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Self-reference and consciousness

  1. Jan 10, 2005 #1


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    This is only a fragment of an idea, but I thought I'd post it to see if anyone else had thought about this and had anything interesting to contribute.

    We are parts of the universe, and we observe it. This is a kind of self-reference. Other examples of self-reference include those typically thought of as absurd, like "this statement is false" and "the set of all sets which don't contain themselves." But are these really absurd, or is it just that they don't fit into the standard formulation of logic? By seriously studying these self-referential concepts, could we gain insight into consciousness? Is there a field that studies self-reference?

    Just as an example of what I mean, take "this statement is false" and "this statement is true." These are both meaningless in a conventional sense. But investigating them a little more, the former is, in a sense "wrong" since it can't be true, and the latter is "right," since it has to be true even though it contains no meaning. Is there some similar, more general way to at least categorize these types of things? I'll think about this some more and come back if I have any useful ideas.

    One more thing. I don't know if anyone has read "Godel, Escher, and Bach" by Douglas Hofstatder, but when I first heard about that book it sounded incredible. It was a book relating "strange loops" (basically the self-referential structures I'm talking about) to consciousness. But it never really delivered on this, as I remember, and I was left disapointed. Did anyone get anything more out of this book than I did?
    Last edited: Jan 10, 2005
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  3. Jan 12, 2005 #2
    Hello StatusX:
    I think you're on to something, although it's a little hazy for me, also. I read Hofstader's book (pretty far back now) and while I'm not sure I got his intended points I stll think I got something out of it and on later readings on Godel.

    While many people (philosopher J.R.Lucas, Sir Roger Penrose) have tried to take Godel and relate it to specific questions about artifical intelligence, etc., these results always are challenged as misguided extrapolations from Godel's setting of formal logical systems. Given these challenges and given that I'm not a logician, I concluded that Penrose-type arguments are not ultimately successful.

    However, the Godel result seems to dovetail with the common-sense notion that one cannot have complete objective knowledge of a system of which one is a part. We humans cannot get outside the world and look back at it. When it comes to consciousness, it shouldn't be surprising that the simulated third-person methodological stance used by science runs into some resistance.

    With regard to strange loops, this is hazy, but I took away the idea that a human being's ultimate grounding in the most fundamental level of the world (being made of atoms, or quantum particles, etc.) enabled us to "bootstrap" ourselves into real knowledge about things despite the fact it is not (impossible to achieve) complete "objective" knowledge.

    On a possibly related note: an interesting thing I noticed recently in the work of some physicists (from the loop quantum gravity persuasion) was that they saw a need to move to an algebra based on intuitionist (rather than first-order classical) logic in order to build a quantum cosmological picture which was consistent with the idea that systems in the world only have a view "from the inside".

    update: I notice there has been Godel discussion on the "Can everything be reduced to Pure physics" thread. I'll have to take a look at that.
    Last edited: Jan 12, 2005
  4. Jan 12, 2005 #3


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    First let me explain what I mean by formally studying these things. We could start with classic boolean logic, and add a symbol 'I'. When 'I' appears in a string, it has the truth value of the string itself. For example, "This statement is false" could be coded as "~I". Rules might be added that dictate how a string containing I could be modified. For example, if P is true, then P Λ I is true, etc. But there are two problems. The first is that paradoxes cannot be dismissed out of hand , but must be dealt with in a structured way. Second, this is not logic, and logic is the basic tool in all formal systems, so our very reasoning about this system cannot follow intuition and must adhere strictly to the rules. Maybe even just the notion of adhering to the rules presupposes classic logic, in which case this system will be very hard to get off the ground.

    The point of the above math was just to show a possible formal way of studying these things. So now let me address the philosophical issues raised by these two problems, which is the real point of the thread.

    One possibilty, as Steve mentioned, is that we cannot look at ourselves objectively, so there will always be things we can't understand, by Godels theorem. One of these may be self-reference itself. When we think about "this statement is false," it is nonsense to us, and we label it a paradox. Perhaps it really is, but maybe it is just beyond our capabilities to understand. Like I mentioned, it is possible that this can't even be studied by a formal system, the most basic tool of math. If our very notion of logic is but a subset, or maybe approximation of true logic, then our reasoning about what lies beyond it is inherently unsound.

    But we can try to guess. Is it possible that this self-reference introduces a type of infinite regress, and it is infinite regrress, or maybe infinity itself that causes the problem? Could the infinite regress inherent in self-referential structures "explode" into conscious experience? These are the kind of questions I mean to ask, and I'm sorry if my first post made it look like this should have been in theory development with the other crackpot ideas. And Steve, thanks for that info about quantum gravity, I'll have to look into that.
    Last edited: Jan 12, 2005
  5. Jan 18, 2005 #4

    You've raised a fascinating issue. There are all sorts of ways to come at it.

    I agree with you about Hofstedter's book. It was very clever but didn't go anywhere. I suspect that this is because he is a physicalist and therefore couldn't see how to resolve all his paradoxes.

    A better place to start is mathematician George Spencer-Brown, whose work I keep recommending. He was a colleague of Bertrand Russell and part of that whole Whitehead, Russell, Frege and so on crowd who got tangled up in self-reference while trying to prove that it is possible to prove things.

    While working on logic circuits for railway switching systems GSB came up against electronic versions of various problems of self-reference, connected with iterative loops and feedback. He found himself using imaginary values within his logical scheme as a solution. Later he developed this into a formal calculus, one in which Russell's paradox and similar problems did not appear.

    He related these issues of self-reference directly to metaphysics and consciousness, and finished up writing a book on how the universe comes into existence as a product of non-dual consciousness. He concluded that Buddhism, Advaita Vedanta etc must be the correct explanation of reality.

    So yes, for him there is very definitely a connection between self-reference and consciousness.

    The incompleteness theorems are also relevant, and relate to GSB's calculus. Any attempt to decide a theorem within a formal system (with the usual provisos) must fail, for no such system can be shown to be both consistent and complete. Yet human beings can decide theorems.

    It is thought that any formal attempt to decide such theorems must give rise to an infinite regress of meta-systems, only to be ended by a conscious being finally making the decision by some extra-logical means. However GSB argues that there is not an infinite regress, there is just an infinite iteration between two ways of looking at it, one that can only be resolved from the metasystem, which is not the final link in a lengthy chain, but is rather the third point of view, one which transcends the two types of two-value formal system in which theorems are must always be (relative to the axioms) true or false.

    He likens this iteration to the feedback circuit which drives the trembler on an electric bell. If you input 1 you get an output of 0, if you input 0 you get 1, and so on ad infinitum.

    He relates this directly to metaphysical questions. If you answer a metaphysical question with a yes and work out the implications you get contradictions, which prompts one to try out no as an answer. But if you try out no as an answer you get contradictions which prompt one to go back to yes, and so on ad infinitum, thus explaining the to-ing and fro-ing of western philsophers from Animaximander to the present and presumably forever.

    His calculus avoids this problem because it is axiomised on something which is beyond the distinction between yes and no. He therefore agrees with Lao-Tsu and the like about reality, although he does not call this undifferentiated thing the 'Tao'.

    He writes "Time is what would be if there were an iteration. Space is what would be if there were an oscillation". (This is from memory, and may be the wrong way around).

    To get back to your question. I'm no writer or mathematician, and cannot give a clear exposition of GSB's mathematics, but there is plenty of good material out there linking self-reference and consciousness, and I'd say it's an issue well worth pursuing. Hofstedter and Russell didn't see it, but many people have.

    PS Don't forget that G-sentences are not paradoxes, for we can decide them. They are only paradoxes within some formal system or other. (Hmm, there may be some objections to that, but I'll wait and see).

    Btw there's an interesting book chapter by Robin Robertson online somewhere that's relevant called "Some-thing from No-thing", specifically discussing GSB, Lao-Tsu and self-reference.
    Last edited: Jan 18, 2005
  6. Jan 18, 2005 #5
    Self-referencing is Purposive. In Transitional Logic (TL), self-referencing is crucial in guiding intelligent systems on their causal and relational pathways (or logical pathways, if you like) in a progressive manner. You need to self-refer otherwise you cannot sense the dynamics or changes in your internal states and respond accordingly. In other words, self-referencing is the life-blood of an intelligent life.

    Some of the paradoxes that I have come across about self-referecing systems are just plain stupid because the creators and propagators of these paradoxes fail to apply appropriate 'EXCLUSIONARY PRINCIPLES' to regulate those self-referencing systems on their logical pathways. The fundamental law is this:

    You self-refer and self-exclude in order to survive!

    As an intelligent system, if I don't self-refer, how would I know the current internal states of myself with which to reactively exclude myself from any danger that may be around me? At the logical level, there are some quantificational devices in TL for mapping self-referenced internal states of an intelligent system onto intervening (potentially anahilative) events in the external world. Don't ask me what they are because I do not want to appear theorising. You know how this forum is. But the most important thing to appreciate now is that in any intelligent system, such as the human conscious system, self-exclusion via self-referencing is so important that survival without one is a non-starter.

    NOTE: There is currently a widespread suspicion, especially amongst computer programmers, computer scientists in general and cognitive scientists, that if a computer program can sense its own internal energy states, syntactical, symantical and other limitations, and use the resulting information to add or reduce its overall instructions set, then not only is such a computer able to think and learn in the normal sense of the word, but also it must be conscious. But at the moment this possibility is hampered by the so-called 'INSTRUCTION SET THEORY' (IST) which holds that no computer program can change its own internal instructions without any intervention of external agents, such as the programmer who wrote it, or a computer programmer that is comissioned to improve it, or another program like a virus. And according to the advocates of this, any computer program that can violate IST (reprogram itself in the strictest sense of the word) is conscious and that nothing should stop us from declaring it as our equal, with the same rights and privileges as humans.
    Last edited: Jan 18, 2005
  7. Jan 18, 2005 #6
    NOTE: Remember that self-referencing is currently in its primitive state, and that to get it to work better, let alone perfect it, we would have to continually revise the system concerned by structurally and functionally re-engineering it. Alternatively, you can wait for the Creator to come and fix it later. When it comes to deciding between the two, that one is beyond me.
  8. Jan 18, 2005 #7
    Hmm. I somehow doubt that the Creator is going to decide to start fixing computers in His spare time.

    You are not talking about self-reference here, you're talking about one part of a system referencing another part of the system. This is a related issues, but quite different in this context. The point about consciousness is that it references itself. Perhaps one could think of it in Kant's terms. Your example is of the phenomenal referencing the phenomenal. The problem here is the noumenal referencing the noumenal.
  9. Jan 18, 2005 #8
    Are you talking about a sefl-referencing phenomenon (something equivalent to nothingness) parisitically energised by the material, if that is ever possible in the first place? I am not in any way suggesting any valid position. The fact that I cannot see and account for something, does not suddenly turn that thing into nothingness. The worst are those who do not admit their natural limitations but try to push dudgy and ill-founded arguments into other people's throats. And besides, how would you know the material is extending into nothingness, and the nothingness mysteriously self-referencing, without first structurally interfering with the whole self to the minutest computational detail? I think we have to wait and see.....and don't worry about me, cos' I am flexible. There is nothing to stop me from changeing my mind if something concrete turns up.
    Last edited: Jan 18, 2005
  10. Jan 18, 2005 #9


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    No, the latter can be false as well.
  11. Jan 18, 2005 #10


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    I had originally supposed that the important self-reference responsible for consciousness is that a part of the universe is examining the universe. This would fit with the Chalmerist view that all information processing systems can experience to some degree. But if it is instead the self-reference of a creature thinking about itself that is important, this would lead to different conclusions. It would mean that only those animals which have a self-model, like chimps and dolphins, can actually experience. Also, it seems likely that a computer program could consider itself and thus be conscious.

    One more thing. At the beginning of the universe is a fundamental self-referencing: the universe created itself (if you take the universe to mean all that is). Could this self-reference be a god-like consciousness? This doesn't fit that comfortably with my other beliefs, but I thought I should mention it because it is an interesting thought.
  12. Jan 18, 2005 #11


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    I'm sorry, true was not what I should have said. But hopefully you see what I mean by right. Consistent might have been a better word.
  13. Jan 18, 2005 #12


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    I'm going to give something a quick shot here. Statements that can be basic propositions in a formal logical system must be 1)factual statements (not commands or questions, etc.) and 2) must refer to something other than themselves. The statement "Adam is 24 years old" qualifies. This seems to be the way you are classifying statements.

    There is a quick problem I see right off the bat. Take the statement "This statement is green." It's self-referential, but we can assign a truth value to it, although the ambiguity results in two possible values. If the statement is referring to the color of the visual representation of the statement, then it is true. If it is referring to the statement itself, then it is false, because statements don't have colors. The point being, though self-referential, a statement of this type is still decidable and can be used in a formal system.

    The problem comes not when we consider statements that are self-referential, but when we consider statements that refer to their own truth value. "This statement is false" is not decidable in any bivalent formal system. Whatever truth value we assign to it, the computation oscillates to the opposite value and back again ad infinitum. We can, however, construct a formal system that does include such statements. As Canute points out, George Spencer Brown did exactly that. Under his system, such a statement would have the value "imaginary." (I don't remember the specific symbol he uses for this, but the three values in his system are "void," "not void," and an oscillation between the two.) It can thus be used in computational processes. I'm not going to draw any metaphysical conclusions from the properties of formal systems, however.
  14. Jan 18, 2005 #13
    The question is this:

    How does a formal system quantificationally exclude a proposition from self-referential error, if any?

    Has anyone yet solved all the outstanding paradoxes (from the liar paradoxes to Rusellian types)? Is there any one system that can be chosen from many existing formal systems to solve these paradoxes? Or, equally, does our Natural language (NL) contain already all the quantificational devices needed to unpack them?
  15. Jan 18, 2005 #14


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    Strictly speaking, a formal system does not refer to the way it is written. The specific symbols we write are just ways of expressing the objects and rules so we can manipulate them, but aren't central to the system. The only self reference possible in a formal system is reference to the truth values of the statements, or possibly to "right/wrong" values or any other properties that are built into the system.

    Which gives me an idea. If I define a stament as "right" if it can be consistently assigned a truth value and "wrong" if it can't, then what about this:

    "This statement is wrong or false"

    I'll let the rest of you think about that one. It might be that we'll need an infinite hierarchy of "truth" values, starting with true/false, then right/wrong, and continuing on. I should probably look up that author you guys are mentioning before I go too much farther.

    Well, as discussed in another thread, "physical" can be defined as being based on math. This might be extended (or reworded, depending on your defintions) to "a property is physical if it can be modelled by a formal system." If so, it may be that to model experience, we need a formal system that treats self-reference, infinite regress, and contradictions in a rigorous way.
    Last edited: Jan 19, 2005
  16. Jan 19, 2005 #15


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    What I'm trying to stress in that other thread is that physical objects always have a relational structure of some sort that behaves in a manner that can be modelled mathematically. It doesn't follow from this that, because a certain mathematical system has certain properties, that physical things, or a universe constructed of physical things, have those same properties. If a particular math is to model a physical relationship, it must fit the phenomena, not the other way around.

    The only reason some people are so high on Brown's math is that it doesn't seem to be built from arbitrary axioms the way other mathematical systems are. I don't know even close to enough about math to evaluate this for myself, but he claims to have derived the properties of his system from the simplest possible distinction between void and that which is not void. If you consider the universe at the most basic level to be composed of the carriers of physical attributes and the space in which they exist, you can see the attraction.
  17. Jan 19, 2005 #16
    That's a big question. Goedel seems to have shown that all but the simplest formal axiomatic systems cannot escape contradictions of self-reference. But formal axiomatic systems can be built which escape this. The Buddhist epistemological system would be an example, or Spencer-Brown's calculus of distinctions, which is equivalent.
  18. Jan 19, 2005 #17


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    I don't understand your point. Surely the physical world has the same relational properties as the final theory describing it. But even if not, what is wrong with expanding math before observation requires it? This has been the trend for the last century or so, and it has worked pretty well.

    I found his model, and didn't find it that compelling. I can explain it briefly:

    = false


    You can model boolean logic using this. For example:

    a -> b = (a)b

    By substitiuting in for a and b the notation for true or false and evaluating according to the rules, you can see these are identical. Now he claims that the rules arise naturally from the concept of distinction itself, but I think it's nothing more than a notational trick. For example, he says that if you think of () as "crossing a boundary", then (()) means crossing a boundary twice, which gets you back where you started (hence the first rule) and ()() means the same crossing is represented twice, which is redundant (hence the second rule). But when used to model boolean logic, these lofty ideas seem to have no relevance, and it seems to be a simple consequence of cleverly chosen notation.

    I'll have to read some more, but it seemed that he assigned true = 1, false = 0, and a contradiction (or infinite oscillation between true and false) = i, the imaginary unit. I don't know how these numbers are significant yet, but if the first part of his theory is any indication, they won't be.
    Last edited: Jan 19, 2005
  19. Jan 20, 2005 #18
    Canute, would you be kind enough to enlighten us a bit further on this 'BUDDHIST-SPENCER-BROWN' resolving system? Give us at least a summary of such system. Thanks.

    Think Natrure....Stay Green! May the 'Book of Nature' serve you well and bring you all that is good!
  20. Jan 20, 2005 #19
    Argh. I'll have a go, but I've never yet managed to get this on paper in a comprehensible way. It'll have to be a long one I'm afraid.

    A formal axiomatic system can be imagined as a broken circle. One starts with an axiom, or axiom set, and this is one end of the circle. The curve represents all the theorems, hypotheses, truths and falsities etc. that can be formally derived from those axioms. The circle is broken because it cannot be completed. Contradictions arise before one can get back to the beginning. To complete the circle would be to axiomatise the system, to self-referentially deduce the truth of ones axioms from ones axioms, which is not possible.

    All systems of deduction used in Western philosophy, mathematics, science are of this type, although in mathematics there may be some exceptions to this (I'm no mathematician).

    A metaphysical example. If one takes it as axiomatic that materialism is true then as one works one's way around the circle deriving truths and falsities from this axiom one eventually meets a contradiction, meaning that one concludes, by formal deduction, that materialism cannot be true. (This is why philosophers generally conclude that materialism is not the case). Similarly, if one takes it as axiomatic that idealism is true the same thing happens. (Although here philosophers are less inclined to accept the implications).

    So, the question of whether materialism or idealism is true is metaphysical. It is not simply that the question is about reality, but that it is undecidable by reason.

    GSB's calculus, and the cosmological models of Buddhism, Taoism and so on are not like this. I'm not sure I can explain this clearly, or rather, I'm sure I cannot, but it's something like this.

    All statements that are 'true' (consistent with the axioms) in one set of formal systems are 'false' (inconsistent with the axioms) in a different (differently axiomatised) set. So truths and falsities within a formal axiomatic system are relative, not absolute.

    For this reason Western philosophical deductive reasoning is only functional up to a point. That point is where contradictions arise, or, as philosopher Colin McGinn puts it, 'ignoramibuses', which are barriers to knowledge, explanatory gaps and so on. This is where the circle has to be broken, resulting in the impossibility of deciding metaphysical questions.

    GSB's calculus is not like this. It is axiomatised on something/nothing that is neither true or false ('something' that is neither one thing or the other, neither something or nothing. a thing about which no statement is strictly true or false).

    However, reasoning requires that we take our axioms to be either true or false, or as one thing or the other. If one takes this axiom (GSB's void) as 'true' (let's say as 'something') then one gets the usual broken circle of derived results. If one takes it as false (as 'nothing') then one also gets a broken circle of results, but one that is the doppleganger of the first one, a mirror image in which the derived truths and falsities are reversed. These two circles represent the total possibility space of outcomes for theorems derived from the two truth values of the axiom. In other words, for any theorem one circle represents all the axiomatised systems in which it is true, the other all the systems in which it is false.

    An example. If one takes the theorem 'materialism is true' as an axiom then it is true that that the physical universe is causally complete. If one takes it as axiomatic that idealism is true then it is false that the physical universe is causally complete. By our usual ways of reasoning one of these systems is correctly axiomatised and one is not. Which is which cannot be decided by formal deduction. Reality cannot be pinned down in this way, for some reason.

    The systems of Buddhism, Taoism, GSB and so on are axiomatised quite differently. This is not for technical reasons, but because, these people claim, the nature of reality is such that what is ultimate, the ultimate axiom if you like, cannot be characterised as being this or that, as having true and false characteristics. It transcends, for instance, even the distinction between existing and not existing (because of the way we define 'exist').

    To take the Buddhist cosmological system as an example. It is well known, and very easy to see, that Buddhists spend their lives contradicting themselves. Ask one whether the physical universe exists and they will prevaricate. In a way it does, and in another way it does not. It depends on which way one wants to axiomatise ones formal system. If one takes what is ultimate as 'something', then yes, it exists. But if one takes it as 'nothing' then no, it does not exist. One can use either of the two broken circles of derived theorems that can be constructed from the fundamental axiom. However both of these systems misrepresent the truth for, as Lao-Tsu says, the Tao cannot be named. It must remain an undefined term in ordinary language, since ordinary language is predicated on two-value logic. That is, one cannot talk about reality without assuming that what is ultimate is either something or nothing.

    But in fact it is not correct to say that it is one or the other. Just like GSB's axiomatic void one is forced to make a distinction in it in order to discuss, calculate or derive conclusions. But that distinction is a false one.

    So Buddhists look at things always in two ways. There are two circles, two formal systems of derived results, that arise from what is axiomatic, each as valid as the other, but statements that are true in one are false in the other. This is related to Chuang-tsu's comment that "True words are paradoxical".

    Thus their formal system, in which they make statements about the nature of the world, is a twin system of circles. Taken together the circles form a complete and consistent formal system. (Despite the contradictions if you look at Buddhist teaching they are strictly consistent with themselves.) But the fundamental axiom on which the two circles rest, and which completes them, is not part of either system, and not consistent with either. If you like both systems (circles) are pragmatic devices. They allow one to discuss reality, but only at the cost of misreprenting it. To truly represent it requires using both systems at once, one in which the world is this way, and one in which it is that way. In this system ALL theorems are decided from the metasystem.

    I'll stop there. If that makes little sense I'm sorry, this is very hard to explain and I'm not great at explanations at the best of times. One more thing though. It is always said that it is not possible to make sense of the idea that 'something', be it GSB's void, Buddhism's 'emptiness', or Taoism's 'Tao' etc, cannot be characterised conceptually (or 'idolised'), or understood by reason alone. By reason what is ultimate must be either one thing or the other, must conform to two-value logic as used by human beings. Rather, this 'something' must be approached via direct experience and not by conceptualisation, deduction and so on. (Christian mystics say one should do it 'immaterially'). So don't worry if that bit makes no sense to you. There's no way to explain why GSB's axiom, the Tao etc are undefined terms. Note though that all formal systems require at least one undefined term in them.
    Last edited: Jan 20, 2005
  21. Jan 20, 2005 #20
    Well, this sounds as if falsity and truth are quantificationally and functionally interchangeable.

    Does this mean that you could do something like this?:

    (1) Materialism is true WHILE Idealism is false (and vice versa)
    (2) Materialism is true WHEN / WHENEVER Idealism is false (and vice versa)
    (3) Materialism is true IFF Idealism is false (and vice versa)

    Have I come any close to getting this big picture? Two sides of the same coin, such that whenever I decided to settle with one side of it, I must also always be aware of the fact that the other side is always immediately there. Right?

    So, can you also under this system imply:

    1) I exist AS MUCH AS I do not exist
    2) I do not exist WHENEVER I exist
    3) I exist UNTIL I do not exist
    4) I may be here AND I may not be here

    Are these equivalent to the system you are describing?

    I am trying my best to understand this twin system. The most puzzling feature of it is understanding how the mind decides which circle or which side of the coin to choose. It seems as if the system is saying: 'take things as they come and adjust your circumstances according which circle or which side of the coin turns up.' Am I close?

    NOTE: In TRANSITIONAL LOGIC (TL) which models itself around our Natural Language (NL), only the one broken circle is dealt with, and the two ends are quantificationally mapped onto each other by the very naturaL reasons that split them up in the first place. According to TL, all the quantificational devices for achieving this are already naturally embeded or contained in NL.
    Last edited: Jan 20, 2005
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