you see not little green lights moving along fixed paths but flashing squares and circles, with the flashing moving from left to right through the figures, but at uneven speeds, sometimes stopping at one place, sometimes continuing all across, often briefly changing colors in places, though sometimes nothing at all happening to the squares and circles –  nothing lit up or moving. This is a very different perspective.

The bottom of the screens says, “Logic L9134A-B45GH82-1.429, near pre-visual inner level 7 awareness logic area HJ-9.” You hit the “more” button, and then decide to click “choice 4,” not having much idea of what the choices mean anyway. On the screen appears, “There are 78 copies of such logic (separable with beta = 5.3). Not fully understood at present. Logic depth 429 (unusually large, but possibly not for logics that get closer to the more concreto-sec attempts of the sentience, which is still basically non-resolved / non-understood even at level 1 of logic structure resolution.) Zero evidence of retinotopic spatiality.”

Suddenly some of the middle squares and circles light up with a few different colors, but equally suddenly they all become quiet. Something just went on in that logic. What was it? You glance at the patient lying on the operating table, wondering who is this person, this being, this sentience, this logic going on. Did it just have some experience? “Behold ourselves,” you think.

 

Back on the screen, after having selected choice 4, several further choices appeared. One says “evolutionary.” Hitting it, the screen adds at the bottom the following additional information for this Logic L9134A-B45GH82-1.429. “There is evidence that structure of this brain logic is derivable from evolutionary logic going on in the environment from 400 to 350 million years ago (see evolutionary logics G983-5865,6,7 (environment logic dynamics K (subtransfer 5 range)), also possible relation to 1.5 billion years ago (environment logic dynamics, posited P41)).” You see that most of the identifying numbers can be clicked on to get a description of that logic.

Interesting, you think. There are logics going on not only in the brain, but also across vast stretches of evolutionary time, and these evolutionary logics gave rise to most of the fundamental logics in the brain; the device can show perspectives on these evolutionary logics too, just by clicking their ID number.

The evolutionary logics and these brain logics are more connected than the previous sentence indicates. But it is time to leave this room.

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This is to say that there are many slight variations of this particular logic, and they are all going on to some degree in this particular physical system of matter in time and space, in this case, in a particular stretch of region in the brain matter of the electrical fish. These variations are because physical reality is a somewhat messy place, especially the brain with all those bushy tree-like neurons leaning up against each other all over the place. For most of the important logics in a brain, they are going on fairly solidly, at least in most fish of the species. But it is never a perfect affair. On one hand no logics ever go on perfectly; on the other, there are many slight variations of a logic, all of them also going on to degrees in the same area.

(Here is a technical aside. This issue of variations of a particular logic, all going on at once, is separate from the issue of various idealizations being approximations, similar to the way in which a number with more and more decimal places approximates a “real” length out in external reality. Except with numbers it is a simple one-dimensional affair, whereas with logics, there may be no limit to the dimensionality. Indeed, these two issues appear even in the way in which a larger logic is structured into smaller part-logics. When one considers the great issues of the metaphysics and ontology of the universe, it really is odd when you think about it. But there it is. That is just how it is.)

 

It should be noted that whether one has little green worms of light crawling around on the screen, or whether all kinds of letters, names, numbers, and parentheses, are ranging over the display, still, in all cases, the viewer must “understand” enough of what is appearing on the screen to know the meaning being referred to. What is on the screen invokes a meaning in our mind, and that is the meaning the device is saying is going on in the brain the device is looking into. In other words, what appears on the screen is not the meaning itself. In all cases, our mind must impute – read –  the meaning from the lines, points, letters, words, and so on, that are on the screen.

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We are Pure Logic, a Secular Miracle

We are not in this mucous-like matter of the brain. We are in the huge logic going on in that wet gray matter. Now logic is a  … well, very abstract thing.

We, our being, is in pure logic. All of our innermost experiences, our innermost being and consciousness itself, is nothing but the most abstract of form, is logic, is pure logic, and in this case, this pure logic happens to be going on in regions of this moist gray matter. Our essence is in logic, which is implemented purely in forms of the dynamics of systems of matter. This is special, unusual, odd. And the more carefully one looks at it, the stranger it gets. It is a kind of secular miracle.

 

The following are excerpts from Chapter 21, Machines, pages 199 to 223.

21 Machines

Introduction

This chapter is about machines and their growth in the future. By the term “machine” we certainly include computers and computer-like devices. We look at future history, at what kind of machines and science will be used, and at how we will get there from the present day. This chapter is about machines helping us dig into sentience in order to understand and solve this ancient mystery.

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… Yet, where there are 3.2 billion letters in the human DNA, there are 100 billion neurons in the brain. …Where the letters of DNA are in effect one huge long string of letters, the 100 billion neurons are not in such a simple relation to each other. Instead, neurons interconnect to many other neurons in a complex three-dimensional space. Future computers must deal with this. Where a letter is just a letter, the state of neuron may undergo some shifting, which will affect how it responds to incoming signals. Future computers must handle this too.

The problem of figuring out even the lowest level of the brain in a more detailed manner is greater by a number of orders of magnitude than figuring out the human genome. And so will be the required computers, their algorithms, their data bases, and the like.

Phases and Exponential Proof

Let us sketch the future phases in the development of our machines, from now to the point where the mystery of sentience is finally solved.

Phase 1. Sensing and monitoring

In this phase of history, scientists and technicians will develop ways to place, in effect, sensors inside the brain. To really have a basis to understand in detail what is going on in the brain, eventually such sensors must be placed at almost every neuron. Even though this is utterly impossible with today’s technology, researchers will start out small, and over years and decades and centuries they will extend their capabilities.

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What Understanding is, and Future Machines.

When the light goes on, when we say, “Oh, now I understand,” what is it that has happened inside our head? It means the pieces have fallen in place. And just what are those pieces and in what way are they now “in place”? To start with, the pieces are some kind of subsystems in our thought processes, with the subsystems having relations of various kinds to each other.

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To understand something, just means that the brain has to find a set of relations all of the right sort; it looks for these from among potential relations. Today researchers cannot say what is the nature of those relations in our head. Nevertheless our brain in fact does work with and recognize the right kind, and when all the relations are of the right sort, then that is when the feeling of “ah, now I see” is generated and is sent into our consciousness logic. Which, by the way, indicates that understanding is one of the feelings that our awareness can have.

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In the far future our machines will increasingly perform these processes of understanding, eventually far surpassing us in some ways. They may even give us concepts and ideas which we are unable to fully grasp, but using them we will be able to see far indeed. And we can do and enjoy this, greatly too.

We might worry about such machines giving us information and telling us what is the truth. But it will be no different than today when experts give us information or tell us what is truth. Today, science, technology, and all areas of expertise have become so extensive that we rarely fully understand any of the things told us. We could not understand it even if we wanted to, unless, first, we spent years of studying background ideas, and second, we obtained detailed results and proofs from the humans who made the statements. Today even scientists in one area of science often cannot fully judge statements made in a nearby area of science. It will be the same in the future with machines. The only difference is that it will be humans and machines that will be the gateway to pronouncements about reality. For most people this will feel no different than today, and even for most (human) scientists it will be no different. They will not be able see the full details of why something is true. In all these cases, truth boils down to judging the validity of a source of information.

 

Will we be able to trust machines as a source of statements about reality? Yes. In fact, we will be able to trust them more than we can trust the human experts of today. Statements that such machine experts make will be provable, just as is a theorem in geometry in high school math, or in other areas of math. The future machine will produce a proof of any statements that it makes. And any humans who want to, can check the proof, either in whole, or randomly select areas, and check that each step in that area follows legally from some earlier steps. More importantly, there will exist any number of independently written computer programs that will automatically check that each step in the proof is valid. So the statements produced by these future machines will be quite certain, indeed, quite more certain than the statements made today by scientists and experts.

These are important issues because some of these proofs may not be understandable, in the large, to humans. Further, they might have hundreds of thousands of steps and could never be fully checked by one human. Yet in all cases, the proofs can be ascertained as correct, and with a greater level of confidence than can a few hundred-step proof today. However, the gist of the proof, the idea behind the proof, may simply be inherently beyond human understanding.

One final comment on these future proofs is in order. To some degree there are different kinds of proof. This is true even in mathematics, where for instance, from the perspective of Brouwer’s intuitionism, only very “constructivist” proofs are allowed … When we move from mathematics to science, the kinds of proofs no doubt get even larger, where for instance one kind of proof involves “thought experiments,” while another involves them not at all. And as we move through various areas of human investigation, there are likely many other categories or classifications of kinds of proof. The above process of computer generation of proofs, as well as independent computer checking of proofs, will flag proofs as to what category they are. The certainty of such flagging we have not at all today. In fact, all our past scientific concepts and ideas will be carefully analyzed by these advanced machines, which will check and classify them much more fully than ever we did or today can.

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Example Capabilities of the Brain

The remainder of this chapter describes some of the amazing processes that go on in the brain. This material, in detail, is not needed for the rest of the book. However it does show in a general way just how surprising is the logical depth that goes on in the gray mass between our ears. As if without effort, the results of these processes appear in our sentience. So we presume there is no effort involved.

Some day, when scientists begin to see how the logical processes described below are carried out, they can move those too partially into our machines. Over time they, the scientists and the machines, will see better and understand more. Thus will develop a synergism between the machines seeing further, leading to more powerful algorithms being put in the machines, so that they see even better, and so on.

The processes presented below, though outside consciousness, compute results that are sent immediately into consciousness; except for the section on biting your tongue.

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Quantificational Issues/”close file”

Here is another example of quantificational meaning, a situation that takes place outside our consciousness, but where clearly some logic of a deeper sort is going on.

Suppose that a person is learning to use one of the standard word processing programs, and that whenever they are done editing a file, they hit the “file exit” and the program closes down (possibly after asking them if they want to save the file). Let us suppose the person has used the program for some time and has always used it in this manner.

One day a friend is visiting, and both happen to be in front of the machine, which has the word processing program running on it. They are exploring the menu, and come across the item “file close”.

“What is this ‘file close’?”

“That closes the file.”

“I thought that’s what ‘file exit” did. I’ve always used ‘file exit’. When I’m done editing a file, I just hit ‘file exit’.”

“‘File close” is for when you have more than one file you’re working on.”

“More than one file? What do you mean. I edit the file I’m working on, and when I’m done I exit.”

“Ah, but if you wanted to, you could be working on more than one file, all at the same time, all in one program, but jumping back and forth between the files whenever you wanted to, jumping back and forth to wherever you left off in the last file.”

“Oh?” the person says with a look of thoughtfulness spreading across their eyes. They never knew that they could be editing more than one file at once.

 

At this point, let us look into the brain of this person who just said “oh?”. Always up till now, somewhere in that big hum between the person’s ears, was a collection of neurons in which was going on the logic that indicated this program was for editing a file. During the time the person said, “oh?”, there was significant shifting in the logic, shifting to a more sophisticated quantificational meaning, where now, the program dealt with a bunch of files. How many? Unknown, in some sense maybe vaguely pictured, or presumed to be pictured, an indefinite number of files, and something equivalent to a generic file with the last position that was being edited; and also a logic has been added that as one jumped to any of these “generic” files, the word processor went to this “last position” associated with this “generic” file. Since in the generic situation the person does not know the exact number of files, all this is created in their head in a generic form. Someday we will look into the brain and see this all this shifting as the person says, “oh?”

 

Following is from page 253.

Experience logics related to evolution logics

In the last section we looked at the surprising complexity of part of what produces the experience of a sound or the experience of light. We looked at all that went on outside the skull, and at some of what went on inside. And all of it was forms going on in the affected matter, consisting of vast numbers of atoms. The forms were logics – meaning – going on in the dynamism of these vast numbers, virtually clouds, of atoms.

In this section we look more carefully at the logic in the head and its relation to the logic that goes on across the long eons of evolution outside the head.

 

Following is from pages 284-285

Definition of Evolution. Logic. Omega

We define evolution as the means by which logic enters into matter. It is the means by which more and more logic comes to be going on in matter. Some scientists say that everything comes from evolution. So they want to make it be an omega. But the idea of logic includes ever ascending rungs of logic, which in the earlier religious conceptions, were viewed as ever advancing toward an omega at least of logic. Evolution is merely the mechanism of moving logic into matter. In fact it seems one could prove theorems to this effect, once one formulated possible mathematical idealizations of the universe and evolution and a space of logic. Everything comes not from evolution but through evolution.

Evolution is the conduit through which logic moves into matter.

 

It should be noted that no matter how deep a logic appears to our understanding, generally it is as capable of passing into matter as is the logic that appears simple to our understanding. All logic, no matter how advanced, is already there to influence the physical. We might see an apparently happenstance characteristic in a form or in a creature, but in reality it may be a logic, or the start of a logic, which we will not be aware of nor understand for 10,000 years. Since all matter is randomly vibrating and so are all the logics built thereon, the random is always ready to start picking up, through the process of evolution, on all possible logic, no matter how off into infinity it is. Pure randomness in the physical reaches out to the infinite in logic.

 

One specific kind of evolution is that which Darwin presented, the process whereby the living things on Earth came to have their present form, that process entailing cyclical multiplicative individual instances of logics fanning out with stages called reproduction, birth, living, dying, all hung together with those little blueprints (DNA) in each individual instance of a logic, along with excessive reproduction as it interacts with the environment, the excessive reproduction being wildly culled away to leave a generalized imprint of the environment’s logic. The next section illustrates regular Darwinian evolution, using house cats running around wild in a valley.

 

 

The following is from pages 318 & 319

All Souls Theorem

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Let us state this formally. Consider the physical body that a sentience is associated with. Supposed that body is frozen as part of cryogenesis, and especially important, suppose that later the body will be successfully unfrozen and brought back to life. By definition, we will call the relation of the sentience to the fabric of the universe during the period that the body is frozen, waiting.

 

Theorem. Suppose a sentience is associated with a physical body and then that body dies. Then forever after, that sentience is waiting.

 

That’s right. Even though no cryogenics is involved, the sentience that was associated with the now dead body is waiting, it is waiting just as much as is the sentience with the body that was cryogenicized and will come back is waiting during the period that the body is cryogenicized. Forgive the awkward grammar, but the theorem is saying that after death, a sentience is waiting no less than if it had been part of a body that was successfully frozen and will be successfully brought back. You say that this is not obvious. And I say, that is right, it is not obvious. That is why it is a theorem. That is why it has to be proved, and that is what we will now do.

 

 

The following is from chapter 34, pages 361 & 363:

34 Standard I, Non-standard I

Standard and Non-standard I

The “standard I” assertion is that our sentience reaches across and envelopes all the time slices of our physical body.  In the standard I, our 4 p.m. being and our 8 p.m. being and our 4 p.m. being tomorrow are all the same being. The “non-standard I” assertion is that there is a separate sentience for each major time-slice of our body, but all the sentiences share the belief system that they are the same, even though they aren’t. They all share what in reality is an illusion that they are the same person.

Presumably, the non-standard I would be more exotic. Still and all, it is the unexpected that appears from the plain old standard-I.

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Perhaps a person’s changing beliefs can affect such changes of sentience; perhaps only hard-wire brain changes can do so. But clearly one way or another, these deformations or changes in the system of signals can radically transform the nature of the sentience, to that of a rug (i.e. no sentience), or of an insect, or to one of separate beings occurring every major time slice and so it is all just a matter of shifting these electric signals, for then the changed electric signals change the nature of the sentience being “reflected.”

 

 

The following is from pages 488 to 489:

Endnote 26 Fallacy That We Know That We Know

Some areas of study assert the statement as an axiom that if a person knows something, then they know that they know that something. This sounds obvious, which is its trouble, because it turns out to be false. To see this, consider a something X that a person might know. Then supposedly

 

They know X

They know that they know X

They know that they know that they know X

 

Ad infinitem, with these being the first three elements of a sequence that goes on for infinity.

 

The summary of the proof that this cannot be goes like this. All these elements in this infinite sequence would have to correspond to different configurations in the brain. But the brain, having only a finite amount of matter, can only have a finite number of configurations of that matter. And that is the proof.

 

We can always analyze some aspects of a proof in more detail.

The matter in the brain is in a continuum of location and motion, and a continuum is infinite in number, so maybe the argument breaks down. The answer is that it does not break down.

Each of the above elements in the infinite sequence must be sufficiently distinguishable …