Old Book: Chapter 1
The All Important Map-Territory Relationship and Assumption Switching
Have a wonderful day In our one-way world. (Peter Gabriel)
On Elephants and Egalitarianism
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." This famous pronouncement of Sherlock Holmes does a pretty good job epitomizing the rationalist viewpoint. The facts and their logical implications may not always lead immediately to the truth, but we can whittle away at the vast array of possibilities until only one explanation remains.
I'm going to use this idea as the basis for a little pronouncement of my own, but there is something rather unreal about Sherlock's statement. It reminds me of the sculptor's depiction of how she crafts the likeness of an elephant from a block of stone. "I just chip away everything that doesn't look like an elephant." The problem in both cases is the lack of a positive proscription. We aren't given anything specific to do. Like an existence proof in mathematics that assures us that a number with such and properties exists, but doesn't give a clue how to determine it.
My version of the art of finding a good explanation resides in generating a fair image of the elephant before the sculpting begins and then having a technique for refining that initial image through the feedback of early results. Truth, as Hannah Arendt has said, is always near the beginning rather than the end of the process. It has to do with the original insight rather than any intellectualization to follow. Facts and logic will chip away some bits of stone, the sharp corners perhaps, that clearly don't belong, giving us a chunk of rock in a generally elephantoid shape, but we won't know where to apply the chisel after that so as to arrive at one definite endpoint. Until we are very near the finish it is impossible to tell if a particular bit of stone is included in the part that looks like an elephant or in the part that doesn't.
Holmes routinely displays excessive confidence in the power of deduction. It is among the most appealing aspects of his stories. We are comforted to think that every question has an answer. Holmes seems to operate under the assumption that truth is always accessible if only we vigilantly attend to the evidence and make no errors. The fact is, however, that if we are to arrive at an answer, we really need to start with a bunch of premises and ignore most possibilities. Answers very different in kind from the one we initially nominate will escape detection. The point is that these "improbable" solutions Holmes refers to, supposing they exist at all, will almost never materialize. Given that, it is almost miraculous that we tend to arrive at answers at all, let alone arrive at right answers.
Though I do then take exception to Holmes' attitude, the quote that I opened this section with does express an insight that I embrace wholeheartedly. Rather than taking it as a manifesto of the brute power of reason, I see it as a concise declaration of freedom in theorizing. Whatever remains, all that remains, of the possibilities that the facts and reason do not eliminate, however improbable, must be true in some sense. That is, as far as our explanations and descriptions are concerned, the roughly hewn stone, the "elephant space," is as close to the truth as we will get, a kind of Rorschach which we may interpret in any of the profoundly or minimally different ways which are not precluded by the facts. Reality provides plenty of wiggle room for explanations. I'll call this notion the Many Truths Model.
Let me be clear about this strange-sounding statement. I do not doubt that there is something that deserves the name reality underlying our explanations. It is only that our ability to nail this reality down is necessarily limited. Any number of descriptions will do equally well. Nature owes no allegiance to any one explanation or theoretical construct. The world simply is. Thus there is no compelling reason to believe that one explanation has a strangle-hold on truth.
The structure of thoughts and theories is not entirely shared by the reality they are intended to epitomize. Our descriptions and rationalizations of events are always based on assumptions, much as geometry rests on its postulates, while the events themselves are not. The foreground of things, what we think about, only emerges once we settle on the background of things that we think with. Because of their structure, all theories and explanations are, to use Robert Nozick's suggestive term, inegalitarian. They are biased by our choice of assumptions or premises. I think the world, on the other hand, is (nearly) completely egalitarian. It picks no favorites, makes no distinction between foreground and background—it simply is. Thus, truths-in-words amount to insights into reality rather than some kind of epitomization of or perfect correspondence to it. What we have, therefore are metaphors. The point of the game is not to find truth but to maximize insight. At best some combination of explanations may circumscribe what is -- but I'm not entirely convinced that even that is possible.
If we accept for a moment the egalitarian view that all explanations which can be true are true in a way, then we ought to feel free to choose between various sets of assumptions. Contradictions to fact only emerge once these assumptions are set. With each new theory we will see another aspect of the one true elephant in the room.
Descriptive Complementarity
Imagine a message written on a sheet of paper. Is the message in the ink? If you burn away the area of the paper that is stained by ink, we can still read the message in the paper stencil left behind. Is the message in the paper or in the spaces between?
If we reconstruct the pieces of stone the artist chipped away to produce the elephant sculpture, won't we have all of the pertinent information contained in the sculpture itself? It would seem that information is not a material thing in the sense of a bit of ink or stone or an electron on a microchip. Information resides in patterns, in distinctions. And there seems to be no special orientation to the patterns that determine information; the ink in the foreground is of no more importance than the paper in the background. We imagine ourselves to be reading the black marks, but they would be meaningless without a contrasting background. It is equally true that we are reading the white spaces between the lines?
It is then possible, as Holmes suggested, to prove that event X happened by showing that all other possible events ~X did not. Changes in one medium are mathematically equivalent to changes in the complementary medium so that by considering everything but X we are by default considering X too. In a well-defined domain, every element of the domain is symmetric to and equivalent to its complement, like the impression of a fossil left in dried clay or the impression we leave behind in a seat cushion.
This complementarity is the basis for what I call Foreground-Background Switching. The space surrounding an object, if we think of space as the geometrical relationship between objects rather than any other physical characteristics, defines the outline of the object as much as its inner dimensions. Physical objects have a reciprocal relationship with their surroundings. We generally think of this space as a background, an arena for action but which is in itself irrelevant to that action. Complementarity implies, however, that the space and the thing in it share equal billing. We can even bring space itself into the foreground.
It is possible to conceive of any pushing as pulling, any receiving as giving. This becomes a virtual tautology when we see the world as relative contrasts rather than "stuff" existing in a background of nothingness. The reality is in the contrasts.
In fact, we rarely know things by their insides, by seeing them directly in isolation from a context. We witness only their effects on that context—the space, other objects, and ultimately ourselves. If the inside is knowable at all, it is only by inferences we draw from the outside, the disturbances these phenomena cause in our consciousnesses. Our information gathering takes place in the receptivity of the background. A distinction or boundary consists equally in what's on either side of it.
Painters talk about the importance of negative space in defining the nature of a composition. Musicians refer to using the silences behind and between notes as an agent for musical expression. These insights are easy to believe in but hard to keep in mind. Linguistic structures orient us toward the foreground so that the reciprocal or complementary descriptions are seen as less natural or secondary.
Since the 14th century when William of Occam first decreed that the correct theory is the simplest one that can account for the facts, scientists have exercised his razor to slice away all "multiplicity of entities." At the same time, however, they may have put a yoke over our free ranging efforts to understand the world. The rigid adherence to Occam's Razor derives from an almost universal faith in the elegance of creation, among even hard-headed scientists and atheists. Neither God nor the Blind Watchmaker apparently would be so hostile as to create a messy, radically impenetrable world. I too experience a sense of awe at nature's beauty and simplicity through my relationship to it and my membership in it, but I think this simplicity is in the world itself rather than in our descriptions of it. To me, it is an act of hubris to think that God created the world in order for us to understand it. It is also highly improbable that we have evolved a linear, subject-object grammar and a noun-verb vocabulary (and/or neuronal structures) which somehow captures a multifarious, nonlinear, nonlinguistic "blooming, buzzing" world without also creating their own artifacts and side-effects. Now, if theoretical elegance cannot legitimately be used as a criterion for determining truth, then, as Paul Feyerabend has said, science will operate best with an "anything goes" attitude.
There is one major objection to such an attitude -- that which accounts for the near total acceptance of the conventional view in the scientific community and in the minds of most educated Westerners. Our inegalitarian theories and thoughts have performed fantastically well in creating technologies to extend human influence and in generating reasonable mathematical explanations for the workings of nature. From the point of view so far expressed here, we must consider this success of the standard models, paraphrasing Wigner, the unreasonable effectiveness of explanation in science and in our every day experience. This miraculous matching between theories and reality may inspire us to think, with Sir James Jeans, that "[t]he world appears more like a great thought than a great machine."
We will see that although I firmly believe in complete freedom in choosing assumptions, the resultant theories themselves which we can generate will be far from chaotic. Not absolutely anything goes; we must account for the facts. I believe there is a structure to the landscape of valid theories. The closest we can come to an intellectual understanding of nature will be in comprehending this structure.
This subtle relationship between what is and what we can say of what is will be an important presence behind the thoughts I offer throughout these essays. Therefore, I beg your indulgence as I lay out what must seem to many to be metaphysical drivel. I'll try to tread lightly.
The Many Truths Model is not really far from the standard, so-called correspondence theory of truth when it comes to statements like "The snow is white" or "I am 6 feet tall." These are truths about conventions. They are true because they refer to categories that all of us agree to accept. The Many Truths version of things diverges from the norm when events get tied up with causes. If we say, for example, that we experience the snow as white because it reflects many frequencies of light and the brain interprets broad combinations of frequencies as white, I see many opportunities to give the same set of physical facts vastly different descriptions. We could say that the light is carrying a message that the snow intended for our eyes or that our minds draw in the information in an active way (see the Eye Rays chapter). I am interested in creating alternatives or complements to statements such as: "The apple fell because of gravity," "Romantic love is nothing but the psychological manifestation of Darwinian drives to insure the propagation of the genotype," "Love is the soul's response upon experiencing resonance" or "We now know that all spider behavior is hard-wired into its tiny brain." I will take particular aim at mechanistic/reductionistic thinking but will also critique airy expressions of supposed mystical insight.
Pretzel Logic
We've heard this admonition before: Don't confuse the map for the territory, the word for the thing. North is not up. Roads are not curves. Countries aren't different colors. Simulation, no matter how good, isn't reality. Things don’t happen because of our correct explanations of them.
The kinds of maps that quantitative science and other expert knowledge provide for explaining the phenomena of the world can be especially seductive, but they too are only maps. Planets do not obey the law of gravitation. Your brain does not have an IQ. Water is not made of hydrogen and oxygen. In particular, principles don't cause events but only explain them. We will have to look carefully at the relationship between causing and explaining, but for now, suffice it to say that the world does not correspond to our maps. The world simply is.
This distinction itself turns out to be more problematic than it seems, but if that was all there were to it, we could count ourselves lucky. There is something more here, something hard to pin down about maps and territories. In the next few pages, we'll see how the Map-Territory (M-T) Relationship is twisted up on itself like a pretzel.
First of all, it is next to impossible to keep this distinction constantly in mind as we go about our lives. We have good reason to cling to our maps. They are, after all, the only way we have to understand the lay of the land. And they do a pretty good job too. None of us (bodhisattvas aside?) have ever seen the territory without some intermediation, some mind map or other. We're all like fish so utterly immersed in our sea of linguistic and symbolic representations that we are unable to see the significance of the representations in themselves. Since our impressions and thoughts are all in the sea of maps, we have no way to record what there is to see when we try to stick our heads out of the water. When we think of it, we realize that the way we conceive of the world requires this duality or separation but it always comes as a revelation. Meanwhile, we merrily go on acting as if IQ, physical laws and so on are real, as if the distinction is irrelevant.
What is this special quality of our maps that they may fool us into thinking they match reality? And more pointedly, what is reality that it allows us to produce meaning through theoretical and linguistic expressions? That's the crux of the issue. Of all the infinitely many possibilities for the nature of reality, it seems to me that very few of them would be amenable to linguistic descriptions within the particular noun/verb structure of human thought and communication. Can our limited wetware devices (our brains) really have evolved a grammar that manages to capture reality in a one-to-one fashion.
Can it really be that all phenomena are expressible in words, all meaningful events represented in meaningful statements? I don't know.
The exact nature of this MT relationship is among the most profound and subtle questions of philosophy. It has preoccupied philosophical writers from Plato and the gospel writer John to Ludwig Wittgenstein. One cannot really begin to frame hypotheses about nature without at least some de facto decision about this relationship.
Those who ignore the MT relationship or find it easy or unimpressive haven't thought about it hard enough! I can jump up and down and point at its significance like I'm doing now, but one really has to experience it for oneself. Like with one of those 3-D computer dot pictures, if we stare at MT vigilantly and slightly cross-eyed, the utter improbability of the relationship, the logical pretzel, emerges in a most surprising and disturbing way.
Because language can embody meaning, I find myself being forced to the surprising conclusion that reality has some structural similarity to human language, grammar and logic -- these artifacts we typically assume are products of biology, evolution and, well, human beings as opposed to Nature at large. In light of this conclusion and the absence of any physical connection that could account for such a structural similarity, our usual assumption of a simple, almost one-to-one relationship where theories and thoughts track the real world, where there are such things as true theories, amounts to a radical form of mysticism.
So, a priori, there must be some distinction between maps and territories, and the distinction must have some repercussions, but we are beguiled by the apparent expressibility of meaning. It would seem that the match between our maps and the territory is both more than we have a right to expect and less than common sense demands. The pretzel twists.
Here is a brief jump-ahead and summary to help flesh out the range of possible MT relationships:
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AN OCTET OF MT THEORIES
It seems to be impossible for me to settle on any final disposition to take toward the relationship between my experience and the world at large, between things internal and things external, between what we think with and what we think about. But here's an octet of competing grand MT theories, some of which will come up again and again, to begin to suggest what I'm talking about.
1. The Apeman MT: Come on! We're just a bunch of less-hairy monkeys running around flinging poop at passers-by and writing books about our itchy crotches. How can we have managed to come across and understood anything true or absolute about the world? The very idea of understanding is itself a ridiculous joke. The Martians are laughing at us! And God is laughing at them! And the godless universe in which we reside is laughing at Her! The world is queerer than we can imagine! How does a species even go about evolving a capacity for final or meaningful knowledge? What we call knowledge is just the glintings of neurons in one tiny corner of the universe. One grunt means hand, another means east, a third means horny. How do we get from there to expressing our feelings about our favorite TV show or writing down an equation that allows us to predict when the comet will return? Can't say. Despite my susceptibility to nearsighted speciesism and the seeming truth of my own thoughts, you can't ever really convince me that anything we think we know has any sort of universality. Hubris! We have cobbled together an impressive array of mental behaviors (for a monkey) that produce our peculiar world, but none of that qualifies as understanding — only self-deception and illusion added to intentionality. Our most sophisticated maps are as a three-year-old's crayon scribblings compared to... compared to something, I'm sure! The very notion of a meaningful conception of maps and territories (qua maps and territories) is undoubtedly impossible (for Martians and Bodhisattvas too) and/or beyond us.
Belief in any degree of meaningful theoretical knowledge involves swallowing a sort of miracle: maps can somehow give true insight into the territory, a good simulation of event x is equal to event x. I'm not quite ready, in this frame of mind, to give myself over to this miracle. Thus, my answer to the question "What is the relationship between our mental representations and the world we seem to be aware of?": "Whuh?"
2. Platonic Idealism MT. There is a deeper reality beyond our minds, but it isn't atoms and the void, not the world of matter. It's a world of permanent forms whose shadows or projections or intersections-with-the-physical-plane we see dancing on the walls of the cave. This MT theory is related to my Allegory of the Cafe (coming to a chapter near you) and Leibniz's Monadology and Bohm's Implicate Order. They all imply that our participation in the very dynamics that the territory puts out preclude any possibility of unmediated exposure to the deepest stuff. We are, in a sense self-blinding. (In the case of the Allegory of the Cafe, the very purpose of our noise-canceling headphones is to the keep out influence from everywhere else, so its no surprise to discover that they make poor instruments for hearing the things that are actually out there). We are only aware of phenomena (the product of the monads, etc.) on the surface of our bubbles, while the underlying sources of the phenomena (the noumena and/or the interiors of the monads themselves) are forever inaccessible (windowless). We can understand the phenomena in a manner of speaking but absolutely no progress can be made toward the Absolute. And it's not necessarily as simple as if there is some noumenon X that we experience as phenomenon x. The plural totality of {X} may give rise to a singular x at some point in spacetime. This unbridgeable separation isn't something to be fretted over, however; it's just the way it is. So, in the end, this MT is indeed em-tee. We can no more know about the relationship between maps and territories than we can about the territories themselves. (A mystic might say that we can turn off the cancellation function of our headphones and some of the world can sneak in unscathed. Which leads to...)
3. The Transcendental/Jedi MT: Maps are perpetually illusory, something to be overcome or bypassed or transcended to achieve direct contact with Being. There is no try, no rational approach to understanding the nature of the deeper reality, but through meditation on it or contemplation of it or total immersion in it, wisdom can be achieved. What is the intellectual manifestation of this enlighten ment? That is, are there enlightened thoughts? Can the Buddha come back from a transcendent state and talk to us about it? I would think not, except to grant Her the ability to say with certainty, "No, that idea betrays such and such an illusion." The most we can ask for is that we come to regard our explanations and descriptions with the just the right of blend of skepticism and belief -- and that would be pretty good!
Perhaps the living world is undergirded or sustained by a sea of Force consisting in the conscious energies of all beings. Deep connection between the individual and the Force which bypasses maps leads to great power for Good ... or Evil.
4. The NT MT: "In the beginning was the Word, and the Word was with God, and the Word was God...[A]ll things were made through him, and without him was not anything made that was made...And the Word was made flesh..." The world is made of or through the speech of God (as in "Let there be light"). Humans (unlike other animals) are also endowed with this godlike capacity of speech, this intimate connection with the Divine Territory. Prayers or magical incantations have the possibility of efficacy because their structures mirror that of nature. The Universe is a text written by God to be read by us. The world was created in order to be understood by the righteous. This MT theory is an ingenious and satisfying settlement of the big MT question. That is, there is no Territory but that which arose mutually with its appropriate set of maps at the dawn of creation. God said, "Let there be light," so that the nature of light itself is forever bound up with the word "light." This isn't very far from Einstein's God who doesn't play dice with the universe, who is subtle but not malicious. That is, the MT connection is mysterious (since it must be taken on faith that God is creating and sustaining that connection), but the world is comprehensible nonetheless (since God has made it thus for us). This MT seems in many ways mystical and unscientific, but it leaves lots of room for science to discover the actual laws of Nature rather than the sort of laws we find in the next MT, which explains how science flourished in the Christian Era. Physics can be lawlike, and correct maps correspond to territories perfectly. (See the Correspondence Theory of Truth).
5. The Falsifiability (or Approximation) MT: Maps are provisional approximations of territories. We can compare various versions of these models to the territory and semi-rationally choose the ones that do the best job for the purposes at hand with the predetermined measurement criteria. No model can ever be known to be final or perfect. Thus, we leave aside the question of truth and knowledge as fruitless and unnecessary. We must satisfy ourselves for now with a particular degree of uncertainty, but as science progresses that uncertainty will shrink. Our maps might not be perfectible but they are always improvable. Since statistics trump explanation, we gather the data and generate Fourier-like theories (see 6 below) that account for them. These theories only apply over limited domains.
The Copenhagen interpretation, devised in response to the multiple and unresolvable explanations of quantum mechanics, really extends to everything; measure and then report on your measurements, but be careful saying what it all means. This MT theory is the point of view scientists should emphasize, in my opinion. That is, it's THE science MT. Unfortunately these damn scientists often lend their science credibility to truthy pronouncements that are way out of bounds — We now understand that a spider's behavior is hard-wired in its tiny brain. Really?
6. The Fourier Sledgehammer MT: The relationship between our maps and the territory is arbitrary or unknowable — and possibly meaningless. The only bits of evidence we have about the supposed territory are its effects on our consciousness bubbles (see later). Those effects trace out deformations to the surface of those bubbles we can picture as highly squiggly graphs (This is a metaphor, people!). Our only way of perceiving the deforming events involves pushing back on them, smoothing them out. Get that? We don't know them until we engage with them and analyze them. Thus, our descriptions and explanations are (based on) this cancellation process. Fourier showed that judicious subtraction of sine waves can cancel any deformation as perfectly as we please, like a body shop banging out dents in a fender. Likewise, little wavelets (bell-shaped Gaussian curves) and other stock objects can in practice do the job as well as Fourier's waves. That is, whatever deformation takes place, we can ex-plain it using any of a variety of off-the-shelf candidates (perhaps atoms and forces, God's will, natural selection, sex drives, the dialectic, class struggle, the conspiracy of the illuminati, grace, good vs. evil, spiritual evolution, etc.). The explanation can work (undo the deformation) to any degree of accuracy and yet bear no meaningful relationship to the actual external events that produced the deformation in the first place (if it even makes sense to suppose there is such a thing as an external event). Any such sledgehammer explanation is by its nature parsimonious in that a single off-the-shelf item does all the work. No multiplicity of causes here. All theories that ex-plain things are correct explanations. Do explanations that include mathematically accurate predictions trump the others, truth-wise? Can't say. The accuracy seems to come from greater attention to detail rather than any superiority of technique. From the Fourier metaphor's perspective, most arbitrary explanations should have some applicability beyond the designated area of cancellation — but less and less so the further out we go from the finite interval over which it was calculated. Thus, they can make relatively decent predictions near the domain of cancellation. That is, it shouldn't be too surprising to get decent predictions from arbitrary explanations in some cases, and that might inspire faith in our explanation, but only explanations that somehow reflect the actual nature of the territory being described should produce really good predictions far from their original domain of applicability. Given a bit of determination and resourcefulness, we can invent enough epicycles to make any basic approach work for us. Given the diversity of opinion in the world and the extraordinary degree of satisfaction people derive from sticking to their various crazy positions, it certainly seems to be borne out that almost any dogma will do just fine (if the ultimate criterion for judging a map is the satisfaction of the map's owner -- and I reckon that's as good a criterion as any). The key to understanding might be "doubling down" on our favored point of view until the world gives up. All explanations are Ptolemaic.
7. The Idealism MT. There is no territory and no maps, only mind. Thoughts aren't representations but instead have their own existence. Bypass the middleman for big savings! The apparent truths or scientific laws may be valid, but only for the minds perceiving them. (Frankly, it's hard for me to know what to make of a pure or simple-minded idealism, and I haven't the education or imagination to devise one that isn't simple-minded)
8. The Feeling MT: Reasoning about the nature of the MT relationship is a fool's errand. It is what it is! A holistic, intuitionist approach to thinking is all we have and all we need. Believe or don't believe, act or don't act, but please don't subject me to your tortured philosophical musings. I mean really. How far has all of this gotten you? Empty (MT) theorizing indeed!
My own usual point of view is a sort of combo of Plato, Fourier, and the Apeman. The typical intelligent middle-class Westerner may spend most of her time in the Feeling camp but will profess to be in the Falsifiabilty camp.
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Maybe there is something to this idea that the territory was made in the image of maps rather than the other way around, and the maps and the territory are thus in some kind of perfect sync. Didn't I just proclaim the Many Truths Theory which says that anything that can be true is true in a way? If we've never seen the territory, then maybe there isn't any to see. Perhaps maps are all there is. We have no facts that can possibly contradict such a position since knowledge always resides in our maps. It is difficult to see how one could go about establishing that there are territories. Maybe those mystics and others who claim direct access to reality have been fooled. How would they know they experienced the real thing rather than merely some other, perhaps more subtle, map? Well, there is one brute fact that points very strongly to a territory; the Cartesian insight, Cogito ergo sum (my consciousness proves there's a me). Unexpectedly, it is the seat of all the maps -- the consciousness -- that offers a territory that's hard to deny. The map-making faculty is the only sure territory.
Anyway, the kinds of arguments for the existence of the territory that are acceptable according to rules of argumentation all reside within maps of various kinds. Thus, the M-T distinction itself is a kind of map. This fact is the likely source of the M-T pretzel. We might have guessed that a map of maps would lead to some sort of difficulty. It is a basic tenet of modern logic, one we will look at in more depth later, that paradoxes often arise when we try to apply a concept to itself. Certain kinds of self-reference are poison to consistency. But, as we shall see, other self-references provide a special kind of power to our explanations.
To be epistemologically correct then, maybe we have to consider alternatives to this map-territory distinction. There are several ways to frame the denial of the claim "Our maps are based on an underlying territory." One would be "There is no territory beneath the maps. There are only maps." I tend to dismiss this one. The formulation I prefer is "The territory is itself made up of maps." This way we get a reversal of priorities. Maps are in some sense more fundamental than territories rather than the other way around. Of course, since the world simply is, at some inaccessible deepest level neither side takes precedence. As the Taoists say, they arise mutually. Maps happen and territories happen. We cannot reason, however, without some kind of order that puts one side of the duality at a deeper level than the other. Reason is sequential and so something must come first.
You will see as we go along that I take this denial of the common sense map-territory notion very seriously and believe it provides insight into the way things work. For the most part, however, since I am bound to go one way or the other, I am going to stick with the conventional side of this dichotomy. My mantra has been "The world simply is." and that's as firm an endorsement of reality and independence of territories as I can imagine.
I argue that it is okay, even desirable, to switch around such basic assumptions as these, but it is equally important from the point of view of comprehensibility to hold as true only one side of a dichotomy at a time. Aristotle's famous Law of Excluded Middle says that a statement and its contradiction (A and not A) can not both be true. Suspending that law isn't wrong in my opinion, but it sure makes a muddle of things. We are allowed to say that the tone of Joyce's Ulysses is simultaneously both happy and desperately sad, but it will become problematic if we try to use that idea as the premise of a term paper. If we accept both A and not A, we can prove absolutely anything at all, since nothing will count as contradictory. We might say that recognizing the legitimacy of both sides simultaneously makes good philosophy and bad science. It can lead to a paralysis of assertion. Our logic can only tolerate a certain degree of fence-sitting. We will need to look at the implications of contradictory hypotheses to gain the most complete descriptions of reality, but if you consider them at the same time, logical deduction goes out the window.
Assumption switching is the main organizational principle of many of my essays. It is my way of giving some form to the anarchy of an anything goes approach. For example, although we usually operate from the assumption that things, left to themselves, will naturally remain as they are, in the next section we will investigate the implications of the opposite assumption -- that things naturally fall apart and thus that stasis is the act of holding off decay (and other reversals). There is an Anti-jump World where things can be caused not to happen existing in the same place and time as our usual world where things are caused to happen.
As I said, we will operate for now under the assumption that territories have an existence independent of maps. The issue then becomes how to understand the relationship between maps and territories, how to form an M-T hypothesis assuming we are forever stuck in the maps. If we want to know the status of our map-derived knowledge we have to try to peek behind the maps. We need to map out the map-territory relationship.
There are at least three problems, three full steps away from the territory, that put distance between us and the attainment of that goal.
1) Information translation: Our perceptions are not the world in itself. They are translations, filtrations and elaborations of the incoming data. Our awareness can only ever be an awareness of our own state. Thus what we see of the outer world is only its effect on us (or our measuring instruments). Neurons respond to a limited range of stimuli, and we presumably perceive only those events that have a possible impact on our survival.
2) Automatic interpretation: Our minds involuntarily project meaning onto the world. We fill gaps in the data to form complete, familiar pictures. Even the three dimensional nature of space, which we seem unable to transcend, is more in here than out there. That is, we project intrinsically dimensionless data about "real" events onto a three dimensional screen.
3) Bio-cultural history: Our conscious explanations for what we see (and don't see) are constructions whose quality is limited by human genetic and cultural history, the power of our imagination and the applicability of our metaphors (not to mention the above imperfections in our perceptions.) These models are mathematico-linguistic, linear and logical. The world is not.
In all three cases there is little we can do to erase that distance between our maps and the territory. We cannot expect to suspend or transcend these limitations. The best we can hope for is a satisfying story of how one stands in relation to the other.
Who needs it!
For most of us the above discussion about the actual existence of a territory distinct from our maps is strangely irrelevant. That is, we believe there is a territory behind the maps but we act on the faith that our maps correspond perfectly with the territory anyway so this is a distinction that makes no difference. (see the Feeling MT above). At heart, we may all tend to believe in the correspondence theory of truth. For example, we do not question the correctness of the 3-dimensional structure of space that our mind maps tell us is there.
Perhaps it is our biological imperatives that make it almost impossible to keep the M-T distinction in mind moment by moment. Living fully in our maps is much more efficient. We never find ourselves saying "If only I had realized that my impressions of the world are not identical with the world, I would have done it all differently!"
Our perceptions rarely betray us. It is probably rare for us to see elephants when they are not there. And just as important, we tend to see them when they are there. Many of our explanations for things, from our rationalizations of the social order to our roles in our personal relationships to the heliocentric model of the solar system, work really well too. They allow us to plan our lives to some extent, avoid dangers, invent, do science, enjoy membership in communities, make bits of the world coherent, put our minds at ease.
Our maps are, after all, based on reality, and good maps give insight into how things work. The fact that we are stuck in our maps isn't a problem if the maps are faultless guides to what is out there or if they are just a few minor adjustments from becoming faultless guides. Perhaps, by trial and error, we can slowly correct our maps until they make a perfect match with the world. (Never mind for now that on the face of things our explanations about, for example, the weather are no more satisfying to us than the idea of rain gods were to the ancients. That is, progress in the realm of explanations is hard to gauge.)
The many successes of our maps tend to confirm our simple assumption of equivalence. We tend to take the boundaries and clear distinctions that the maps offer us as real and inherent in the territory itself. The problem, as I see it, is that maps always artificially separate foregrounds from backgrounds. We seem only to be able to extract meaning from relations, by comparing an object to its environment. As we become inured to them, we begin to see these separations as natural. Thus we tend to believe in (or at least act as if we believe in) what I will call a One-Way View of Truth or map-territory equivalence that takes a particular background for granted.
The One-Way View, part of our dominant cultural version of the M-T relationship, says every statement has a definite relationship to reality. It either matches it or it doesn't match. If the statement is true then the alternatives to it are false. Either the earth is the center of the universe or the Sun is. All ambiguities are derived from a lack of precision in our definitions and/or in our knowledge. If we could somehow transcend the limitations on our knowledge imposed by our biology and our historical blinders we could verify the truth or falsity of statements by checking to see if they match what is. Presumably, all such statements which match a single aspect of reality would have to be logically equivalent. Truth, that is, seems to go one way.
I don't believe in the One-Way View, at least not completely, because I do not believe in the naturalness of any presumed background.
[I tend to think that the One-Way View holds sway because of the historical uses of power. It was and is the most effective way to exert power and influence to be the one who determines the one monolithic truth. Thus, for example, the speech and manners of the privileged and powerful classes in England and America became the true correct speech and manners of those countries.]
It is easy with practice to perform a Foreground-Background Switch which makes our assumptions the object of study. Call it axiomatic relativity. Just as Einstein's relativity boils down to the notion that there are no privileged observers or frames of reference, this relativity says there are no privileged premises. Everything is worthy of explanation in its turn. The One-Way View needs to be supplemented with a two-way or many-way view. Again, I think that a superposition of views based on contradictory assumptions gives the fullest understanding; the main example of complementary assumptions which we will explore in the next section is
Things stay the same unless something causes them to change.
vs.
Things change unless they are prevented from doing so.
It is my contention that most scientific and rational thinking is based on the former assumption. I will try to flesh out a world-view based on the latter. Since, by my account, neither assumption is truer than the other, it is only by overlaying these worldviews that we can best understand what's really going on. Explanations provide insight not certainty, so we want to have as many of them around as we can keep straight.
There are again self-referential complexifications that arise from taking this approach. The application of my Two-Way view to itself leads us, paradoxically, to accept the legitimacy of the insights gained from the One-Way View. Briefly, if each of any pair of opposite assumptions give insight as the Two-Way View implies, then the One-Way/Two-Way pair must themselves each apply over their own limited range. There is a sense then that assuming the truth of the Two-Way View implies its own falsity. Thus it becomes easier to see how the One-Way View has stood up so well: It doesn't contradict itself. As I see it, this is just another twist in the pretzel, and we shouldn't let it deter us. We have to accept the legitimacy of both orientations.
The extraordinary power of mathematics has also given us profound reasons to solidify our faith in the One-Way View. The equations of gravitation, for example, allow us to predict solar eclipses thousands of years in advance, and quantum mechanics and its equations allowed scientists to correctly predict the existence of particles that were not theretofore suspected to exist. Scientific theories sometimes contain these amazing mathematical engines which seem to mimic the way the world calculates. They lend a sense of having absolutely captured the essence of the matter, especially when they begin offering satisfying answers to questions they were not originally designed to answer.
[symbolic mathematics is more plastic than ordinary language and has a kind of complementarity built into it. One equation can be interpreted many ways.]
It often seems to scientists therefore that the mathematics is the reality. Reality is One-Way and that way is the way of mathematics. By making our maps sufficiently mathematical and abstract, then perhaps we can arrive at perfect equivalence and obliterate the M-T distinction altogether. The scientific culture has taken this view as an article of faith, and I think there is some merit to it. The language of mathematics does have certain special attributes, which ameliorate the One-Way/Two Way distinction, but I don't think math can eliminate the distinction altogether.
The scientific culture that holds mathematics in such a special place still takes as its dominant metaphor that the workings of the universe, including perhaps ourselves, are like that of a machine. Alan Watts has called this perspective the Fully Automatic Model. It says that there are inviolate laws which perfectly determine every event as surely as if the universe were made of gears and pulleys (more surely even). The machine universe is constructed piece by piece from isolated and essentially inert parts which behave in a simple, lawlike manner. The machine is fueled by "stuff" called energy which seems to have an existence independent of the parts. Once the machine is ready and set in motion, it runs smoothly and predictably without further interference.
Although philosophically and scientifically we seem to have progressed past the narrow confines of the Fully Automatic Model of the universe, our culture still suffers under the weight of its mechanistic, fragmenting metaphors. The model helped to usher in an increasingly secularized view of humanity, that often leaves us feeling empty and alienated.
The Fully Automatic Model is the kind of reductionistic extreme to which a One-Way View of Truth inexorably leads. The laws created to account for the strange world of the quantum, along with other discoveries and problems in logic have diminished the viability of the Fully Automatic Model. Uncertainty, "lawlessness" and paradox seem to be built into the structure of the universe so it looks less and less like a machine. There is an awareness in the scientific community, especially among physicists, that the Fully Automatic Model is outmoded. In fact the official line in physics has long been that any interpretation of the equations in mechanistic or literal terms is bound to lead to inaccuracies. Despite this awareness, we find the mechanistic metaphor hard to shake because there are no acceptable alternatives to supersede it. Our One-Way View tells us that either this machine model is correct or its opposite must have some legitimacy. That is, for example, if we cannot ultimately treat the parts of the universe as separate, localized and inert, then we must treat them as one undivided whole, each bit enfolding the rest and enfolded in the rest.
Most of us are highly uncomfortable with this version of holism. It says that, if the lines on the map are always artificial and to some extent arbitrary, then it makes no sense to abstract, for instance, a thing like me from the flow of events in this room. The processes that constitute me extend not only as far as my finger tips but into the far reaches of my influence—out to where my exhalations mingle with the atmosphere, into the minds of the students I have taught and everything which I have touched, back into the lives of my ancestors and forward to my descendants. There would seem to be a kind of diffuse version of me permeating the universe, while all others and the whole itself permeate me. This holistic scenario ought to be just as valid for an electron as it is for me. Where is it possible to draw absolute and definite lines and maintain an identity when everything is intrinsically smeared and interpenetrating?
A One-Way view forces us to choose between holism and "partism" and you can see why scientists would choose the latter. Holism requires that the machinelike causation of naive science be replaced with interactivity and exchange. Carried to its extreme, holism offers no objects to single out for study. Science works by analysis, taking things apart, and holism recognizes no parts to take.
The prevalence of the One-Way View at least partly derives from the structure of communication. Our explanations, scientific and otherwise, are expressed in terms of language and grammar, nouns and verbs, etc. and in terms of mathematics and logical inference. None of these structures necessarily bear any special relationship to the things in themselves. The choices of subjects and objects give an orientation to truth, abstracting a foreground from a background of assumptions. Conferring "nounness" implies a kind of independence that marks it as distinct from other events. We can only perceive something in relation to this background, but nature acknowledges none. No one language, however rarefied, and no One-Way theory epitomizes the things out there.
The lingering Enlightenment view that the Creator made the world so as to be comprehensible by Man no longer passes muster. The world wasn't put here to be described, to be mappable, so we have no compelling reason to believe that perfect maps exist. The world simply is. As I said earlier, the nature of that simple being seems a priori to be unlikely to conform to our ability to perceive it, describe it, explain it. It really would be the crowning achievement of evolution if we somehow evolved, through ostensibly blind natural selection no less, actual linguistic brain structures that allow us to epitomize the world in itself.
Again the one knockout argument against what I'm saying here is that, despite what are to me convincing arguments and evidence against the One-Way view that assumes a map-territory equivalence.