Does Self-Reference Hold the Key to Understanding Consciousness?

[StatusX]

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?

 

[Steve Esser]

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.

 

[StatusX]

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 possibility, 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.

 

[Canute]

StatusX

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.

 

[Philocrat]

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?

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.

 

[Philocrat]

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.

 

[Canute]

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.

 

[Philocrat]

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.

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.

 

[Hurkyl]

and the latter is "right," since it has to be true even though it contains no meaning.

No, the latter can be false as well.

 

[StatusX]

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.

 

[StatusX]

No, the latter can be false as well.

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.

 

[loseyourname]

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.

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.

 

[Philocrat]

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 anyone 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?

 

[StatusX]

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.

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.

I'm not going to draw any metaphysical conclusions from the properties of formal systems, however.

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 modeled 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.

 

[loseyourname]

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 modeled 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.

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 modeled 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.

 

[Canute]

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 anyone 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?

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.

 

[StatusX]

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 modeled 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.

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.

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.

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

()=true
= false

rules:
(())=
()()=()

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.

 

[Philocrat]

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.

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!

 

[Canute]

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.

 

[Philocrat]

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.

Well, this sounds as if falsity and truth are quantificationally and functionally interchangeable.

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.

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?

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".

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?

Thus their formal system, in which they make statements about the nature of the world, is a twin system of circles.

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 Langauge (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.

 

[StatusX]

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.

OK, maybe you can clairfy a few of my misunderstandings, because it all seems like nonsense to me. Are they saying we can't know anything for sure? Well, yes, as far as the external world, that is obvious. But we can know for sure what red looks like, for example. Are they saying there will always remain certain questions that can never be answered? Again, obviously this is the case since something had to create itself for the universe to exist. I'm not interested in using nonsensical poems or the like to study what we cannot understand. We cannot understand it, as a mouse can't understand relativity, and that's that. And like I said in my last post, I don't see how this void distinction stuff is relevant when applied to formal logic.

 

[Canute]

Well, this sounds as if falsity and truth are quantificationally and functionally interchangeable.

I'm not sure what you mean by 'quantificationally' or 'functionally' here. But no, the suggestion is not that truth and falsity are interchangeable. If someone says 'It is raining', then this is true or false depending on whether it is raining. In everyday affairs such truths and falsities are not interchangeable. The problems start when someone says 'rain exists', which takes one into deeper waters, if you'll excuse the pun.

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)

I think the answer is no. The point here is that in western philosophical thinking there are two fundamental aspects to reality, mind and matter. One of these must be taken as fundamental. So in this scheme of thinking either materialism or idealism is true, and the other false. Philosophers facing this question iterate between the two answers (in GSB's terms), because neither can be shown to make formally logical sense. So there is no system in which materialism is true or in which idealism is true, except those which take the truth of one or the other as axiomatic (iow as an assumption).

However this problem disappears if one accepts, knows, assumes, presumes etc. that neither are properly true or false, but that there are two ways of looking at it. The 'transcendent' view, the view from the metasystem if you like, what Buddhists call 'the view from nowhere', is that there is some truth in materialism and some truth in idealism, but the real truth, what is really the case, is that neither of them is what is the case, for what is the case cannot be characterised by the words 'materialism' or 'idealism'.

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?

I think so, but I may be misunderstanding your words here. To stick with materialism and idealism for a moment, you cannot (if you are intellectually honest) come down in favour of one side or the other, since both give rise to contradictions. One of the (many) reasons Buddhism (or the 'non-dual' view in general) is called the 'middle way' is that it threads a path between all such antimonies, not answering one way or the other, since neither answer accords with reason. The trick in understanding this view (by reason as opposed to practice) is therefore to find a third answer, one which accounts for the contradictions that arise in materialism and idealism. This is why in certain traditions of Zen koans which present this sort of paradox in a very blunt and simple way are used to trigger insight.

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?

If I understand you correctly then no, this doesn't work. But it all depends on what you mean by 'exist'. I'm getting out of my depths here but I'll keep going. Buddhists use the term 'is' rather than 'exists' to characterise what is ultimate, since 'exist' is usually narrowly defined. For instance, for science if something cannot be observed or conclusively inferred from what can be observed, then it does not exist. In this sense a Buddhist would agree that what is ultimate does not exist. But nevertheless it is.

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?

In a way. The nearest analogy I can think of is QM. If I ask a physicist whether a wavicle is a particle or a wave then my question embodies the assumption that it is exclusively one or the other, and therefore it cannot be answered. What a wavicle is is neither, or both, depending on how you look at it. To theorise about it we must take it as one or the other, and do so consistently. However to do this is to mischarecterise it. So one could say that QM uses a twin system of formal systems, one in which wavicles are waves, one in which they are particles. Both are pragmatic devices, and very useful, but what a wavicle actually is neither a wave or a particle but something for which we don't have a concept.

NOTE: In TRANSITIONAL LOGIC (TL) which models itself around our Natural Langauge (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.

I'm not sure what you mean here.

 

[Canute]

OK, maybe you can clairfy a few of my misunderstandings, because it all seems like nonsense to me.

Yeah I can quite understand that. It's partly to do with my feeble explanation, but even with a good explanation it can seem like nonsense.

Are they saying we can't know anything for sure?

No, definitely not.

Well, yes, as far as the external world, that is obvious. But we can know for sure what red looks like, for example. Are they saying there will always remain certain questions that can never be answered?

Yes. Metaphysical questions cannot be answered because they are predicated on dual thinking, in which one or the other answer must be true and the other false. But such questions can be transcended, in other words the reason that they are undecidable by reason can be understood, and what is the case can be understood.

Again, obviously this is the case since something had to create itself for the universe to exist.

This is precisely what they say can be understood. Lao-Tsu writes "Knowing the ancient beginnings is the essence of Tao". He means that the central knowledge gained in Taoist practice is the understanding of how the universe comes into existence. This is why GSB's book is called 'Laws of Form'.

I'm not interested in using nonsensical poems or the like to study what we cannot understand.

I agree, and so would a Buddhist or Taoist. Poems should be meaningful and not nonsensical, and should deal with what we can understand.

We cannot understand it, as a mouse can't understand relativity, and that's that.

It's true that this is what we're usually taught, and it is the almost unanimous conclusion of theists, scientists and western philosophers. However as yet there is no proof of it, so it can be no more than an opinion.

And like I said in my last post, I don't see how this void distinction stuff is relevant when applied to formal logic.

I'm no logician, but bear in mind that the four colour problem can be solved in GSB's calculus, and that it solves Russell's paradox without having to rely on some spurious theory of 'classes'. Russell himself was very complimentary about it, saying "GSB has succeeded in doing what, in mathematics, is very rare indeed. He has revealed a new calculus of great power and simplicity..."

 

[StatusX]

Yes. Metaphysical questions cannot be answered because they are predicated on dual thinking, in which one or the other answer must be true and the other false. But such questions can be transcended, in other words the reason that they are undecidable by reason can be understood, and what is the case can be understood.

Well, it would be pretty difficult to break completely from dual thinking. For example, consider the statement "The origins of the universe can be understood if two-value logic is abandoned." Or the statement that a proposed "zen" explanation is correct. Are statements like these also denied truth values? Does that question have a yes or no answer? Does that one? ...and, so on. I'm skeptical of abondoning logic, since it has given us a lot more useful information about the world then zen or GSB.

It's true that this is what we're usually taught, and it is the almost unanimous conclusion of theists, scientists and western philosophers. However as yet there is no proof of it, so it can be no more than an opinion.

Maybe, but here's a way to think of it. When we have a final theory of everything - and I mean everything, from gravity to neuroscience to consciousness - will we be able to prove it correct? Well, what we could do, in theory, is use these theories to come up with a reductive explanation of why we came up with our little theory of everything in the first place, and why we believe it. It seems like Godel would have something to say about this, but I'm not sure yet.

I'm no logician, but bear in mind that the four colour problem can be solved in GSB's calculus, and that it solves Russell's paradox without having to rely on some spurious theory of 'classes'. Russell himself was very complimentary about it, saying "GSB has succeeded in doing what, in mathematics, is very rare indeed. He has revealed a new calculus of great power and simplicity..."

I've read all this, but the book is out of print. Maybe it's another crackpot idea, or maybe we're just not ready for it yet. The internet has suprisngly little to offer about the theory, so if you know any good sources, I'd still like to see if this is worth exploring.

 

[Canute]

Well, it would be pretty difficult to break completely from dual thinking. For example, consider the statement "The origins of the universe can be understood if two-value logic is abandoned." Or the statement that a proposed "zen" explanation is correct. Are statements like these also denied truth values? Does that question have a yes or no answer? Does that one? ...and, so on.

There's quite a number of issues here. Firstly, in Zen, Advaita etc one is not required to give up two-value reasoning, but rather to discover it's limitations. There's nothing wrong with this kind of reasoning as far as it goes, but it does not go far enough for us to understand our origins by reasoning alone. This is analogous to saying that we cannot know what a clarinet sounds like by reasoning alone, but that we cannot understand how a clarinet works unless we use some reasoning. There is no suggestion in these practises that one needs to abandon rationality.

Strangely you're right about the two statements you give as examples. Neither has a straight yes or no truth-value. For the first, reasoning must be transcended in order to grasp a fundamental truth, but this truth cannot bring any understanding of the details of how the world works without reasoning about it. For the second, in Zen there is no 'explanation of everything' that can be given. If there was then Zen masters would give it. Everything can, in principle at least, be understood, but it cannot be explained, since the understanding depends on experience and experiences cannot be communicated.

I'm skeptical of abondoning logic, since it has given us a lot more useful information about the world then zen or GSB.

I agree about logic, we should never abandon it, except temporarily when we abandon reasoning to focus on experiencing instead. But logic shows that there are strict limits to logic, and it would not be rational to ignore these limits or what they might imply for knowledge. On the second point I suppose it depends on what you call useful.

Btw I'm well aware that there's no way that I can make a case for Zen or Taosist practise as a means of understanding our origins. All I'm trying to do is show that there's nothing inherently implausible or illogical about the idea. In the end the only way to know whether they are an effective means or not is to find out by doing that practice. I might say that playing the guitar is wonderfully enjoyable, but there wouldn't be much point in me trying to construct a logical argument to convince anyone who didn't play, Equivalently I might say that strawberries taste good, but I couldn't demonstrate of proof of it. Experience always trumps formal logic.

Maybe, but here's a way to think of it. When we have a final theory of everything - and I mean everything, from gravity to neuroscience to consciousness - will we be able to prove it correct? Well, what we could do, in theory, is use these theories to come up with a reductive explanation of why we came up with our little theory of everything in the first place, and why we believe it. It seems like Godel would have something to say about this, but I'm not sure yet.

Yes, this is what Stephen Hawking concludes, that we cannot develop a theory of everything (in any proper sense) because of the limits to formal reasoning. The key issue here is that a theory is not knowledge, hence scientists never claim to be dealing with truth and falsity, just with best fit, predictability, usefulness and so on.

I've read all this, but the book is out of print. Maybe it's another crackpot idea, or maybe we're just not ready for it yet. The internet has suprisngly little to offer about the theory, so if you know any good sources, I'd still like to see if this is worth exploring.

I had a lot of trouble getting a copy, but found one s/h on Amazon in the end. To be honest I understand very little of his mathematics, which is mostly what the book cosists of. But the general principles are all that really matter imo. These are discussed online. There was a site called 'Laws of Form' but GSB was trying to get it closed since he didn't approve of all it conntained, and perhaps he's succeeded. On the site it gave transcripts of some of his talks at Essalin in the 60's, which are useful, and some of the background to the ideas. Whether any of this is still out there I don't know. If I have time I'll go have a look and get back to you.

Sorry to always write so much. Brevity isn't one of my strengths.

 

[Canute]

Here are some links:

http://multiforms.netfirms.com/multiforms_1.html

http://www.lawsofform.org/

http://www.enolagaia.com/GSB.html

 

[Philocrat]

If I understand you correctly then no, this doesn't work. But it all depends on what you mean by 'exist'. I'm getting out of my depths here but I'll keep going. Buddhists use the term 'is' rather than 'exists' to characterise what is ultimate, since 'exist' is usually narrowly defined. For instance, for science if something cannot be observed or conclusively inferred from what can be observed, then it does not exist. In this sense a Buddhist would agree that what is ultimate does not exist. But nevertheless it is.

So, could I say, for example:


1) God is Everything
2) Everything is what it is
3) I am what I am

They all seem to eliminate the dual thinking that your system demands. Don’t they? If so, do you accept this yourself as a better way of reasoning, let alone intellectually acceptable?

In a way. The nearest analogy I can think of is QM. If I ask a physicist whether a wavicle is a particle or a wave then my question embodies the assumption that it is exclusively one or the other, and therefore it cannot be answered. What a wavicle is is neither, or both, depending on how you look at it. To theorise about it we must take it as one or the other, and do so consistently. However to do this is to mischarecterise it. So one could say that QM uses a twin system of formal systems, one in which wavicles are waves, one in which they are particles. Both are pragmatic devices, and very useful, but what a wavicle actually is neither a wave or a particle but something for which we don't have a concept.

Is this equivalent to implying that:

1) Wavicle is neither a wave nor a particle?

Or;

2) Wavicle is both a wave and a particle?

Such that if it is (1), you give it a different a name or leave it completely devoid of a name? Or if it is (2) you assign both properties to it and rename it, or simply treat is as nameless? Even if (2) were arguably the case, wouldn’t you have to give some idea of how wavicle becomes partly a wave and partly a particle? Or if it were (1) that you hung on to, wouldn’t this leave you in the same boat as scientists who intellectually give up searching or looking as soon as they reach COP (Critical Observation Point)? That is, once things have reached a point at QM where they become unobservable, they suddenly give up on the very logic that was guiding them to this point? It looks as if you are cutting corners and proposing a form of monism! Or is this not?

On a whole, it seems as if you are suggesting that Disjunctions, LEM and the lot should be done away with altogether. I have gone down on record on this PF for rebelling against the DUAL COMPONENTS of Logic, such as LEM, mainly on the grounds of bad habit about their usages. My campaign is mainly to eliminate vagueness in the application of certain dual components of logic like LEM, but never on the grounds of completely eliminating them. My main worry is when, for example, people attempt to apply LEM in situations with multiple truth-values that range over a given scale of reference or simply treat LEM as if it applies accurately to every situation. Or are you suggesting that there is a logical system (or even any of our Natural Languages) that can function without these dual components? It looks like sweeping everything under the carpet and then saying to every passer-by “Please just trust me, don’t question anything, and have faith on whatever comes by?” Or am I missing the point?

The next point is this. We know that BIVALENCE LOGIC (or Two-Valued Logic, as they usually call it) has two fundamental truth-values ‘True’ and ‘False’. And we also know that MULTIVALENCE LOGIC (or Many-Valued Logic) has also been developed up to the level of Fuzziness. All that this really means is that Many-valued logic has many truth values which could range from true, false, contingently true, possibly, necessary, possibly-necessary, up to absolutely necessary. Unless I am misunderstanding you, if the dual component of NL that nearly all forms of logic automatically adopt is denied under Buddha-BSG Logic, then so must multiple components that allow NL and Many-Valued Logic to function as they do be inevitably denied under the same schema. Right? Or are you suggesting that Buddha-BSG’s Logic has no truth –value, let alone truth-values?

Well, it seems to me that if all these were true:

1) NL itself would functionally grind to a halt because the dual component is ‘FUNCTION-CRITICAL’ (a working part you cannot do without)
2) Science would grind to a halt as it relies on this same dual component to reason and hypothesise to a certain point…..scientific progress of any kind would be thrown out of the window!
3) Many other forms of Logic would on the same token evaporate

In TL that you asked me about, and which I am currently messing around with, nothing essential is taken out of NL. Many forms of Logic habitually take logic out of NL, purport to clarify or purify it, and then repackage it and naively claim to have found a new Logically perfect Langauge for a particular discipline. Well, this is to the contrary in TL, for TL does not take logic out of NL but rather it clarifies the logic within it. The whole emphasis is on teaching clarity and eliminating vagueness at every level of the human education. So, the fundamental maxim of TL is this: if you claim to have taken logic out of NL to purify or perfect it, then when you finish doing so, put it back where you took it from so that the native speakers of NL, after being trained in it, can use it to think, speak, write and act more clearly in the society that they share with others. And this frankly implies that you must teach this newly revamped logic to every member of the society and not just turn it into communication tools for the elites or the privileged members of the society only and then sit back and expect an ‘invisible hand to fix the rest’. As I have argued elsewhere, this has the potential of curing misunderstandings and physical conflicts that usually result from vagueness in our reasoning and general communication with each other.


One last thing, it would be more helpful if you could point us to the exact Notations in Buddha-BSG’s Logic that demonstrates how the following types of statements are precisely clarified or disambiguated:

1) All Cretans are Liars
2) The statement on this line is false
3) There is no me
4) Nothing exists (or perhaps, in your own system ‘Nothing is’)

NOTE: Don’t misunderstand me, I am not in any shape or form trying to claim that what you are describing is completely senseless, I am merely trying to understand the system of logic that you are describing in relation to (1) how NL works in general, and (2) how NL is systematically mapped onto the way we are physically (and perhaps, mentally, as well) configured. For I seem to see nothing which logically rules this.

 

[Canute]

So, could I say, for example:


1) God is Everything
2) Everything is what it is
3) I am what I am

They all seem to eliminate the dual thinking that your system demands. Don’t they? If so, do you accept this yourself as a better way of reasoning, let alone intellectually acceptable?

The second two statements seem to be tautologies, so have no implications. But the first is very relevant. It brings to mind Spinoza. In my opinion he is the Western philosopher who came closest to constructing a 'non-dual' view of the world by reason (perhaps excepting one or two of the very early Greeks philosphers). But he didn't quite make it, and to say 'God is everything', which I believe is what he concluded, is in fact a dual view. In the non-dual view there is a sense in which it is correct (especially using Spinoza's notion of God), but a sense in which it is not. This partly because to an extent it is monism, (it suggests that everything is one thing) and partly because in this other view there is no God if 'God' is defined as an entity external to oneself. There is certainly no God in anything like a institutional Christian sense.

The third statement brings to mind the God of the old testament who, when asked about himeself replies "I am that I am".

Is this equivalent to implying that:

1) Wavicle is neither a wave nor a particle?

Or;

2) Wavicle is both a wave and a particle?

Well, neither and both of these I think. It wouldn't be right to say that a wavicle is neither, since it has the aspects of both, but it wouldn't be right to say it is both, since what it is, intrinsically, is neither. Equivalently in Buddhism what is ultimate is said to be not something, not nothing, not both something and nothing, and not neither something nor nothing. It is beyond these distinctions both ontologically and epistemilogically. This is why it cannot be conceived, just as wavicles cannot be conceived. Richard Feynman said in a lecture once that "The way we have to describe nature is generally incomprehensible to us". This is also the Buddhist view. It cannot be described properly, and any attempt to do so gives rise to paradoxes of self-reference.

Such that if it is (1), you give it a different a name or leave it completely devoid of a name? Or if it is (2) you assign both properties to it and rename it, or simply treat is as nameless? Even if (2) were arguably the case, wouldn’t you have to give some idea of how wavicle becomes partly a wave and partly a particle? Or if it were (1) that you hung on to, wouldn’t this leave you in the same boat as scientists who intellectually give up searching or looking as soon as they reach COP (Critical Observation Point)? That is, once things have reached a point at QM where they become unobservable, they suddenly give up on the very logic that was guiding them to this point?

The answer is that QM and Taoism (for example) have many similarities between their epistemilogocal systems, but that they are fundamentally different. QM has to stop at the COP, for reason and measurement can go no further. But Taoists can carry on, for they are studying essence, not aspects. (Or, perhaps, studying the noumenal rather than the phenomenal). This allows experience to take over from reason at the COP, or where reason comes to its limit.

It looks as if you are cutting corners and proposing a form of monism! Or is this not?

No, not monism. Monism is predicated on a fundamental distinction between one and many. This distinction is dualism.

On a whole, it seems as if you are suggesting that Disjunctions, LEM and the lot should be done away with altogether. I have gone down on record on this PF for rebelling against the DUAL COMPONENTS of Logic, such as LEM, mainly on the grounds of bad habit about their usages. My campaign is mainly to eliminate vagueness in the application of certain dual components of logic like LEM, but never on the grounds of completely eliminating them. My main worry is when, for example, people attempt to apply LEM in situations with multiple truth-values that range over a given scale of reference or simply treat LEM as if it applies accurately to every situation.

One can't do away with dual reasoning, it's the only kind there is. But one can bear in mind that there's always two ways of looking at things. Again this is reminiscent of QM, in which we can happily use the concept of wave or particle as our starting point for theorising, as long as we always bear in mind that a wavicle is not one or the other.

I'd agree with your objections to the innapropriate application of the LEM. What I've been suggesting is that it is particularly innapropriate when applied to 'reality', what is fundamental, and that this is the reason that metaphysical questions are undecidable. To assume they are decidable is to assume that reality must be exclusively this or that.

Or are you suggesting that there is a logical system (or even any of our Natural Languages) that can function without these dual components?

Yes and no. Above I tried to show that a formal axiomatic system could be constructed which takes account of the problems of dual reasoning, and which can represent or symbolise the two ways of looking at things, just as in QM. But this system does not exactly get rid of dualism, it just takes account of it. It is from the metasystem that this dualism can finally be resolved into the non-dual view, not from within the system. As for natural language, Lao-Tau says both that the Tao cannot be named but also that the Tao must be talked. In other words, despite the truth of the former it is necessary to do the latter. Again the equivalence to QM is clear.

It looks like sweeping everything under the carpet and then saying to every passer-by “Please just trust me, don’t question anything, and have faith on whatever comes by?” Or am I missing the point?

In a way I suppose you're right. But this is no more than to say that you can't know what a clarinet sounds like without having the experience of hearing one. That is also an appeal to mysticism.

The next point is this. We know that BIVALENCE LOGIC (or Two-Valued Logic, as they usually call it) has two fundamental truth-values ‘True’ and ‘False’. And we also know that MULTIVALENCE LOGIC (or Many-Valued Logic) has also been developed up to the level of Fuzziness. All that this really means is that Many-valued logic has many truth values which could range from true, false, contingently true, possibly, necessary, possibly-necessary, up to absolutely necessary. Unless I am misunderstanding you, if the dual component of NL that nearly all forms of logic automatically adopt is denied under Buddha-BSG Logic, then so must multiple components that allow NL and Many-Valued Logic to function as they do be inevitably denied under the same schema. Right? Or are you suggesting that Buddha-BSG’s Logic has no truth –value, let alone truth-values?

Another good question. In a very real sense in the no-dual view of reality all statements are neither true or false. They are true or false only relative to some set of axioms which are themselves neither true or false within the system, nor true or false in an absolute sense.

But this is not to say that statements cannot have an absolute truth-value, just that statements which are predicated on dual assumptions cannot have one. So the statement "philosophical idealism is true" is neither true nor false in this view, since what is the case could be characterised as idealism, but there another way of looking at it by which it cannot be so characterised.

In this view a true statement would be a tautology (e.g. "everything is what it is") or (apparently) self-contradictory, as in "the Tao cannot be characterised as being either something or nothing". In the latter statement formal logic seems to be contradicted, but it is precisely equivalent to saying that a wavicle cannot be characterised as a wave or a particle, and is stated for the same reason, that it is what is the case.

Well, it seems to me that if all these were true:

1) NL itself would functionally grind to a halt because the dual component is ‘FUNCTION-CRITICAL’ (a working part you cannot do without)
2) Science would grind to a halt as it relies on this same dual component to reason and hypothesise to a certain point…..scientific progress of any kind would be thrown out of the window!
3) Many other forms of Logic would on the same token evaporate

This is true. It is the result of taking this other view of reality. But it's only true in an absilute sense. It is still useful to say 'it is raining' or 'F=ma', as long as we do not confuse the axioms on which we base these statements for the absolute truths then all is well. It's when we get to the absolute, when we start doing metaphysics, that these systems of logic finally fail.

In TL that you asked me about, and which I am currently messing around with, nothing essential is taken out of NL. Many forms of Logic habitually take logic out of NL, purport to clarify or purify it, and then repackage it and naively claim to have found a new Logically perfect Langauge for a particular discipline. Well, this is to the contrary in TL, for TL does not take logic out of NL but rather it clarifies the logic within it. The whole emphasis is on teaching clarity and eliminating vagueness at every level of the human education. So, the fundamental maxim of TL is this: if you claim to have taken logic out of NL to purify or perfect it, then when you finish doing so, put it back where you took it from so that the native speakers of NL, after being trained in it, can use it to think, speak, write and act more clearly in the society that they share with others. And this frankly implies that you must teach this newly revamped logic to every member of the society and not just turn it into communication tools for the elites or the privileged members of the society only and then sit back and expect an ‘invisible hand to fix the rest’. As I have argued elsewhere, this has the potential of curing misunderstandings and physical conflicts that usually result from vagueness in our reasoning and general communication with each other.

I'm not sure I completely understand that, but I think I see your objection. The point here though is that Taoism, Buddhism etc are not intellectual disciplines requiring great cleverness or social programmes of re-education to understand. Many Taoist masters have been illiterate peasant farmers. The resolution of these logical paradoxes we're discussing is not to be found through the intellect. It can largely be done in that way, and doing it is extremely useful, but in the end it is the practise that brings the understanding. So anyone can understand, but the more one approaches that understanding intellectually the more complicated it can seem, and the more one can relate it to problems in science or philosophy. In the end though it couldn't be simpler to understand the fundamental truth that Taoism, Buddhism, Advaita and so on embody, for it requires not-thinking, not-conceptualising, not-objectifying etc, just sitting, what is called zazen. Sounds daft I know, I used to think it was completely absurd and completely contrary to reason, but that's all it requires. (This is what Les Sleeth is always suggesting).

This is why proponents of this view range from those like Ryokan, who just write simple poetry (or perhaps one should say deceptively simple poetry) and Nargaruna, who writes about the nature of time, space and so on. In one way the world is very complex, and in another very simple. You can come at it both ways. To really derail the discussion and probably get the thread closed I'll quote Jesus when he says that to understand "You must be cunning as serpents and simple as doves".

One last thing, it would be more helpful if you could point us to the exact Notations in Buddha-BSG’s Logic that demonstrates how the following types of statements are precisely clarified or disambiguated:

1) All Cretans are Liars
2) The statement on this line is false
3) There is no me
4) Nothing exists (or perhaps, in your own system ‘Nothing is’)

NOTE: Don’t misunderstand me, I am not in any shape or form trying to claim that what you are describing is completely senseless,

No, I appreciate that. You've made some very good points. On this one I can't respond however. I cannot actually do GSB's mathematics. But I'll wander around the last one a bit.

To contrast nothing with something is dualistic reasoning. In GSB's terms it is to make a distinction in the void. That is, his axiomatic void is neither something nor nothing, but is split into these two aspects when we make this distinction. It is in the nature of a void that we must characterise it or conceive of it as either something or nothing, (hence the endlessly non-halting discussions about 'nothing' in this forum and all the way back to Parmeneides), for what could one call it if not one or the other? For him this is how form arises from formlessness, not just in mathematics, but in cosmogeny. In a sense one could say that he agrees with John Wheeler that universes are created by observers.