Is Consciousness Truly Outside the Physical Realm?

[Doctordick]

I think I'm right in saying that all formal systems of explanation must contain at least one undefined term to avoid circularity and must be able to handle it. ... (Your paper sounds interesting. Did you post a link earlier? If so I'll go find it.)

You need to check out http://home.jam.rr.com/dicksfiles/Explain/Explain.htm . The problem is that you may not be able to follow it. If you let me know what you don't understand, I will try to help you; it is actually all quite straight forward logic but it is not trivial and may require considerable thought.

Have fun -- Dick

 

[Canute]

Hmm. You're right, I don't understand half of it. Still, I have a couple of comments, in case they're of interest.

The significant factor often omitted in any discussion is that a translation from one language to another (including translation of invented machine language representations used by computers) actually constitutes an explanation of what is being said in the original language.

That seems a very good and often overlooked point. A long time ago I read an introductory book on symbolic logic, about which I knew absolutely nothing. By the time I finished it I had decided, for the reasons you give here, that as a means of generating information it was a waste of time. All the information had to be known before it could be symbolised. I raised this with the then Head of Philosophy at Uni. of Bristol, expecting to be laughed at, and was astonished to learn that he agreed. This was the moment I realized that one didn't have to be as clever as Bertrand Russell to do philosophy.

Whatever it is that is to be explained, it can be thought of as information.

You don't define information and so I'm not sure what you mean by this. I'd rather say that whatever it is that is to be explained, it must be thought of as information, but this may be unimportant to your argument. I'm still trying to figure out if everything that can be known would qualify as information. I'm not sure. What I'm pondering is that information implies an information space (Shannon etc.) and thus something that is not information. This is far from irrelevant to the current something/nothing topic. David Chalmers equates the psychophysical features of the world with information states but fails to come up with an explanation of the information space, which by your argument, as I understand it, would not actually be explicable (except by a endless regress of such spaces).

That is, it seems to me that if all the information is known, then any questions about the information can be answered (in fact, that could be regarded as the definition of "knowing").

This is only statement that I both understood and really disagreed with. It seems easy to show that it is possible to know more than one can explain. (Consider the example of Mary the colour scientist, as often discussed in relation to the problem of consciousness). Ostensive definitions seem to qualify as explanations and this confuses the issue somewhat. How would you answer the question: What is 'red'? I know what it is, but I couldn't answer the question if asked by a blind man. Is this a problem? Or did I miss the point?

On the other hand, if the information is understood (explainable), then questions about the information can be answered given only limited or incomplete knowledge of the underlying information: i.e., limited subsets of the information. What I am saying is that understanding implies it is possible to predict expectations for information not known; the explanation constitutes a method which provides one with those rational expectations for unknown information consistent with what is known.

Likewise, I don't think you've shown that understanding and explicability are the same thing. I do agree that understanding implies the ability to extrapolate from the known to the unknown, but only if the unknown is logically supervenient on the known (i.e. only if the unknown is already analytically contained in the known and thus in a sense already known).

 

[moving finger]

Hi Doctordick

What I am saying is that we can assume nothing if we really intend to investigate anything honestly and that can only be done if we set up a way of handling those premises in the absence of definition itself (outside analytic definitions that is). The subject of my paper is the establishment of a method of logically handling things which are undefined. I hold that the concept of "an explanation" is the most fundamental concept of science itself.

Hmmmm. OK. But I believe any particular explanation entails assumptions.

Your statement that we can assume nothing if we really intend to investigate anything honestly would require, in the case of empirical investigation, access to “certain truth” about the world, which I do not think is possible.

To me, an “honest investigation” is one which places both rationality and logic above all else (certainly above any preconceived intuitions), which faces its assumptions head-on, and which has no aspects which are “off-limits” to investigation.

I tend to agree with your point that an explanation may be a very fundamental concept – after the concept of information. If we define an explanation as a mapping between two or more sets of information then it is the information which is fundamental. This definition of explanation accords with the idea that any explanation entails assumptions – an explanation is nothing more nor less than a mapping between two or more sets of information, we may call one or more of these sets the “assumptions”, and the explanation then maps from these assumptions to another set of information.

I don't know that I would use the word "adds" anything as it obviously "adds" nothing; however, if "nothing" (from an ontological perspective) is all that is required, it certainly reduces ontology to uncontroversial issue. But that is a deep and profound conclusion far down the line. (And one I would love to talk about to someone interested and rational.)

“Nothing is all that is required”? I believe in an underlying (ontic) reality, I cannot bring myself to believe that the phenomenal world of our experience is based on absolutely nothing. But I also accept that we can never have certain knowledge of what that underlying reality is, we can never know the “ding an sich”.

If you want to understand my various comments, we will first have to establish a clear understanding of that paper as everything I have to show you arises from solutions to the equation at the end of the paper. Please don't be put off by anything in that paper; I am ready to explain the rational of any part of it. It may be a short paper but there is a lot there.

I tried reading your paper and appendices. I’m hopeless at maths so I got lost when you started introducing equations. If understanding your argument entails understanding the maths then we’ll have to agree to let it go at that.

Before getting lost, I grasped the idea that you are modeling explanations in terms of a mapping between a potentially infinite number of sets of information, each set of information being of finite cardinality, and including the real-number time-dependency of each of these sets. And you show that these parameters can (obviously) be mapped to the 3D (x, tau, t) real number space. This defines a set of points in 3D space, and an explanation is then interpreted as a mapping of one finite subset of such points to another finite subset. Correct? This seems quite reasonable and straightforward.

Best Regards

 

[Doctordick]

Hmm. You're right, I don't understand half of it.

Rome wasn't built in a day. That paper has to be understood one point at a time and cannot be conquered by subconscious acquisition.

You don't define information and so I'm not sure what you mean by this.

You must understand that, except for mathematics and logic (which is used solely for communication as an understood well defined language) I am beginning from a position of absolute ignorance. The concept called "an explanation" (which I hold to be the central concept of all thought) is quite pervasive throughout the world of intellectual attempts at general communication. This alone suggests it is an important concept worthy of a decent definition. My comments in the opening of that paper are, in essence, an attempt to use English (an extremely vague and ill defined language) to corral the idea in common use.

Certainly the term "information" is not a well defined concept. I am using it as a simple name for "what it is that we want our explanation to explain". As such, my usage of the term is as analytical as is my definition of "an explanation". Again the arguments I put forth in English amount to little more than a demonstration that my usage is not totally inconsistent with common usage of the term.

I'm still trying to figure out if everything that can be known would qualify as information.

I am merely using it as a symbol for what is to be explained, making no constraint whatsoever on what that might be. You are trying to establish an underlying definition which implies the starting point you wish to use (the first thing defined) is not "an explanation".

That is, it seems to me that if all the information is known, then any questions about the information can be answered (in fact, that could be regarded as the definition of "knowing").

This is only statement that I both understood and really disagreed with. It seems easy to show that it is possible to know more than one can explain.

I think you misunderstood my meaning in that quote. When I said "all the information", I meant "ALL" the information; that would mean that absolutely nothing was "not known". In such a circumstance, certainly no questions could exist which could not be answered. Again, all I am doing is using English to corral the idea in common use as I am well aware of the fact that actual meanings of words in English are quite difficult to pin down exactly. The point of the paragraph was to illustrate the issue that explanations constrain our expectations with regard to facts we do not know. I think you did miss the point.

Likewise, I don't think you've shown that understanding and explicability are the same thing. I do agree that understanding implies the ability to extrapolate from the known to the unknown, but only if the unknown is logically supervenient on the known (i.e. only if the unknown is already analytically contained in the known and thus in a sense already known).

Once again, you are trying to establish underlying definitions which implies that your starting point (the first thing defined) is not "an explanation". I am afraid that the course you wish to take is a well trodden path known full well to lead nowhere except to infinite regress. What I am trying to show is that my analytic exact definition of the concept "an explanation" is unique in that it does provide a valid starting point which avoids the issue of infinite regress.

My definition is exactly expressible in the language of mathematics. I define "An explanation" to be a method of obtaining expectations from given known information and I show you exactly how to express that definition as a mathematical relationship.

Hi MF,

Sorry to hear of your dislike of mathematics. As Feynman said, "mathematics is the distilled essence of logic". Without it, our ability to relate large volumes of information is insufficient to the task which confronts us.

OK. But I believe any particular explanation entails assumptions.

You are making the same mistake as Canute. Your comment implies the word "assumption" be defined before one can define an explanation. As I said to Canute, that path leads nowhere except to infinite regression.

Your statement that we can assume nothing if we really intend to investigate anything honestly would require, in the case of empirical investigation, access to “certain truth” about the world, which I do not think is possible.

I think you are confusing two very different issues. The concept "certain truth" implies you understand something whereas, the concept of explaining what you know need not include understanding of any kind. That is to say, you are presupposing an understanding of what that is about the world you do have access to. I, on the other hand, am simply stating that whatever it is that you have access to, in the initial state, you certainly don't understand any of it; a totally different statement. Would you go so far as to propose we have access to nothing about the world? That's pure Solipsism.

I tend to agree with your point that an explanation may be a very fundamental concept – after the concept of information.

Again, you head down that path of infinite regression. Exactly how do you propose to explain to me your concept of information without understanding "an explanation"?

If we define an explanation as a mapping between two or more sets of information then it is the information which is fundamental.

No because now you must define "a mapping", various sets of information and, explain these things. They cannot be more basic than the concept of an explanation.

“Nothing is all that is required”? I believe in an underlying (ontic) reality, I cannot bring myself to believe that the phenomenal world of our experience is based on absolutely nothing.

You just said above that "access to 'certain truth' is not possible. If that is the case, then what is your belief in the phenomenal world based on? I think that your thinking is embedded in that issue of infinite regression; essentially in the idea that some construct representing reality which was created by your subconscious is the starting point for your analysis. I want you to step back and consider the problem of generating that construct.

I tried reading your paper and appendices. I’m hopeless at maths so I got lost when you started introducing equations. If understanding your argument entails understanding the maths then we’ll have to agree to let it go at that.

Well, unless you are prepared to learn a little mathematics, we may have to let it go at that.

This defines a set of points in 3D space, and an explanation is then interpreted as a mapping of one finite subset of such points to another finite subset. Correct? This seems quite reasonable and straightforward.

I define "An explanation" to be a method of obtaining expectations from given known information. The "given known information" is represented by a set of points in that [x,tau,t ] space. Unknown information is also represented as a set of points in that same [x,tau,t] space. Your expectations for the unknown information consists of the probability you assign to a specific case. The explanation is the method of obtaining that probability as a function of the specific set of points. So all explanations can be seen as a representations of a function and my fundamental equation is a universal constraint on all internally consistent explanations of any information (any set of points in the [x,tau,t] space).

The situation is that to understand anything at all, you must construct in your own head exactly what you think the communication symbols mean and your only source of information consists of the communication symbols themselves. Think of the nerve activity reaching your brain as your source of information; before you can understand anything, you must first give meaning to the activity of a nerve or set of nerves. How do you propose that problem should be approached? What is the basis for your explanation that a signal on the optic nerve yields information about what you see? Is it not the result of discovering a method of predicting consistent expectations based on given known information (the nerve activity previously detected)?

Have fun -- Dick

 

[Canute]

Dick

As such, my usage of the term is as analytical as is my definition of "an explanation". Again the arguments I put forth in English amount to little more than a demonstration that my usage is not totally inconsistent with common usage of the term.

An analytical definition? Is such a thing possible? I'm not sure. Is not your definition of explanation a synthetic explanation of what you mean by explanation?

I think you misunderstood my meaning in that quote. When I said "all the information", I meant "ALL" the information; that would mean that absolutely nothing was "not known". In such a circumstance, certainly no questions could exist which could not be answered.

This is the central point it seems to me. You appear to ignore Godel, Church et al. Your definition of explanation seems to skim over some important issues.

I think you did miss the point. Once again, you are trying to establish underlying definitions which implies that your starting point (the first thing defined) is not "an explanation". I am afraid that the course you wish to take is a well trodden path known full well to lead nowhere except to infinite regress.

I don't agree (yet). I feel it's your (implied) circular definitions of information, explanation and knowledge that lead to a regress. Am I right in saying that for you knowledge = information = what can be explained?

What I am trying to show is that my analytic exact definition of the concept "an explanation" is unique in that it does provide a valid starting point which avoids the issue of infinite regress.

By your definition must an explanation be complete, consistent and in the form of an formal axiomatic system? If not, then how can one rely on the 'expectations' it generates? Would you count an ostensive definition as an explanation?

I define "An explanation" to be a method of obtaining expectations from given known information and I show you exactly how to express that definition as a mathematical relationship.

I have a problem with this. This is not the form (fundamental) explanations take in physics. These all start with axioms whose truth values are not known. Could you give an example of an explanation (theory, description) that starts with known information?

You are making the same mistake as Canute. Your comment implies the word "assumption" be defined before one can define an explanation.

Do you not have to make one or two assumptions in order to arrive at your definition of 'explanation', if we define 'assumption' as per the dictionary?

Would you go so far as to propose we have access to nothing about the world? That's pure Solipsism.

It seems to me that solipsism is a doctrine derived from our access to the certain knowledge that solipsism is unfalsifiable. Is it not the case that an explanation (theory, description etc.) which assumes or predicts that solipsism is true or false is undecidable?

You just said above that "access to 'certain truth' is not possible. If that is the case, then what is your belief in the phenomenal world based on? I think that your thinking is embedded in that issue of infinite regression; essentially in the idea that some construct representing reality which was created by your subconscious is the starting point for your analysis. I want you to step back and consider the problem of generating that construct.

Yes, I disagreed with that point also. But I see the problem as being with the idea that certain truth (upper-case 'Knowledge') is not possible. If solipsism is unfalsifiable then this is not the case.

Think of the nerve activity reaching your brain as your source of information;

Ah. Are we assuming here that all knowledge depends on nerve activity reaching our brains? If so then I think this should be made clear up front. Would this be how we know that we are conscious, and thus of the unfalsifiability of solipsism? I find this doubtful. You seem to accept Descartes' implied elision of thinking and being, but this would be to make an assumption.

Btw, just shooting the breeze - I'm aware your mathematical proof may stand up despite these objections.

Canute

 

[Paul Martin]

Hi MF,

Could you perhaps provide the logical argument that shows the notion of a set of all logical possibilities inevitably leads to contradictions?

Yes. As I mentioned in my previous post, Russell presented this argument to Frege and by so doing, destroyed Frege's life's work. To make it easier for me, and also to acquaint readers who aren't familiar with Russell's challenge to Frege, I will quote Isaac Asimov's account of the affair, which includes the logical argument you asked for. This is found on page 518 of "Asimov's Biographical Encyclopedia of Science and Technology, Second Revised Edition", Doubleday, 1982:

"[Friedrich Ludwig Gottlob] Frege is...known for a colossal and unique intellectual catastrophe. In the 1880s he began the preparation of a gigantic work applying symbolic logic to arithmetic and attempting to build up the entire structure of mathematics, including the very concept of number, on a rigorous and contradiction-free basis. The first volume of his tremendous work appeared in 1893 and the second in 1903.

"While the second volume was yet in galleys, the young Bertrand Russell...addressed a query to Frege. How would Frege's system, asked Russell, deal with the particular paradox that we can here explain as follows: " 'Classes' are groups of similar objects. Some classes are themselves members of the class they describe. For instance, 'the class of all phrases' is itself a phrase. On the other hand there are classes that are not themselves members of the class they describe. Thus, 'the class of all cats' is not itself a cat. So one might speak of 'the class of all classes that are members of themselves' and 'the class of all classes that are not members of themselves.' "

"Well, then, asked Russell of Frege, is the "class of all classes that are not members of itself" a member of itself or not? If it is a member of itself then it is one of those classes that are not members of themselves. On the other hand, if it is not a member of itself then it must be a member of the other class of all classes that are members of themselves. But if it is a member of itself -- You can go on forever, you see, and get nowhere. On consideration Frege realized his system was helpless to resolve it and was forced to add a final paragraph to the second volume of his lifework, admitting that the very foundation of his reasoning was shattered and the books therefore worthless. He published no more after that."

From that I think we should learn that not only is nothing in reality infinite, but that any notion that includes infinity should be excluded from mathematics because it will drag inconsistencies with it.

Why does this lead to the notion that nothing is infinite?

(How do you guys nest these quotes like you do?)

I think we cannot reasonably claim that anything is infinite unless and until we clearly define the term 'infinite'. The ancients glibly used the term and declared many things to be infinite without a definition that is satisfactory, at least to me. Georg Cantor was the first to rigorously define the notion of infinity and to deduce the consequences of his definitions. He immediately encountered paradoxes. Rather than reject his notions, as Kronecker and Brouwer thought, and as I still think, mathematicians have instead tried to avoid the inconsistencies. If anything, real, conceptual, or otherwise, does indeed conform to Cantor's definitions, then we know that inconsistencies are inevitably introduced. This seems impossible and/or unacceptable to me. If there are other definitions for 'infinity' which do not introduce contradictions, I am unaware of any of them.

Are you saying that the laws of physics (as opposed to the laws of mathematics) are logically necessary, entailed by the condition of consistency?

Yes. I am convinced that Dr. Dick has proved this to be the case. IMHO, his work should be classified as a theorem of mathematics. I see it as a greatly generalized Noether's Theorem. She proved that symmetry implies conservation laws; Dr. Dick proved that consistency implies all the laws of physics.

Thus the PC does not create the laws of mathematics or the laws of physics; whatever the PC does, it does under the constraint of these laws? Is this what you are saying?

Not exactly. PC chooses this constraint by choosing to remain consistent. The constraint itself has two components: 1) there is the self-imposed constraint of the willful decision and resolve to abide by the rules of consistency, and 2) there are the constraints which are implicit in the logical consequences of sticking to the chosen rules. It is this second component which has been analyzed by Dr. Dick.

This is logically equivalent to you choosing to play chess. You willfully decide to play chess and to abide by the rules. If you do, then one consequential constraint is that your rook cannot move diagonally. If PC chooses to violate the constraint of remaining consistent, then inconsistencies will result. Since (we suppose) our physical universe is consistent, we can conclude that PC chose not to violate the constraint with respect to our physical universe.

How does the PC choose this at the outset, when it has nothing (no logic) to work with?

Good question. Maybe George Spencer-Brown or Chris Langan has worked out the details of how this evolved. My guess is that it developed slowly. The notions of logical consequence and consistency would have to be worked out way ahead of any such choice. It might have started by PC imagining and constructing many "bit sets", noticing patterns, making definitions, testing algorithms, etc.

When I ponder how this might have happened, it seems like the possibility of inventing music might have happened early in the process. It seems to me that bird songs, whale songs, and even human music, might be a recapitulation of that primordial music. Pythagoras might have had it right. From our Goethe/Beethoven conversation, we concluded that music is fundamentally vibrations, which can be seen as nothing but repeating patterns. As the patterns get more complex, secondary effects emerge, such as overtones, beat frequencies, and rhythms. The repetition occurs at multiple levels, from the basic tonal frequencies to the major themes of the composition. There would be much in such a scenario for PC to notice, discover, and know, all of which would add to the accumulating knowledge base. Notions as complex as logical consequence and consistency would not noticeably emerge, IMHO, until quite a complex repertoire of compositions had been composed, or invented. Of course you know this is all speculation. But then, I think that in your question, you asked me to speculate.

Invented, or discovered? Which is it to be?

Since you are trying to pin me down, I'll say, as I have before, invented by PC and discovered by "humans". I put "humans" in quotes to make sure you understand that it is not the human body or brain doing the discovering. It is still PC (or more accurately a significantly more evolved version of PC) doing the discovering via the limiting (i.e. constraining) process of working remotely through a human brain.

Being the first to discover something does not mean that one has invented that something. Or are you defining “invention” as “to discover something for the first time”?

I think it is a little more complicated than that. If the invention is the adoption of some arbitrary set of rules, then there may be some implications of following those rules. Those implications may not be known at the time the rules are adopted but may be discovered later as the implications of following the rules play out. So whether you call the first instance of such an implication a discovery, or part of the invention, I think is merely semantics. The rules are invented; the consequences are discovered by deciding to follow the rules.

Your argument seems incoherent.

Where?

You are saying that PC, having chosen to be consistent, is thereafter constrained by logic and the laws of mathematics and physics,

Yes.

which implies that the PC supervenes on logic and the laws of mathematics and physics,

Yes.

the PC does not create logic and the laws of mathematics and physics, it simply decides whether to be consistent or not, and everything else follows from that,

Yes.

which implies that these things exist prior to the PC’s choice of whether to be consistent or not.

No. That is not implied. As you said, "everything else follows" which does not imply pre-existence. Nothing prevents PC from making different choices at different times. Now Chess; now Checkers.

It seem you define invention as “to discover something for the first time”?

Not necessarily (see above) but first-time discovery happens too.

You are saying the PC is constrained by the rules, but the PC also starts with a blank slate and makes up the rules? Do you not see the contradiction in such a view?

No, I don't see a contradiction. PC is constrained only by the consequences of the rules it has chosen after making them up out of whole cloth. Dick showed that if consistency is chosen, laws of physics constrain the evolution of physical objects and relationships. The rules of chess constrain the bishop from occupying a square of a different color in the same way.

What comes first – the constraint imposed by the rule, or the making up of the rule?

Good question, but I'd say the making up of the rule comes "first". This gets into the messy arena of time. The notion of "first" makes sense only in the context of one specific temporal dimension.

I'm a little too tired right now to get into my view of multiple temporal dimensions, but let me just say that I think time, or a temporal dimension, is exactly, and nothing more than, a parameter measuring the progress of PC traversing a specific world line in some "physical" structure. The world lines themselves can be seen as geometric lines in a space of multiple spatial dimensions. This means that each world line has its own time, as SR has revealed in our particular physical world. It also means that the notion of "first" is relative to whose, or which, temporal dimension you are referring to. It also means that from some points of view, e.g. PC traversing no world line at some "moment", there is no time or action at all. This is the Buddhist's Nirvana.

Thus there are pre-existing laws of consistency which determine whether a particular rule is consistent or not (and this is true in absence of PC).

No. As I explained above, the laws are not "pre-existing".

And having chosen to be consistent, the PC is now constrained to working within the set of consistent rules.

Yes. You have stated a tautology here which must obviously be true. Choosing to be consistent is identically the same as choosing to be constrained to working within the set of consistent rules. So having chosen to be consistent, PC is now constrained to be consistent.

Having decided to be consistent, the PC can now only “create” (or think that it creates) rules which are consistent,

No. Nothing prevents PC from deciding to be consistent and then later "creating" rules leading to inconsistencies. But the moment those inconsistencies appear, PC is no longer consistent and the decision to remain so is revoked. PC cannot be consistent and inconsistent at once. (IMHO PC "creates" by thinking that it creates, as you seem to imply.)

but in fact whether a rule that the PC thinks it has created is consistent or not is already determined before the PC thinks about it.

No more than the rules for how a free throw is to be conducted was already determined before the game of basketball was invented or thought about.

The PC is not free to “create” just any rule it likes, it is constrained by the fact that the rules it “creates” are already determined from the rules of consistency. Correct?

Close. The PC is not free to "create" any set or combination of rules it likes. If one of the chosen rules is to remain consistent, then no inconsistent rule may be accepted in addition. And if consistency is chosen, then Dick's Theorem shows precisely what the concomitant constraints are.

Given the constraint of operating in 2 dimensional Euclidean space (where by Euclidean space I mean the space complies with the 5 axioms of Euclid’s geometry, including the parallel postulate), do you think the PC could create a right-angled triangle where the cube of the hypotenuse is equal to the sum of the cubes of the other two sides?

No. But PC is not necessarily given that Euclidean constraint when it comes to constructing universes.

Good talking with you, MF. Sorry for the delay; we had a death in the family.

Warm regards,

Paul

 

[Paul Martin]

Hi Lars,

But Paul, could the "the ability to know" instead be "the ability to experience." Or is that too far from what you mean?

Yes indeed. That's not far at all from what I mean. After thinking about what word to use, I think there is an even better one: "the ability to realize".

Somehow in the evolution of our language, 'realize' has acquired two meanings, both of which apply to the notion I am trying to convey. In the sense of suddenly understanding, or apprehending, or coming to know something, "the ability to know" is synonymous with "the ability to realize". In the other, more literal, sense, 'realize' is nearly synonymous with 'reify'. That is, "the ability to realize" is the same as "the ability to create" or "the ability to invent". I say "nearly synonymous" because whereas 'reify' means only "to treat (an abstraction) as substantially existing" (Webster), 'realize' means "to make real" (Webster again). It seems that the word 'realize' was coined specifically for my purposes. I think I will change my language and begin to talk about "the ability to realize" as the fundamental essence of consciousness and thus of reality.

In thinking about your question, Lars, it also occurred to me that I have been making an error of conflation that I should address here. MF has pointed this error out a couple of times, but I haven't faced it like I should have. The problem is that I sometimes conflate the ontological essence of reality with the primordial essence. I have claimed that consciousness, or the ability to know, or now, the ability to realize, is both the primordial starting point of all of reality, and also the fundamental ontological essence of the consciousness that we experience.

The example that shook me this morning while thinking about your question is the example of computers. If we asked what the ontological essence of a computer is, in the same way Goethe and Beethoven asked about the essence of music in my dialog with MF, we would have to say something like "logic gates". All computers are built up as a connected set of operational logic gates regardless of how those gates are implemented. But if we were to ask what was the primordial computer, or the very first instance of something that evolved into a computer, we would have to say that it was something like Babbage's Engine, or Jacquard's loom, or an abacus, or notches cut into a bone, or some other physical artifact. You could, of course, see those artifacts as embodying logic gates in a sense, but I would say that the respective inventors did not realize that anything like a logic gate was involved.

So in my two quests -- to identify the fundamental essence of consciousness, and to identify the primordial ontological essence -- the words I choose to express my guesses need not necessarily be the same.

By separating out the two questions, it should help me overcome MF's persistent objection that my primordial PC is too complex. The assumption he makes is that PC in its primordial state is endowed with many of the extremely complex capabilities that we seem to have as conscious humans. I, on the other hand, suppose that those complex capabilities evolved over immense stretches of time (and in multiple temporal dimensions at that) and that the primordial state of PC was extremely simple and limited.

Using my new terminology, I would suggest that the primordial PC was nothing but the most rudimentary ability to realize, in the sense of the ability to know. As soon as any bit of knowledge was acquired, the ability to know about it meant that the bit "existed" in some sense. In this sense, the bit was realized in the sense that it actually became real.

By contrast, the consciousness that we experience as humans is extremely complex and rich. Our ability to realize in both senses seem to be only a small part of our total mental abilities. I think now that it might be premature to suppose that all conscious aspects can be derived from a fundamental ability to realize, although that still seems to be a possibility.

I am rambling now, so I'd better stop. Thanks for your question, Lars. It made me think.

Warm regards,

Paul

 

[Doctordick]

Hi Canute,

I think you are missing the main issue of my presentation.

An analytical definition? Is such a thing possible? I'm not sure. Is not your definition of explanation a synthetic explanation of what you mean by explanation?

Sloppiness on my part. I should have perhaps not used the word "definition".

I define "An explanation" to be a method of obtaining expectations from given known information and I show you exactly how to express that definition as a mathematical relationship.

Let us change that to, "I consider the "method of developing expectations" to be the fundamental concept essential to understanding anything. Expressing that concept in English is not an easy thing. The word "developing" could be replaced by "determining", "acquiring", "thinking of", "coming up with", etc.; whatever makes more sense to you.

We certainly have expectations: what we think the facts are (true or false). And we have come to have them; therefore a method must exist for doing so. I am putting forth, as an "analytical truth" per Imanual Kant, that "an explanation" is the common name I will use for that method. Most of the English leading up to my conclusion concerning the proper way of approaching the problem is devoted to the issue that the concept I am talking about is essentially consistent with the common usage of the term "explanation". A is what is being explained and must remain totally undefined as its definition is part and parcel of the explanation: what you call it is of no real interest here. "Information" is no more than a name I use to refer to it (or rather pieces of it that the "method" is based upon).

One of the fundamental characteristics of "our expectations" is that they change. In common parlance, they change because we discover our expectations are wrong. Again, C is (again as an analytical truth) whatever it is that our explanation uses and B(t) constitutes that change (which adds to C as we, as could be said, learn more of A). Thus I only have two things here: C (whatever it is that we really know) and P(B(t)) what our expectations are. The only constraint I use is that, as C consists of the collection of all B(t) we know, P(B(t)) must be consistent with C.

One thing that Paul invariably seems to miss is that the consistency required here has nothing at all to do with any consistency in C. The consistency lies entirely with the method of obtaining P(B(t)). If that method is inconsistent, it is simply worthless as it clearly fails to provide one with expectations consistent with C. It's that simple.

I don't agree (yet). I feel it's your (implied) circular definitions of information, explanation and knowledge that lead to a regress. Am I right in saying that for you knowledge = information = what can be explained?

I would make but one simple but very important change: in any presentation by me on this subject, knowledge = information = what "is being explained".

By your definition must an explanation be complete, consistent and in the form of an formal axiomatic system?

No. All it need do is provide expectations consistent with C, (what you know or, more accurately, consistent with C+D, what you think you know). If your expectations are not consistent with what you think you know why would you think it reasonable to rely on your expectations? Would I count an ostensive definition as an explanation? As a method of obtaining expectations from given information, it certainly seems to be consistent with everything I am saying.

I have a problem with this. This is not the form (fundamental) explanations take in physics. These all start with axioms whose truth values are not known.

You are omitting (as understood) 99.99 percent of those fundamental explanations. They first assume you understand the language the professor is speaking, they then assume the axioms being stated are understood, that you understand that the truth values of those axioms are not known and, finally, they presume you understand the logic they use. They all start with lots and lots of "known" information; the issue just isn't raised.

Do you not have to make one or two assumptions in order to arrive at your definition of 'explanation', if we define 'assumption' as per the dictionary?

Well certainly. I have to assume you understand English, logic and at least a little mathematics. But that is a little beside the point. The real issue here is, what assumptions have I made to deduce my fundamental equation ; show me a single step in that deduction which assumes something about what C actually is.

It seems to me that solipsism is a doctrine derived from our access to the certain knowledge that solipsism is unfalsifiable. Is it not the case that an explanation (theory, description etc.) which assumes or predicts that solipsism is true or false is undecidable?

Yes, that is entirely true and the issue is embedded within my deduction. At no place do I contend that a difference between C and D can be determined. Solipsism, from the perspective of my deduction is no more or less than assuming that the set C vanishes. The entire deduction still survives as valid.

Ah. Are we assuming here that all knowledge depends on nerve activity reaching our brains?

No, it's even worse than that. The existence of those nerves and your brain is part and parcel of your an explanation of your expectations. We are making no such assumption; I only used it to direct your attention to the fundamental problem of explaining things.

You seem to accept Descartes' implied elision of thinking and being, but this would be to make an assumption.

No, once again you are bringing up a specific explanation (I presume you meant illusion or delusion as elision is "the omission or slurring over a vowel, syllable, etc. in pronunciation: often used in poetry when a word ending in a vowel is followed by a word beginning with a silent h or a vowel".) I simply don't worry about such advanced and complex things built from advanced and complex ideas already proposed as explanations of reality. That is exactly where my difficulty with Paul occurs.

To recapitulate, what I show is that any explanation (any method of obtaining expectations from one's knowledge) must obey my fundamental equation. I can show (if I ever find someone both interested and capable of following my algebra) that the fundamental elements of C must obey a number of known relationships. I can show that Schrodinger's equation is an approximation to my equation (and thus that classical mechanics, which can be deduced from Schrodinger's equation, must also be valid). I can show that Dirac's equation is an approximate solution to that self same equation and further, that E&M is no more than another approximation. I can answer the questions "Why does the world appear to be three dimensional?"; "Why is there no magnetic monopole?"; "Why is time travel impossible?"; "Why do advanced physics theories require additional dimensions?".

I can prove that modern physics is a tautology and, once you understand the tautology, the problem between relativity and quantum mechanics vanishes. This is exactly what Paul is referring to when he says

Yes. I am convinced that Dr. Dick has proved this to be the case.

Paul was a mathematician and he has gone through much of my work. What he seems to have missed is that the fundamental elements of any explanation must obey my equation. What that means is that absolutely any valid explanation of anything must be built from fundamental elements obeying the rules of physics. This is almost the definition of "emergent" qualities. That is to say, an explanation of consciousness, awareness, intelligence, thought or any complex phenomena, if it is to be valid, must be expressible in terms of fundamental entities obeying what we have come to call the "laws of physics".

You might ask, if I can show all that, how come I am an unknown? The answer is simple in view of the fact that I am a quack as evidenced by the fact that no one could possibly show such a thing. It follows, as the night the day, that any competent scientist is wasting their time looking at my work. No one has ever pointed out a real error in my presentation, but they are all quite confident it cannot possibly be correct.

Have fun -- Dick

 

[Canute]

Paul

It seems relevant to your point about complexity that traditionally the Sufis say that Knowledge is a dot, a singularity, and that it is conscious beings that create all the complexity. (I've seen this 'dot' discussed by one Sufi in terms of the BB singularity). I think the point here is that almost everything we normally call knowledge is of things the Sufis say do not really exist (appearances, Maya etc), and thus is not Knowledge but confusion. Putting it awkwardly omniscience, in this view, is more simple that physics. This seems to support your view.

Btw - How do you feel about Spencer Brown after all this time? Since we last discussed all this I've discovered Francis Bradley, whose argument supports Brown's. Do you know his writing?

Dick

I don't entirely follow them but I see you do have answers to my objections. Could you unpack this statement a little:

That is to say, an explanation of consciousness, awareness, intelligence, thought or any complex phenomena, if it is to be valid, must be expressible in terms of fundamental entities obeying what we have come to call the "laws of physics".

Is this an ontological or epistemilogical statement? I ask because according to one 'explanation of everything' there is no such thing as a fundamental entity. However, the rules of explanations demand there be such a thing, so even if one holds this view one is forced to refer to such an entity for epistemilogical/theoretical reasons. This confuses the issues somewhat, in such a way that your statement would be true, but only because of the rules of explanations do not agree with the rules of the universe. This relates to my woolly point about the possible difference between knowledge and information that can be explained. (I take it the 'laws of physics' here also include the laws of logic).

Would it be possible to briefly state in English what it is your proof proves?

Cheers
Canute

 

[Paul Martin]

Hi Canute,

It seems relevant to your point about complexity that traditionally the Sufis say that Knowledge is a dot, a singularity, and that it is conscious beings that create all the complexity. (I've seen this 'dot' discussed by one Sufi in terms of the BB singularity). I think the point here is that almost everything we normally call knowledge is of things the Sufis say do not really exist (appearances, Maya etc), and thus is not Knowledge but confusion. Putting it awkwardly omniscience, in this view, is more simple that physics. This seems to support your view.

I agree. Everything you said here seems the same way to me. I think the Sufis are among a large number of people who have had a glimpse of a greater reality than the 4D physical world of science. I also think that none of those people can adequately express in language what they glimpsed and that all attempts to do so have resulted in little if any understanding and vast amounts of confusion and error. To be fair, I think those people do gain something in their glimpse which helps them lead a better life and which might provide a good example to others. But when it comes to explanations, or descriptions in language, I think it doesn't go much beyond admonitions like, "Love your neighbor as yourself", etc. Certainly nothing has been gained that has been useful in furthering our scientific understanding of the physical world.

But my guess as to what is going on in the biggest picture of reality is right in line with what you said here with maybe one exception. You mention "conscious beings" in the plural making it sound as if there are multiple conscious beings. As you know, I think that there is only one conscious being in all of reality, and that what appear to be multiple "conscious beings", such as humans or other animals, are in reality remotely controlled vehicles, all being driven by the one consciousness, or by a higher level vehicle which is ultimately driven by the one consciousness through a hierarchy of remotely controlled vehicles. So if you consider these vehicles to be "conscious beings", then I agree that they are directly responsible for the creation and construction of all complexity.

Among the constructions, our physical world since the Big Bang being only one such, there are world lines describing the activities of "conscious beings" (really remotely controlled vehicles) which exist in that structure, and when the one consciousness traverses one of those world lines and is attending to it, the life of that vehicle is experienced. Languages are part of that structure and any information encoded in languages is necessarily wrong or incomplete, so I would agree that what we call knowledge is really nothing but confusion at some level. Some of it might be useful, but it still contains errors and is incomplete. I think mathematics is the best way to minimize the errors, and I think that is the reason mathematics has been so useful in attempting to describe our physical universe. It is the approach we should continue to exploit. That is the approach of Dr. Dick and all successful physical scientists.

As for omniscience, I don't think it exists. I think that even that one consciousness doesn't and can't know everything possible, and doesn't and can't even know everything about all that has been constructed so far. Nevertheless, it must know a hugely staggering and impressive amount. Anyone who can rig up such a precise Big Bang that will result in the biological life we know deserves our utmost respect. On the other hand, IMHO, it is just us.

Btw - How do you feel about Spencer Brown after all this time?

I'm sorry to say that I haven't learned any more about Spencer-Brown or his ideas since we last talked. I still feel the same way: I suspect that he might have discovered how all of reality might have evolved (at least the very initial stages) from a knowledge base of only a single bit and only the most rudimentary ability to know, or realize, that that bit existed.

Since we last discussed all this I've discovered Francis Bradley, whose argument supports Brown's. Do you know his writing?

No, I don't. Could you possibly provide a link to an introduction?

Good talking with you again, Canute.

Warm regards,

Paul

 

[Paul Martin]

Hi again, Canute,

I am going to be a little presumptuous here and try to answer your question to Dr. Dick:

Would it be possible to briefly state in English what it is your proof proves?

I have been working with Dick for many years trying to understand his work and his result. I think I understand some of it, and I think Dick gives me credit for understanding some of it. On the other hand, Dick claims that I don't quite get it. I have made many attempts to "get it" including the approach of trying to write English prose which captures the essence of his result. Dick has agreed to help me correct and refine these attempts, but unfortunately, I have not spent the time it requires to get it right.

I have, however, started the project, and since my objective is to provide exactly what you have asked for, I thought it might be of some use to present this work in its unfinished and unofficial state. It might provide a starting point for some readers to engage in further dialog with Dick and thereby come to a more complete understanding than I was able to achieve myself. So, with all those caveats, you may take a look at five different attempts at describing Dick's work beginning with the following link:

http://paulandellen.com/ideas/tfor.htm

Warm regards,

Paul

 

[Doctordick]

Paul, thanks for your continued support. I do appreciate you even if I seem to give you a hard time sometimes. The only real complaint I have on your understanding is that you think the numbers represent physical things. They don't, they represent references to elements being explained (fundamental elements of the explanation), a subtle difference as "physical things" are not really a totally undefined concept. The issue is that your PC does not escape the proof.

By the way, you asked how to embed quotes within quotes. It's very simple. I will specify the method first with carrots as command limits and then write the same thing with square brackets as command limits.

<QUOTE=Paul Martin>But Canute, you already said "biggrin"
<QUOTE=Canute>Dick is a quack
<QUOTE=Doctordick>That is what everyone says! "rofl"</QUOTE>Well at least we all agree! "yuck"</QUOTE>That we all agree!</QUOTE>
Exactly the same thing with square brackets replacing the carrots and colons (:)replacing the quotes (")

But Canute, you already said

Dick is a quack

That is what everyone says!

Well at least we all agree!

That we all agree!

Does that clear the problem up?

Hi Canute,

It is entirely an epistemological statement! The ontological basis is the undefined set C which can be absolutely anything. The result (that the behavior of the fundamental entities is described by my equation) is thus totally independent of ontological considerations. It follows that the proof removes ontology from any serious interest (whatever ontology you happen to chose as the basis for your arguments, the behavior of the entities so designated can be described by the laws of physics if your explanation is internally consistent).

I ask because according to one 'explanation of everything' there is no such thing as a fundamental entity. However, the rules of explanations demand there be such a thing, so even if one holds this view one is forced to refer to such an entity for epistemological/theoretical reasons.

You are quite right, this problem does indeed confuse the issue quite a bit. What I have discovered was a logical way of handling that deep and profound difficulty: simply make sure that you can refer to the ontology without defining it no matter what it might be. That is the essence of my undefined sets A, B(t), C and D. That approach led me to what I call my fundamental equation (a relationship which must be true absolutely independent of the ontology).

When I started down that path, my only interest was to get an exact grasp on the problem which actually faced us: the problem of understanding a universe given absolutely nothing to go on (everything is embeded in what we are trying to understand: i.e., there exists no way to confirm our interpretations are correct outside consistency itself). I had proved that equation had to be true five years before I managed to solve it. When I finally discovered an attack capable of solving it, I was absolutely astonished by the solutions. I tried to publish but could find no journal even willing to send it to referees. The physics journals said it was philosophy, the philosophers said it was mathematics and the mathematicians said it was physics. The fact is (and I can show it explicitly) that most all of the so called "laws of physics" are no more than solutions to that equation.

(I take it the 'laws of physics' here also include the laws of logic).

In my mind, no. I regard logic as a branch of mathematics which I define to be the invention and study of internally self consistent systems. I consider it a relatively exact language for communicating complex relationships. In my head, the "laws of physics" constitute the rules of behavior governing the things which we think make up reality.

Would it be possible to briefly state in English what it is your proof proves?

With regard to that issue, I would like to quote your comment to Pit2 in the thread "Causality in the subjective world".

Of course, this begs the question of whether physical laws arise from the laws of reasoning or vice versa, but generally we automatically assume the latter. Personally, I find it more likely that the laws of reason are prior to the laws of physics.

I have proved exactly what you have stated as "more likely". It makes utterly no difference what the rules of the universe are (it can even be a totally indeterminate thing), its behavior can be explained by the laws of physics.

The laws of physics amounts to no more than a data compression mechanism to keep track of what has happened. The field and the results of their experiments is totally analogous to the Dewey Decimal system for keeping track of books in a library. That is to say, it is a tautology: the laws of physics are a direct consequence of the definitions upon which the field is built. These definitions clearly arose because our subconscious minds found those particular concepts useful for predicting what will happen. It turns out that the single most important fact upon which everything we know is based is, "the future will look a lot like the past" whether looked at in detail or in overview. That's essentially the hypothesis which generates my equation and it turns out that there is nothing in physics to suggest the issue goes any deeper than that.

I am afraid modern physics is indeed a religion. They think their experiments prove something about the universe in exactly the same sense that astrologers thought that their examples supported their beliefs. The facts are the facts and it is only our interpretation of those facts which provide us with explanations. My problem, is that people who have the training to follow my math, will not look at it because it threatens their expertise. You should take a look at a certain thread on this subject on http://www.scienceforums.net/forums/showthread.php?t=20615 if you really want to see how professionals respond to me. I think Severian (their physics expert) is probably actually a professor of graduate studies: however, I don't think his ability to think is anything to brag about. You might find what I said there interesting and maybe educational.

But of course, I am a "quack" -- Dick

 

[Canute]

Paul - great to be talking again. I see we still almost agree but not quite.

For example, I cannot agree with your disparaging remarks about Sufism. Have you read the literature?

When I spoke of 'conscious beings' I was speaking conventionally. I should have made that clear. There are of course no such things.

Among the constructions, our physical world since the Big Bang being only one such, there are world lines describing the activities of "conscious beings" (really remotely controlled vehicles) which exist in that structure, and when the one consciousness traverses one of those world lines and is attending to it, the life of that vehicle is experienced.

That makes sense. But are you sure these vehicles are controlled? Who is doing the controlling? If it is PC then it would have to be fantastically complex to control all these things at once. Yet to be fundamental it would have to be simplicity itself. This antimony suggest to me that your view is not quite right. I also doubt that the life of the vehicle is only experienced when PC traverses and attends to its world-line. I'd rather think that the world-lines are not separate from PC.

Have you come across Gurdjieff on free-will? His view was that if we are aware of who we are then we have free-will. If we are not then we are slaves to deterministic (psychophysical) forces. More generally, this is the esoteric view. Thus PC would have freewill but the remote vehicles would not, not unless they were aware of who they are, which in this view would be PC.

Languages are part of that structure and any information encoded in languages is necessarily wrong or incomplete, so I would agree that what we call knowledge is really nothing but confusion at some level.

It's worse than that, I think. If the mystics are right then the truth about consciousness is actually paradoxical in ordinary language. Does freewill exist? From the above you see that there are two points of view, the conventional and the ultimate. As a result the question does not have a yes or no answer. In the literature it is never given one. Natural language cannot cope with things like PC or wave-particles. (Of course, the question is actually more complex, since the whole idea of will, of any kind, is a can of worms).

But knowledge is not confusion by definition. If it is knowledge it cannot be confusion. What turns into confusion is theory and conjecture, not knowledge. Natural language cannot cope with a wave-particle, but this does prevent us from using them in theories, it just means that the theory has to have two contradictory aspects, just like the doctrine of Sufism. But certain knowledge does not come in form of natural language and theories, from which only provisional knowledge can be derived.

I think mathematics is the best way to minimize the errors, and I think that is the reason mathematics has been so useful in attempting to describe our physical universe. It is the approach we should continue to exploit. That is the approach of Dr. Dick and all successful physical scientists.

I agree inasmuch as mathematics is good way of thinking about the issues in the abstract and accurately. However, according to Brown, as you know, a fundamental mathematical theory of everything must have two aspects, like quantum theory. Otherwise PC has to be left out and the theory becomes less than a theory of everything. It would become a theory in which PC's dual-aspects were treated as two different entities rather than as dual-aspects of one 'thing'. Imagine a quantum theory in which waves and particles are treated as two different things in a ontological sense. It would be nonsensical.

As for omniscience, I don't think it exists. I think that even that one consciousness doesn't and can't know everything possible, and doesn't and can't even know everything about all that has been constructed so far.

This may just depend on what we mean by omniscience. There is a view that simply knowing who we are is a form of omniscience. (How to characterise the omniscience of a Buddha is a subject of continued debate among Buddhist philosophers, since only a Buddha knows. By the way, Spencer Brown told me he is a Buddha.) Equivalent to my comment earlier, the Sufis say omniscience is a dot. I suppose the question is really whether omnsicience consists in knowing and understanding the simple and fundamental principle underlying the existence of everything, or the set of principles, or whether it consists in knowing lots of the details.

Nevertheless, it must know a hugely staggering and impressive amount. Anyone who can rig up such a precise Big Bang that will result in the biological life we know deserves our utmost respect. On the other hand, IMHO, it is just us.

Yeah. I can't get the hang of the idea that this was a calculated outcome rather than one that is inevitable given the nature of PC. Lao Tsu says the laws come from 'the Tao being what it is'. This makes more sense to me.

I'm sorry that you haven't got to grips with Spencer Brown. However, whereas before I couldn't really explain what he was saying I probably can now, although I'm sure he wouldn't think so, so if you want to talk about him some time I'm up for it.

I suspect that he might have discovered how all of reality might have evolved (at least the very initial stages) from a knowledge base of only a single bit and only the most rudimentary ability to know, or realize, that that bit existed.

This may be about as well as it could be put without sounding mystical. However, as Aristotle remarked, true knowledge is identical with its object, and Brown's calculus deals with this problem.

I haven't got any links for Bradley unfortunately. The relevant text is Appearance and Reality. This is difficult to get hold of. I saw a s/h copy for sale recently at £180. Fortunately the local library tracked down a dusty and long forgotten copy. But I was only allowed to keep it for a fortnight, on pain of death. It's damn complicated, one of the hardest metaphysical texts I've ever read. He gives a logical proof that nothing exists, and implies that PC (which is not what he calls it) both exists and not-exists depending on how you look at it. Nagarjuna's proof is an easier read.

You would probably like him because he proves, or tries to, that all idea of plurality give rise to contradictions. This would include the idea that solipsism is false. I've got a few extracts somewhere. Online there is a site giving a clear and accurate chapter by chapter summary, but I've forgotten where. If I remember right from my search there are not many sites to trawl through.

Cheers
Canute

 

[Paul Martin]

Hi Canute,

Your post was a superb example of understatement; I agree with everything you wrote.

It is great to be talking with you again, and I agree that we still almost agree.

For example, your taking my remarks about Sufism as "disparaging" is a little harsher than I intended. No, I have not read the Sufi literature, but I have a nodding acquaintance from reading about Sufism by various authors. I did not intend to single them out. If you take another look at what I wrote, you will see that I lumped them together with all other sagacious, prophetic, mystic, wise, enlightened, and otherwise insightful humans that ever existed. And I merely noted that they are subject to the same limitations of language as all the others. These are the same limitations that prevent you and me, or MF and me, or Dr. Dick and me, from eliminating the "almost" that persistently modifies our "agreement". I think we might be as close to agreement as we can get without "going mathematical".

When I spoke of 'conscious beings' I was speaking conventionally. I should have made that clear. There are of course no such things.

No problem; that's the way I took it. But I should have made myself more clear. I meant to imply that there are actually three ways to see "conscious beings": 1) the conventional way as individual human beings, 2) PC, or the ultimate and only conscious being, which if isolated from all thought-structures would not be conscious of anything at all (meaning that there is no such thing as a "conscious being", (This is when PC is in the state of traversing no world line, and consequently time does not move at all.) and 3) Natural Individuals in the sense of Gregg Rosenberg which occupy several levels of existence having different temporal and spatial dimensions from each other (our physical world being only one of them). These Natural Individuals are not actually conscious, but exhibit conscious behavior because they are driven, or controlled, or operated by some other Natural Individual (as it progressively attends to the world line of the first Natural Individual) from a higher level in the hierarchy. Only the very top Natural Individual is really conscious, subject to the comments in 2) above.

That makes sense. But are you sure these vehicles are controlled? Who is doing the controlling? If it is PC then it would have to be fantastically complex to control all these things at once.

I think reality is fantastically complex.

Yet to be fundamental it would have to be simplicity itself.

I think PC was simplicity itself in the very beginning. I think it evolved to its current complexity during stretches of time prior to our Big Bang that would make our mere 14 billion years only a fleeting moment by comparison.

This antimony suggest to me that your view is not quite right.

I agree that it does suggest an antinomy, but I think the resolution is in the possibility of multiple temporal dimensions and their relationship to PC's attention. If PC is attending to a particular world line, then time is flowing in that structure from the perspective of the Natural Individual defining that world line. Whether PC can back off one level and observe this activity of following multiple world lines at once, or in some multiplexing or time-sharing pattern is not clear. If so, then that observation would be yet a new world-line being followed by PC's attention and would thus create another dimension of time (I have referred to this as Cosmic Time in other communications). The specific mechanisms for achieving the multiplexing etc. could be at least as complex as the ones we are familiar with here in our physical reality, and there is no reason to suppose that there aren't even more clever and complex mechanisms at PC's disposal. After all, there are those multiple levels of Natural Individuals, each of which could play a different contributing role. But,...in the event that PC is not attending to any world line, then we have the situation described by the Buddhists of nothing but a dot of reality with no time, no consciousness, no movement, nor anything else. It's a mystery where all those thought-structures are then, but then again, in that circumstance there is no "then".

I also doubt that the life of the vehicle is only experienced when PC traverses and attends to its world-line. I'd rather think that the world-lines are not separate from PC.

I agree. This is a reasonable doubt. But I think the problem is nothing more than semantics and is part of the limitation of language that we both acknowledge. What do we mean by 'life' anyway? And what do we mean by 'experience'? And if the world lines are nothing but thought-constructions of PC, then you couldn't really say that they are separate from PC. I don't think we can get much closer using vernacular language.

Have you come across Gurdjieff on free-will? His view was that if we are aware of who we are then we have free-will. If we are not then we are slaves to deterministic (psychophysical) forces. More generally, this is the esoteric view. Thus PC would have freewill but the remote vehicles would not, not unless they were aware of who they are, which in this view would be PC.

I'm not familiar with his work, although I have heard of it. From what you wrote, his view seems consistent with my view of PC. The real question here is, "Who exactly do we think we are?".

But knowledge is not confusion by definition. If it is knowledge it cannot be confusion. What turns into confusion is theory and conjecture, not knowledge. Natural language cannot cope with a wave-particle, but this does prevent us from using them in theories, it just means that the theory has to have two contradictory aspects, just like the doctrine of Sufism. But certain knowledge does not come in form of natural language and theories, from which only provisional knowledge can be derived.

Exactly right! It is only when we try to express knowledge in language that the confusion enters. These attempts at expression are the "explanations" that Dr. Dick has analyzed and it is these that are subject to the constraints he has discovered.

This may just depend on what we mean by omniscience. There is a view that simply knowing who we are is a form of omniscience.

Right again. The view of omniscience as knowing all that can be known is, IMHO, nonsense for the same reasons I tried to argue with MF that any consideration of "all" of any set of possibilities is nonsense. If, however, we consider 'omniscience' to mean knowledge of everything known, then we must ask, "Known to whom?". Of course in my scheme there is only one knower, viz. PC, but in conventional usage we consider that individual humans can "know" in a certain sense. In my view, there is undoubtedly information stored in brain structures, in DNA structures, in libraries, and on hard drives. Should this be considered "known information"? Well, yes, it makes a certain amount of sense to do so. But it complicates the question of what we mean by 'omniscience'.

This takes me to another subject that I have thought and written about, but which I haven't discussed on this forum at all. I have called it the "Transfer of Omniscience" in some of my essays, but I realize that it is bad usage of the term 'omniscience'. Bad usage aside, what I mean is that in the biggest picture of reality there is an oscillation which has the lowest of all frequencies. That oscillation is the transfer of knowledge from PC to the various structures constructed by PC. These structures consist not only of the subordinate Natural Individuals, which vicariously provide PC with experience at that level, but also the "physical" information storage structures in that world of the type I just listed. At the largest scale, knowledge of what can and does go on in the various universes that have been tried out so far, gradually gets encoded into structures in those very universes. PC still has access to the knowledge, but it is increasingly vicarious involving increasingly complex mechanisms for communication. Eventually, all existing knowledge is encoded in physical structures and is available to the Natural Individual(s) at all levels which puts it (them) in a position to try for an even more complex experiment in constructing universes armed with the new knowledge. In a sense this could be seen as PC giving way to the physical Natural Individual and fading into the background. But in another sense, it is simply the addition of another level of remoteness between PC and the developing reality. As the new experiment unfolds (think of a new and different Big Bang) there are no Natural Individuals in the new structure, so all knowledge is now lodged in PC (with the help of the previous structures). Only after much evolution of the new universe does knowledge begin to build up in its structures and thus complete a cycle of oscillation.

I probably shouldn't have gone into that, but your interest and our near agreement sort of pushed the right button and I couldn't help it. Sorry if I put anyone off by going into it.

Yeah. I can't get the hang of the idea that this was a calculated outcome rather than one that is inevitable given the nature of PC. Lao Tsu says the laws come from 'the Tao being what it is'. This makes more sense to me.

I think it was a calculated outcome in exactly the same sense that the Mandelbrot Set is the calculated outcome of Benoit Mandelbrot's investigations of the algorithm he used to define the set. He certainly didn't predict the outcome and probably couldn't have imagined the resulting complexity. But nevertheless it is that algorithm which inevitably produces the complex nature of the set. I think PC constructs universes in exactly the same way. I'd say that the laws come from the Tao, being simply what PC chose them to be.

I'm sorry that you haven't got to grips with Spencer Brown. However, whereas before I couldn't really explain what he was saying I probably can now, although I'm sure he wouldn't think so, so if you want to talk about him some time I'm up for it.

Well, thanks, but I'm too old and tired to get too much deeper into Spencer Brown's math, or even Dick's math for that matter. Since I agree with what I think each of them has developed, I am not motivated to put a lot of effort into understanding it much better. If I were to go back to school and study some math subject, it would be to study the foundations of math seriously. As you know, I have some serious disagreements with most mathematicians in this area and as a result, I am motivated to put some energy into it. One of these years, when some of the pressures on my time are relaxed a little, I fully intend to go back to school and study foundations. I really think they have got some things wrong. But that's another subject.

Good talking with you, Canute.

Warm regards to all and thanks to all those who read these posts.

Paul

 

[Canute]

Dick

I don't understand your maths but seem to agree with much of what you say. I'll check out your's and Paul's link to try and get up to speed.

Paul

If you take another look at what I wrote, you will see that I lumped them together with all other sagacious, prophetic, mystic, wise, enlightened, and otherwise insightful humans that ever existed. And I merely noted that they are subject to the same limitations of language as all the others. These are the same limitations that prevent you and me, or MF and me, or Dr. Dick and me, from eliminating the "almost" that persistently modifies our "agreement". I think we might be as close to agreement as we can get without "going mathematical".

Sorry about this, but I feel our disagreement is more fundamental, not a matter of language at all. But the limitations of language certainly don't help. On the whole I've been too quick to make objections rather than gain a better understanding of your views, a habit of mine. A question then: Do you conclude that the view of the mystics is conjectural? Or do you conclude that they know the facts but cannot communicate them because of language (etc) problems? For a specific case take GSB. Do you think he is guessing or just trying to explain something he knows?

No problem; that's the way I took it. But I should have made myself more clear. I meant to imply that there are actually three ways to see "conscious beings": 1) the conventional way as individual human beings, 2) PC, or the ultimate and only conscious being, which if isolated from all thought-structures would not be conscious of anything at all (meaning that there is no such thing as a "conscious being", (This is when PC is in the state of traversing no world line, and consequently time does not move at all.) and 3) Natural Individuals in the sense of Gregg Rosenberg ...

I never did get the hang of GR's natural individuals. His ideas were too complex for me. Can we leave them out and include everything under 1 and 2?

I think reality is fantastically complex.

I think PC was simplicity itself in the very beginning. I think it evolved to its current complexity during stretches of time prior to our Big Bang that would make our mere 14 billion years only a fleeting moment by comparison.

This states that PC is subject to change and thus time. Do you really mean this? If so I disagree with you. Logically, it seems to me, whatever it is it still is and always will be, beginnless and without end. The idea of 'stretches of time' prior to the BB seems unscientific and logically dubious. The idea that what is fundamental has a beginning seems highly paradoxical to me.

I agree that it does suggest an antinomy, but I think the resolution is in the possibility of multiple temporal dimensions and their relationship to PC's attention.

Well, I'd say time does not flow at all unless someone is paying attention.

But,...in the event that PC is not attending to any world line, then we have the situation described by the Buddhists of nothing but a dot of reality with no time, no consciousness, no movement, nor anything else.It's a mystery where all those thought-structures are then, but then again, in that circumstance there is no "then".

Yeah, this is my problem of PC evolving in time. What time? The thought structures are 'mere appearances' for Buddhists, no more real than pianos and ceiphids. Btw, the Sufis say that the sign of a realized person is that for them there is no time other than the time they are in.

The idea that PC is sometimes paying attention to a world-line and sometimes not would contradict the idea that PC watches every sparrow that falls, thus your view contradicts that of Jesus. This may not bother you, but I suspect he knew what he was talking about. If all is One, as I think you suggest, then how could PC ever not be present?

The real question here is, "Who exactly do we think we are?".

I agree. Although I'd phrase it, 'Who exactly are we? I'd suggest that we can't know this by thinking about who we are, only by being who we are.

Exactly right! It is only when we try to express knowledge in language that the confusion enters. These attempts at expression are the "explanations" that Dr. Dick has analyzed and it is these that are subject to the constraints he has discovered.

I'm still trying to get to grips with his view so can't comment. I mostly agree about expressing knowledge but feel the problem is much more complicated than this. For example, the confusion is not necessarily in the explanation but may be just in the mind of the beholder of the explanation.

If, however, we consider 'omniscience' to mean knowledge of everything known, then we must ask, "Known to whom?". Of course in my scheme there is only one knower, viz. PC,

Exactly. It follows that we could say there is only one thing to know, since all else is logically supervenient on this. In other words, if we know our axiom is true then any further truths and falsities we derive from this axiom are already analytically contained within it.

but in conventional usage we consider that individual humans can "know" in a certain sense.

This may be the ideal starting point from which to disentangle our differences. Russell questioned whether human beings could know anything at all. It is impossible to demonstrate that they can. So how do we know anything? And how do we know we know we know it? Cetainly not by deriving theorems from uncertain axioms. But how can we know our axioms are true? According to Russell we can't. But Russell was a devout non-mystic, and thus could have no theory of knowledge. He assumed that knowledge was the same thing as explanation or proof by demonstration, and this assumption seems to underly some of what you are suggesting, and maybe also Dick. Can you give your views on the relationship between knowledge, proof and explanation? This might clear up some possible misunderstandings. (By 'explanation' I would mean also a description or a theory).

In my view, there is undoubtedly information stored in brain structures, in DNA structures, in libraries, and on hard drives. Should this be considered "known information"? Well, yes, it makes a certain amount of sense to do so.

Not to me. This is provisional information, true of false if, and only if, the axioms from which it is derived are known to be true, and only if we know our reasoning is sound (which of course we never can).

As an experiment try picking one piece of knowledge that you know with absolute certainty and then figure out how you know it. It will not be anything to do with explanations, theories, formal proofs, libraries, hard drives and so on.

This takes me to another subject that I have thought and written about, but which I haven't discussed on this forum at all. I have called it the "Transfer of Omniscience" in some of my essays, but I realize that it is bad usage of the term 'omniscience'. Bad usage aside, what I mean is that in the biggest picture of reality there is an oscillation which has the lowest of all frequencies. That oscillation is the transfer of knowledge from PC to the various structures constructed by PC.

Interesting. Is this the music of the spheres? In my view knowledge cannot transfered. As Zen master Hongzhi puts it, we cannot borrow knowledge. I cannot follow your omnsiscience idea through, partly because I'm still confused about 'natural individuals'. I would point out though that in one view PC is knowledge.

I think it was a calculated outcome in exactly the same sense that the Mandelbrot Set is the calculated outcome of Benoit Mandelbrot's investigations of the algorithm he used to define the set. He certainly didn't predict the outcome and probably couldn't have imagined the resulting complexity. But nevertheless it is that algorithm which inevitably produces the complex nature of the set. I think PC constructs universes in exactly the same way. I'd say that the laws come from the Tao, being simply what PC chose them to be.

As usual I half agree, but I'm sticking with Lao Tsu. I don't think PC constructs universes but rather that they are reified according to GSB's laws, as an inexorable consequence of what PC is. Although this is a sense a mystical view it also seems more scientifically plausible to me.

Well, thanks, but I'm too old and tired to get too much deeper into Spencer Brown's math,

The details of the maths are unimportant to your (and my) interests. The principles on which Brown builds his calculus are all that matter, and these are simple, even with very little knowledge of mathematics. I feel that you must know about these principles in order to solve the problems that arise in your PC theory. This is just an opinion of course. However, for example, these principles overcome your complexity/simplicity problem. They also resolve the dualism/monism antimony that will arise sooner or later as your ideas turn into a formal cosmology.

Now I'll go and check the link you gave. I'd like to discuss this in terms of Dick's proof, since it seems relevant, but I don't understand it yet.

Bye for now
Canute

 

[Canute]

Wow. I just read the introductory essays online at the address you (Paul) posted. I now have 5,867 questions. My interest in your (Dick) approach is this.

I have been trying for a while now to construct a proof that Buddhist doctrine is true. Yes, I know this sounds like a ridiculous project. I have had some success, but want to do better. Other people have succeeded, in my opinion, but their proofs are rather innaccesible. (E.g the complexity of Bradley's, or the Wittgestein-like brevity of Nagarjuna's).

It seems to me that your proof (Dick) might represent one way of doing it. I do not agree with some of your assumptions but that doesn't matter at all. If your proof holds, given the assumptions, then it is a successful proof. Perhaps by showing your proof is a reductio proof of the falsity of your assuptions I can prove that the universe is not consistent with your assumptions but with Buddhist doctrine.

Now, it might sound as if I want to pick holes in your proof, but this is not the case. There's a lot I don't understand about it, but it wouldn't surprise me greatly if it is a proof. If it were, this would be consistent with my view, that what you've proved is true given the assumptions.

So I would really like to understand more about this. I now see why you (Paul) connected this proof with your own ideas. Would you two be prepared to discuss a couple of those essays in detail? I can ask all my questions as they come up and hopefully gain a reasonable understanding of what this is all about. Unfortunately, I will not be able to understand the mathematics, but I'm hoping this won't matter. Can I start a thread? Perhaps I could post one the essays and ask questions arising from them. Or shall we just discuss it here? Or would this be boring for you since you've been talking about it for quite a while?

Canute

 

[Paul Martin]

Hi Canute,

Sorry about this, but I feel our disagreement is more fundamental, not a matter of language at all. But the limitations of language certainly don't help.

Well Canute, to the contrary, I think this is about the only thing you wrote in your post with which I disagree. Not that I disagree that you feel that way, but that I disagree that we have a fundamental disagreement. I think the problem is only semantics.

Do you conclude that the view of the mystics is conjectural? Or do you conclude that they know the facts but cannot communicate them because of language (etc) problems?

I think they know some facts but they cannot communicate them because of language problems. I think that when they attempt to articulate what they know in language, they resort to some conjecture in order to make sense of what they know. That conjecture introduces some ambiguity, confusion, and error, and the language compounds the problem.

For a specific case take GSB. Do you think he is guessing or just trying to explain something he knows?

I can only guess at the answer since I am not very familiar with GSB or his work. But my guess is that he does know something (Even I know something; I know that thought happens). The fact that GSB uses the language of mathematics rather than vernacular English to try to explain what he knows (or guesses, as the case may be), is to his credit. I think his conclusions should be credible if he has done his maths right, which I suspect he has.

Speaking of GSB, you didn't comment on whether my assessment of his work is close to being right or not. I said, "I suspect that he might have discovered how all of reality might have evolved (at least the very initial stages) from a knowledge base of only a single bit and only the most rudimentary ability to know, or realize, that that bit existed." Am I far off?

No problem; that's the way I took it. But I should have made myself more clear. I meant to imply that there are actually three ways to see "conscious beings": 1) the conventional way as individual human beings, 2) PC, or the ultimate and only conscious being, which if isolated from all thought-structures would not be conscious of anything at all (meaning that there is no such thing as a "conscious being", (This is when PC is in the state of traversing no world line, and consequently time does not move at all.) and 3) Natural Individuals in the sense of Gregg Rosenberg ...

I never did get the hang of GR's natural individuals. His ideas were too complex for me. Can we leave them out and include everything under 1 and 2?

(Thanks, Dick. I learn a lot from you.)

Yes, we can leave them out. The hierarchy of conscious beings in other worlds is pure speculation on my part. It makes sense to me for several reasons, and I was delighted to learn that GR's notion of Natural Individuals described my imagined hierarchy and its occupants almost exactly. The only difference is that he imbues NIs with consciousness, whereas I claim that all consciousness resides only at the very top NI, viz. PC. So, yes, in reality, 2) is the only case that obtains, but 1) is useful to consider when conducting human affairs (along the lines taught by Nagarjuna, if I understood the lesson correctly). 3) would be useful only if my speculation is correct and if we were trying to explain what might be going on in those other worlds. Those are both huge "ifs" and are good reasons to honor your request to "leave them out".

This states that PC is subject to change and thus time. Do you really mean this? If so I disagree with you.

I'd say 'subject' is too strong of a word. Instead I'd say that PC is capable of change. Not that PC is capable of changing it's fundamental nature, but only in the sense that PC can change its thoughts. PC has free will to attend to particular thoughts or not to attend to any thoughts. If PC is not attending to any thoughts, then there is no change and thus there is no time. This is the state of Nirvana. I think enlightened meditators can achieve this state by eliminating all thoughts from their "mind". I put "mind" in quotes to emphasize the fact that we are not talking about a human mind, but the mind, which is synonymous with PC itself. That is the only mind used by humans anyway.

But,...it is also possible that PC does entertain thoughts and attend to them. (These are the two truths as taught by Nagarguna in the Madhyamaka School.) This thought is the mechanism which produces change, time, physical reality, and everything else that exists. It is only a matter of semantics whether or not you consider these things real. The Madhyamaka School views them as real in order that we can reasonably conduct human affairs. The Yogachara School views them as unreal, because they really are unreal in the physical sense people usually think of reality. I think we all agree (you, me, science, and Buddhism) except for semantics.

Logically, it seems to me, whatever it is it still is and always will be, beginnless and without end.

Yes, I agree. But it must also seem to you that some things change, for example things in our physical world. Those constitute the "two truths".

The idea of 'stretches of time' prior to the BB seems unscientific and logically dubious.

I can't speak for science, but it seems to me that cosmologists are getting awfully close to accepting some notion of time outside of the temporal dimension in our BB generated world. Hawking, for example, talks about "imaginary time".

As for being logically dubious, it depends on how 'time' is defined. In my definition, where time is a parameter marking the progress of PC's attention along some world line, there is no logical reason why all world lines must exist in our BB generated 4D world. Thus there could be world lines traversed by PC in hyperdimensional space defining long stretches of time prior to the BB.

My notion is also consistent with SR in that time is relative to the motion of the clock, or the observer (which in all cases is ultimately PC). If the motion of photons can construct world lines which PC can traverse and attend to (the exact scenario Einstein wondered about when he pondered what it would be like to travel at the speed of light), and if PC does (or did) attend to a particular photon produced by the original CMB radiation, by my definition, no time would have passed for PC from the BB until that photon entered our COBE instrumentation. That is consistent with SR, and it also fairly well describes the Buddhist notion of Nirvana. The whole notion may seem logically dubious at first blush, but I think it makes perfect sense and ties many disparate ideas together.

The idea that what is fundamental has a beginning seems highly paradoxical to me.

It does to me too. But that conundrum appears, as I have said many times, in each and every and all attempts, by philosophers, scientists, theologians, mystics, quacks, and anyone else, to describe the ultimate beginning of reality.

Well, I'd say time does not flow at all unless someone is paying attention.

I agree completely. In my view, there is only one candidate for the "someone" who is paying attention, and that is PC. So my definition of time -- a parameter marking the progress of PC paying attention to a world line -- seems exactly equivalent to what you said here.

Yeah, this is my problem of PC evolving in time. What time? The thought structures are 'mere appearances' for Buddhists, no more real than pianos and ceiphids. Btw, the Sufis say that the sign of a realized person is that for them there is no time other than the time they are in.

Maybe the problem can be fixed by noting that it is not PC that is evolving, but instead only the thoughts of PC evolve. The rest, I think we have already covered.

Can you give your views on the relationship between knowledge, proof and explanation? This might clear up some possible misunderstandings. (By 'explanation' I would mean also a description or a theory).

I'll try. Bear in mind all of the following is prefaced by a big IMHO.

You didn't include 'information' in your list, but I'll add it because I think it plays a role in what we are trying to express. I think Shannon's definition of 'information' is good, but incomplete. He essentially says that information is a difference that makes a difference. He left out the thing or entity or person to whom the difference makes that difference. In my view, there are two types of candidates: information can make a difference to some conscious entity, or it can make a difference to some non-conscious entity. These two match exactly with Gregg Rosenberg's two principles inherent in a Natural Individual.

The receptive principle allows the NI to receive information, and thus to "know". Using this principle, a conscious entity can notice the difference embodied by a bit of information, and thereby come to know that there is that difference. (Of course in my view there is only one such conscious entity, and that is PC).

The effective principle allows information to induce changes which make a difference to non-conscious entities. For example, when two particles interact, the information content of each, such as position, spin, charge, etc., induce changes, and thus make a difference, to the system of particles involved in the interaction. You could say that the other particles "know" about the influential particle, and maybe particles are indeed conscious entities. But I don't think so. I think they are non-conscious entities which are influenced by information that they receive via the effective principle.

As I said somewhere before, I see these two principles as the two sides of the coined word 'realize'. The effective principle (unconsciously) "realizes" physical changes as a result of information flow, and the receptive principle (consciously) "realizes" knowledge in the sense of "knowing" (the acquisition process being "learning") information.

Information can make a difference unconsciously to physical things, and it can make a difference to a conscious entity by adding to its accumulating store of knowledge.

So, to deal with the first of the concepts you asked about, knowledge is information acquired by a conscious entity.

Moving on to "explanation", this is the attempt to express knowledge in language. Langauge is a system of coding which allows for the transfer of knowledge from one conscious entity to another (or to the same one) with a non-conscious medium facilitating the transfer. That transfer may take a long time if the medium is something like a book, or it may not take long if it is patterns in vibrating air.

In order to be effective, i.e. not introduce errors into the transfer, not only must the transmission be error free, but the rules of the language must be unambiguous to the sender and the receiver. Wittgenstein has demonstrated that this last cannot be achieved. So all explanations are thus left with this problem of ambiguity. They are also subject to the limitations and constraints discovered by Dick and expressed in his theorem.

Moving on to "proof", we have at least two types. One is the type used in courtrooms and in ordinary use of language. The ambiguities inherent in language make all such proofs controversial.

The other type is that used in mathematics. The rules of the language of mathematics have been specifically chosen to minimize the ambiguities and errors that are inherent in all languages. In mathematics, (if the rules are followed) all such errors and ambiguities inhere in the undefined primitives and in the chosen axioms. If one assumes that the primitives and the axioms are consistent and make some kind of sense, then one can be assured that the theorems also are consistent and make some kind of sense. But that is all that can be said. Moreover, the assumption can not in principle be verified. In the mathematical context, a proof is simply a demonstration that all the rules have been followed in the derivation of a theorem.

Interesting. Is this the music of the spheres?

I think it is part of the music of the spheres. I think it is the lowest frequency tone. I think the light that Les Sleeth and others talk about is the highese frequency tone. All the rest of reality is composed of tones in between.

In my view knowledge cannot transfered. As Zen master Hongzhi puts it, we cannot borrow knowledge.

I agree. I explained above why I think so.

I cannot follow your omnsiscience idea through, partly because I'm still confused about 'natural individuals'.

I hope that what I have written here helps a little.

I would point out though that in one view PC is knowledge.

Yes, I am aware of that view. However to me there is a distinction between the knower and the known. In fact, it occurs to me that this very distinction may be one of the first ones acquired by PC thus kicking off the evolution according to GSB's formulas.

As usual I half agree, but I'm sticking with Lao Tsu. I don't think PC constructs universes but rather that they are reified according to GSB's laws, as an inexorable consequence of what PC is. Although this is a sense a mystical view it also seems more scientifically plausible to me.

I can't find the half where we disagree. I agree completely with what you said. I don't think PC constructs universes in the usual materialistic sense, but rather, as you said, reifies the chosen concepts in order to construct purely imaginary universes in the sense of Berkeley and of the Buddhists. And, I agree that this reification is done according to GSB's laws as an inexorable consequence of what PC is. I think we agree completely here.

Although this is a sense a mystical view it also seems more scientifically plausible to me.

Me too. Now, if we could only get some scientists to open their minds enough to consider these ideas as real possibilities, they might be able to make some more progress toward an understanding of consciousness, human behavior, the initial BB conditions, the remaining mysteries of biology, etc.

Warm regards,

Paul

 

[Paul Martin]

Hi Canute,

Thanks for visiting my website and reading those essays. You have my permission to quote anything there in part or in whole as long as you provide a reference link to where you got them.

I am willing to discuss anything you would like, although I can't defend (or even describe) Dick's results very well. I'm sure he will help us, though.

Paul

 

[moving finger]

OK. But I believe any particular explanation entails assumptions.

You are making the same mistake as Canute. Your comment implies the word "assumption" be defined before one can define an explanation. As I said to Canute, that path leads nowhere except to infinite regression.

And you, with respect, are making the mistake of assuming that explanation can be defined without tautology or infinite regress.

I have not said that one cannot define an explanation in absence of assumptions. The definition of an explanation does not necessarily entail assumptions – it only entails a definition (but try to define a term without using other terms – one ends up either in infinite regress or tautology).

An explanation in absence of any assumption is meaningless. In your paper, you (effectively) define an explanation as a mapping of one set of information (assumptions) to another. Clearly the mapping can exist in absence of the information; but in absence of all information the mapping has no meaning. In other words, the mapping (the explanation) needs to be grounded in information (assumptions) to give it any meaning.

Your statement that we can assume nothing if we really intend to investigate anything honestly would require, in the case of empirical investigation, access to “certain truth” about the world, which I do not think is possible.

I think you are confusing two very different issues. The concept "certain truth" implies you understand something whereas, the concept of explaining what you know need not include understanding of any kind.

I am simply saying that any investigation entails assumptions in the form of information. I have said nothing about understanding. You seem to claim that investigation is possible without any assumptions (information).

That is to say, you are presupposing an understanding of what that is about the world you do have access to.

I am presupposing nothing of the kind. I am saying that to investigate anything we must start with information. Nothing in this entails understanding.

I, on the other hand, am simply stating that whatever it is that you have access to, in the initial state, you certainly don't understand any of it; a totally different statement.

You, on the other hand, seem to be saying that one does not need anything at all in the “initial state”.

Would you go so far as to propose we have access to nothing about the world? That's pure Solipsism.

You seem to have the wrong end of the stick. I am saying just the opposite – what we have access to is information.

I tend to agree with your point that an explanation may be a very fundamental concept – after the concept of information.

Again, you head down that path of infinite regression. Exactly how do you propose to explain to me your concept of information without understanding "an explanation"?

Is infinite regress worse than tautology? Your own definition of an “explanation" is “a method of obtaining expectations from given known information”, and your definition of “information” is “what it is that we want our explanation to explain”. Not very enlightening, is it?

If we define an explanation as a mapping between two or more sets of information then it is the information which is fundamental.

No because now you must define "a mapping", various sets of information and, explain these things. They cannot be more basic than the concept of an explanation.

And your definition of explanation is “a method of obtaining expectations from given known information” – can you define “method”, “expectations”, “given”, “known” and “information” without either tautology or infinite regress?

“Nothing is all that is required”? I believe in an underlying (ontic) reality, I cannot bring myself to believe that the phenomenal world of our experience is based on absolutely nothing.

You just said above that "access to 'certain truth' is not possible. If that is the case, then what is your belief in the phenomenal world based on? I think that your thinking is embedded in that issue of infinite regression; essentially in the idea that some construct representing reality which was created by your subconscious is the starting point for your analysis. I want you to step back and consider the problem of generating that construct.

One can believe that there is an underlying reality, and at the same time deny that it is possible to know with certainty what that reality is. This does not involve any contradiction.

I fail to see how you can generate the phenomenal world from “nothing” – if this is indeed what you are saying?

This defines a set of points in 3D space, and an explanation is then interpreted as a mapping of one finite subset of such points to another finite subset. Correct? This seems quite reasonable and straightforward.

I define "An explanation" to be a method of obtaining expectations from given known information.

Ooops, there it is again. I thought the concept of explanation was fundamental, and did not require any prior concept of information?

The "given known information" is represented by a set of points in that [x,tau,t ] space. …… Is it not the result of discovering a method of predicting consistent expectations based on given known information (the nerve activity previously detected)?

“given known information”? I thought explanation preceded everything? Why then must information be “given”?

"[Friedrich Ludwig Gottlob] Frege is... He published no more after that."

This shows simply that we cannot answer all possible questions about the naïve idea of the set of all sets (ie some questions are unanswerable). Naïve set theory was superceded by various axiomatic set theories (of which Zermelo-Fraenkel (ZF) set theory is the most well known) which avoid Russell’s paradox. Godel later showed that no system of set theory can be shown to be both consistent and complete, but even this does not entail paradox. It entails only that the set of all logical possibilities cannot be shown to be complete if we also wish it to be consistent. What does this mean? It means simply that the set of all logical possibilities cannot be a complete set.

From that I think we should learn that not only is nothing in reality infinite, but that any notion that includes infinity should be excluded from mathematics because it will drag inconsistencies with it.

One cannot legislate against the question that Russell asked. One cannot simply say “we will prohibit consideration of infinite sets” and then blindly hope the paradox goes away. The problem highlighted by Russell remains – there are some questions which cannot be answered. Even if legislation is introduced to exclude infinity from mathematics, one can still ask the question “is the class of all classes that are not members of themselves a member of itself?”, and the question is still unanswerable.

Why does this lead to the notion that nothing is infinite?

I think we cannot reasonably claim that anything is infinite unless and until we clearly define the term 'infinite'. …… If there are other definitions for 'infinity' which do not introduce contradictions, I am unaware of any of them.

I have my own thoughts about the paradoxes introduced by the concept of infinity in conventional number theory – it has to do not with the concept of infinity itself, but with the rather strange notion that mathematicians seem to have of an integer. For some strange reason, in conventional number theory we choose to define an integer as an arbitrarily large number, with every integer representable by a finite string of digits. But it is impossible to uniquely identify every member of an infinite set with finite strings, which implies that an infinite set of integers must contain members of infinite length, which in turn contradicts the definition of an integer.

Are you saying that the laws of physics (as opposed to the laws of mathematics) are logically necessary, entailed by the condition of consistency?

Yes. I am convinced that Dr. Dick has proved this to be the case.

I haven’t seen it myself.

IMHO, his work should be classified as a theorem of mathematics. I see it as a greatly generalized Noether's Theorem. She proved that symmetry implies conservation laws; Dr. Dick proved that consistency implies all the laws of physics.

Where has he done this?

Thus the PC does not create the laws of mathematics or the laws of physics; whatever the PC does, it does under the constraint of these laws? Is this what you are saying?

Not exactly. PC chooses this constraint by choosing to remain consistent. The constraint itself has two components: 1) there is the self-imposed constraint of the willful decision and resolve to abide by the rules of consistency, and 2) there are the constraints which are implicit in the logical consequences of sticking to the chosen rules. It is this second component which has been analyzed by Dr. Dick.

OK, so the PC makes a choice, and thereafter the PC is constrained by the laws of mathematics and physics, yes? Apart from “making the choice to be consistent”, the PC does not actually create these laws, the laws follow on as a necessary consequence of the PC’s consistency decision?

This is logically equivalent to you choosing to play chess. You willfully decide to play chess and to abide by the rules. If you do, then one consequential constraint is that your rook cannot move diagonally. If PC chooses to violate the constraint of remaining consistent, then inconsistencies will result. Since (we suppose) our physical universe is consistent, we can conclude that PC chose not to violate the constraint with respect to our physical universe.

This indeed seems to confirm that the PC does not actually create the laws, the laws follow on as a necessary consequence of the PC’s consistency decision. Correct?

How does the PC choose this at the outset, when it has nothing (no logic) to work with?

Good question. Maybe George Spencer-Brown or Chris Langan has worked out the details of how this evolved. My guess is that it developed slowly. The notions of logical consequence and consistency would have to be worked out way ahead of any such choice. It might have started by PC imagining and constructing many "bit sets", noticing patterns, making definitions, testing algorithms, etc.

OK, so the first thing the PC did was in fact NOT that it chose to be consistent. It first had to experiment with many different possibilities, until it gained enough information about the world to then make a rational decision to be consistent?

When I ponder how this might have happened, it seems like the possibility of inventing music might have happened early in the process……. Of course you know this is all speculation. But then, I think that in your question, you asked me to speculate.

It seems that your PC is becoming less and less primordial as we go along. We are already now speculating about some kind of background environment in which the PC learns (about logic, consistency etc), and we also seem to think that the laws of logics, mathematics and physics are constrained to be necessary by virtue of consistency, quite independent of the experimentation by the PC.

Being the first to discover something does not mean that one has invented that something. Or are you defining “invention” as “to discover something for the first time”?

I think it is a little more complicated than that. If the invention is the adoption of some arbitrary set of rules, then there may be some implications of following those rules. Those implications may not be known at the time the rules are adopted but may be discovered later as the implications of following the rules play out. So whether you call the first instance of such an implication a discovery, or part of the invention, I think is merely semantics. The rules are invented; the consequences are discovered by deciding to follow the rules.

We’ll have to agree to disagree. To me, all invention is simply a particular form of discovery.

which implies that these things exist prior to the PC’s choice of whether to be consistent or not.

No. That is not implied. As you said, "everything else follows" which does not imply pre-existence.

If the PC supervenes on, and does not create, the laws of logic and of mathematics, then it follows that these laws EITHER exist prior to the PC coming along, OR that they spontaneously come into existence at the moment of creation of the PC. Which?

No, I don't see a contradiction. PC is constrained only by the consequences of the rules it has chosen after making them up out of whole cloth.

But you have just said that the PC supervenes on the laws of logic and mathematics. Now it seems you are saying the reverse.

Dick showed that if consistency is chosen, laws of physics constrain the evolution of physical objects and relationships.

Sorry, where has he shown this?

What comes first – the constraint imposed by the rule, or the making up of the rule?

Good question, but I'd say the making up of the rule comes "first".

But this implies that the rules (of logic and mathematics) supervene on the PC, not the other way about (which is the reverse of what you agreed above).

This gets into the messy arena of time. The notion of "first" makes sense only in the context of one specific temporal dimension.

OK, I shall try to avoid reference to time by using supervenience instead. Do the rules supervene on the PC, or does the PC supervene on the rules? (you seem to have claimed both so far).

And having chosen to be consistent, the PC is now constrained to working within the set of consistent rules.

Yes. You have stated a tautology here which must obviously be true.

Not if the PC creates the rules. If the PC creates the rules of consistency then it is not constrained to anything in particular. You clearly do not believe the PC creates the rules, therefore the statement is (to you) tautological.

IMHO PC "creates" by thinking that it creates, as you seem to imply.

That is interesting. Perhaps the PC only thinks that it is inventing as well?

but in fact whether a rule that the PC thinks it has created is consistent or not is already determined before the PC thinks about it.

No more than the rules for how a free throw is to be conducted was already determined before the game of basketball was invented or thought about.

The analogy rests on the fact that the rules of basketball are logically contingent and not necessary - someone invented or “made up” the rules of basketball.
Are you now saying the rules of logic and mathematics are contingent and not necessary, and that the PC invented or “made up” the rules?

Given the constraint of operating in 2 dimensional Euclidean space (where by Euclidean space I mean the space complies with the 5 axioms of Euclid’s geometry, including the parallel postulate), do you think the PC could create a right-angled triangle where the cube of the hypotenuse is equal to the sum of the cubes of the other two sides?

No. But PC is not necessarily given that Euclidean constraint when it comes to constructing universes.

Understood (the Euclidean constraint is not a law, it is an assumption or axiom – as I keep pointing out to Dick, we cannot make any progress without assumptions), but the fact remains (if I now understand you correctly) that the laws of mathematics are not under the PC’s control. This is where the analogy with basketball falls down. The PC is free to create/invent/make up any law of basketball as it feels like, but the PC is not free to create/invent/make up the laws of mathematics “as it feels like”.

Good talking with you, MF. Sorry for the delay; we had a death in the family.

Very sorry to hear that – my condolences and best wishes

That is to say, an explanation of consciousness, awareness, intelligence, thought or any complex phenomena, if it is to be valid, must be expressible in terms of fundamental entities obeying what we have come to call the "laws of physics".

Sorry, but that doesn’t seem much of an insight to me – that any valid explanation must be expressible in terms of entities “obeying” what we have come to call the “laws of physics”? I could have told you that (though I would stop short of using the word “obey”).

Best Regards

 

[Canute]

Well Canute, to the contrary, I think this is about the only thing you wrote in your post with which I disagree. Not that I disagree that you feel that way, but that I disagree that we have a fundamental disagreement.

What confuses me is that you agree with me far more often than I agree with you. Never mind, it'll all come out in the wash.

The fact that GSB uses the language of mathematics rather than vernacular English to try to explain what he knows (or guesses, as the case may be), is to his credit. I think his conclusions should be credible if he has done his maths right, which I suspect he has.

Actually he says most of what's important in prose. For example:

From 'Laws of Form' -G. S. Brown

"The position is simply this. In ordinary algebra, complex values are accepted as a matter of course, and the more advanced techniques would be impossible without them. In Boolean algebra (and thus, for example, in all our reasoning processes) we disallow them. Whitehead and Russell introduced a special rule, which they called the Theory of Types, expressly to do so. Mistakenly, as it now turns out. So, in this field, the more advanced techniques, although not impossible, simply don’t yet exist. At the present moment we are constrained, in our reasoning processes, to do it the way it was done in Aristotle’s day."

[However, says Brown, we need not be so constrained.]

"What we do … is extend the concept to Boolean algebras, which means that a valid argument may contain not just three classes of statement, but four: true, false, meaningless and imaginary. The implications of this, in the fields of logic, philosophy, mathematics, and even physics, are profound."

That pretty much says it all for me.

Speaking of GSB, you didn't comment on whether my assessment of his work is close to being right or not. I said, "I suspect that he might have discovered how all of reality might have evolved (at least the very initial stages) from a knowledge base of only a single bit and only the most rudimentary ability to know, or realize, that that bit existed." Am I far off?

In my opinion (!) this is not quite right, but not far off. It's the 'rudimentary ability to know' that bothers me. Also, the term 'existed' here would be incorrect. The existence/non-existence distinction is ultimately a category error in Brown's view (and Nagarjuna's).

But,...it is also possible that PC does entertain thoughts and attend to them. (These are the two truths as taught by Nagarguna in the Madhyamaka School.)

Do you mean by this that PC thinks and not-thinks, depending on how you look at it?

The Madhyamaka School views them as real in order that we can reasonably conduct human affairs. The Yogachara School views them as unreal, because they really are unreal in the physical sense people usually think of reality.

Are you sure? The Middle Way doctrine states that mental and corporeal phenomena are 'empty', in the sense that they have no essence or inherent existence. As far as I know this goes for all schools, but I have not looked into them all so may be wrong. My feeling is that to think otherwise would contradict the sutras, which none of the schools knowingly do.

I can't speak for science, but it seems to me that cosmologists are getting awfully close to accepting some notion of time outside of the temporal dimension in our BB generated world. Hawking, for example, talks about "imaginary time".

Yes, but then Edward Lear talks about jaberwockies.

I just can't get the hang of the idea of time outside spacetime or stretches of time 'prior' to the beginning of spacetime.

It does to me too. But that conundrum appears, as I have said many times, in each and every and all attempts, by philosophers, scientists, theologians, mystics, quacks, and anyone else, to describe the ultimate beginning of reality.

What conundrum? The idea that what is fundamental is beginnless? I should have thought this very reasonable. Bear in mind that for Brown and Nagarjuna it is incorrect to say that what is fundamental exists. For the latter emptiness itself is empty. This puts a different complexion on the 'beginning' question.

I agree completely. In my view, there is only one candidate for the "someone" who is paying attention, and that is PC. So my definition of time -- a parameter marking the progress of PC paying attention to a world line -- seems exactly equivalent to what you said here.
Maybe the problem can be fixed by noting that it is not PC that is evolving, but instead only the thoughts of PC evolve.

I'm ok with that. (However, I'm going along with your idea of PC here. In reality I suspect it's not quite the right idea or, rather, a slightly misleading term). Also, sticking to your metaphors, I can't see how a world-line can exist unless someone is paying attention to it.

I think it is part of the music of the spheres. I think it is the lowest frequency tone. I think the light that Les Sleeth and others talk about is the highese frequency tone. All the rest of reality is composed of tones in between.

Hmm. Sounds like the emanations of Krishna. I have no thoughts on this one.

However to me there is a distinction between the knower and the known. In fact, it occurs to me that this very distinction may be one of the first ones acquired by PC thus kicking off the evolution according to GSB's formulas.

Yes, here I do agree, and I suspect Brown might also. Equivalently, this distinction may be between self and other, or subject and object. True knowledge, however, would be the identity of these dualities. This takes us on to knowledge, proof etc. I struggled a bit with your outline of these things, so I'll give my view and see what you think.

Information - as per your view (Shannon et al. - differences that make a difference). However in order for information to exist an information space must exist. The space cannot exist prior to the information nor vice versa. Thus there is something inherently paradoxical about the notion that information is all that exists. (Imo this is Chalmers' problem with his double-aspect theory of information/consciousness - do you know this? It is very relevant to your ideas). This seems also to be a problem for Dick, unless I have misunrstood something, since only information can be represented by numbers, not the space within which it arises, which is Brown's nondual void.

Proof - For me there are four kinds of proof. Inference by induction or deduction, and abduction (in C. S. Peirce's and Sherlock Holmes's sense - as infererence to the best explanation, ideally the only one not falsified). The fourth would be proof by direct experience, which might be called verification or ostensive proof. This latter is Aristotle's knowledge by identity.

Knowledge - Two kinds, relative and absolute. Relative knowledge (provisional, contingent) would be that 2 + 2 =4, or that the Earth orbits the sun. Absolute knowledge would be knowledge by identity, e.g. the unfalsifiability of solipsism, the 'I am' of the Sufis, the void spoken of by Brown).

Explanation (theory, description etc) - a formal system of terms and symbols in which relative truths and falsities are demonstrated to be derivable from axioms. The axioms may be postulates or they may be known facts. ('Known facts' would have to be absolute knowledge). Explanations would normally be subject to the limits of the incompletenss theorem. No explanation could communicate certain knowledge, although they may point towards it, or explain where it can be found.

What do you think?

I can't find the half where we disagree. I agree completely with what you said. I don't think PC constructs universes in the usual materialistic sense, but rather, as you said, reifies the chosen concepts in order to construct purely imaginary universes in the sense of Berkeley and of the Buddhists. And, I agree that this reification is done according to GSB's laws as an inexorable consequence of what PC is.

Perhaps it's a matter of language. The way you speak of PC sometimes suggests Creationism to me, that PC creates universes by intention and lays down the laws by which they will evolve. But if spacetime universes follow directly from what is, then no intention or will can be involved.

I've thought about our agreement/disagreement. The notion of nonduality or advaita seems to be missing from your view, yet it is central for Brown, Lao Tsu, Bradley, Buddha etc. (and could be said to be one meaning of 'Middle Way'). Perhaps this is the source of the problem. Could this be it?

For example, I think you said that your position is dualism.(?) Yet (metaphysical) dualism is false in mysticism, so is monism and pluralism. If your view is any of these three then we have a fundamental disgreement. (Hooray -there's nothing to talk about if we don't disagree)

I see I still write too much. Sorry.

Regards
Canute

 

[Canute]

Dick

It occurs to me that what I wrote earlier about your work may have sounded rather dismissive of it. This is not at all how I meant it to sound. I'm genuinely interested and want to understand it properly. As I say, I'd like to start a thread to discuss it in detail but don't want to do that until I know you want to discuss it. I hope what I said earlier won't put you off.

Canute

 

[moving finger]

The fact is (and I can show it explicitly) that most all of the so called "laws of physics" are no more than solutions to that equation.

Are you saying here that our so-called “laws of physics” are the ONLY solutions to that equation?
In other words, can we, with no additional assumptions, derive our so-called “laws of physics” from that equation?
If yes, can you give examples of physical laws which can be so derived?

Have you come across Gurdjieff on free-will? His view was that if we are aware of who we are then we have free-will. If we are not then we are slaves to deterministic (psychophysical) forces.

My interpretation would be : If we “own” our beliefs, if we accept “ownership” of the causal sources of our choices and actions (no matter whether those causal sources are themselves caused) then in effect we act with free will. (This is not the same kind of free will that libertarians claim to believe in – but then the libertarian kind of free will is incoherent).

Languages are part of that structure and any information encoded in languages is necessarily wrong or incomplete, so I would agree that what we call knowledge is really nothing but confusion at some level.

The same applies to the language of mathematics (either incomplete or inconsistent)

It's worse than that, I think. If the mystics are right then the truth about consciousness is actually paradoxical in ordinary language.

What paradox?

Does freewill exist? From the above you see that there are two points of view, the conventional and the ultimate. As a result the question does not have a yes or no answer. In the literature it is never given one.

There is plenty of literature supporting both yes and no. The real problem is that first one must define precisely what one means by “free will”.

Natural language cannot cope with things like PC or wave-particles.

The problem with “wave-particles” is that most of us want to call a quantum object either a particle (it has definite position) or a wave (it has definite momentum) – the fact is that it is neither particle nor wave. We need to start thinking “outside the box” of waves and particles.

The view of omniscience as knowing all that can be known is, IMHO, nonsense for the same reasons I tried to argue with MF that any consideration of "all" of any set of possibilities is nonsense.

It is only nonsense if one rejects the idea of an infinite or unbounded set. Is the “set of all integers” nonsense?

The fact is that any “unbounded set of all things” (following Godel) is either an inconsistent set or is an incomplete set – why would this make it “nonsense”? All we need to remember is that whenever we talk of an “unbounded set of all things” (such as the knowledge of an omniscient being) we are talking of an incomplete set – a set which, no matter how big it is, can always be added to (like the set of integers).

In my view, there is undoubtedly information stored in brain structures, in DNA structures, in libraries, and on hard drives. Should this be considered "known information"? Well, yes, it makes a certain amount of sense to do so. But it complicates the question of what we mean by 'omniscience'.

Information does not entail knowledge (at least not by the conventional definition of knowledge – perhaps you have a different definition?)

Sorry if I put anyone off by going into it.

Paul – sorry, but your ideas sound more and more like religion or mysticism than philosophy……

These are the same limitations that prevent you and me, or MF and me, or Dr. Dick and me, from eliminating the "almost" that persistently modifies our "agreement". I think we might be as close to agreement as we can get without "going mathematical".

Unfortunately, it seems to me that you, Canute & Dr Dick are closer to agreeing with each other than I am to agreeing with any of you. My personal philosophy is directed at explaining the world with the minimum of assumptions, and to me the assumption of the PC (or any other fundamental conscious entity) doesn’t seem to explain anything useful, but instead wraps up within itself so much that is not explained.

This may be the ideal starting point from which to disentangle our differences. Russell questioned whether human beings could know anything at all. It is impossible to demonstrate that they can. So how do we know anything? And how do we know we know we know it? Cetainly not by deriving theorems from uncertain axioms. But how can we know our axioms are true? According to Russell we can't. But Russell was a devout non-mystic, and thus could have no theory of knowledge. He assumed that knowledge was the same thing as explanation or proof by demonstration, and this assumption seems to underly some of what you are suggesting, and maybe also Dick. Can you give your views on the relationship between knowledge, proof and explanation? This might clear up some possible misunderstandings. (By 'explanation' I would mean also a description or a theory).

I think you need to be clear about your definition of “knowledge” – can you clarify what you mean when you talk of “knowledge”? (I suspect when you talk of knowledge you are thinking of “certain knowledge” – which imho would be a mistake).

As an experiment try picking one piece of knowledge that you know with absolute certainty and then figure out how you know it. It will not be anything to do with explanations, theories, formal proofs, libraries, hard drives and so on.

Do we know anything with absolute certainty?

But that conundrum appears, as I have said many times, in each and every and all attempts, by philosophers, scientists, theologians, mystics, quacks, and anyone else, to describe the ultimate beginning of reality.

Which is why the notion of “no beginning” is appealing.
If there is a beginning to time, then we need an explanation for that beginning.
If there is no beginning to time, then no explanation for any beginning is needed.

From 'Laws of Form' -G. S. Brown
What we do … is extend the concept to Boolean algebras, which means that a valid argument may contain not just three classes of statement, but four: true, false, meaningless and imaginary.

Could you give an example of an imaginary statement which is neither true, false, nor meaningless?

Proof - For me there are four kinds of proof. Inference by induction or deduction, and abduction (in C. S. Peirce's and Sherlock Holmes's sense - as infererence to the best explanation, ideally the only one not falsified). The fourth would be proof by direct experience, which might be called verification or ostensive proof. This latter is Aristotle's knowledge by identity.

Proof by deduction tells us nothing new about the world (ie nothing that is not already logically contained within the assumptions). All proofs by deduction are either analytic truths (truths by definition) or are tautologies.
Your “proof by abduction” is essentially a form of proof either by induction or deduction (unless you can come up with an example of proof by “abduction” which is neither induction nor deduction).
Proof by direct experience is effectively a form of proof by induction (with the single possible exception that experience tells us, by definition, that there is “something rather than nothing” – this may be the single “proof by experience” which is deductive rather than inductive).

Thus the only useful method of proof we have boils down to proof by induction – and all inductive truth is probabilistic and not certain.

Knowledge - Two kinds, relative and absolute. Relative knowledge (provisional, contingent) would be that 2 + 2 =4, or that the Earth orbits the sun. Absolute knowledge would be knowledge by identity, e.g. the unfalsifiability of solipsism, the 'I am' of the Sufis, the void spoken of by Brown).

The only “absolute” knowledge (imho) is “something exists”. What this something is, we do not necessarily know. All we know for certain is that something (as opposed to nothing) exists.

Explanation (theory, description etc) - a formal system of terms and symbols in which relative truths and falsities are demonstrated to be derivable from axioms. The axioms may be postulates or they may be known facts. ('Known facts' would have to be absolute knowledge). Explanations would normally be subject to the limits of the incompletenss theorem. No explanation could communicate certain knowledge, although they may point towards it, or explain where it can be found.

I prefer Dr Dick’s interpretation of “explanation” – an explanation is simply a way of describing one set of information in terms of another set of information (or : an explanation is a mapping, or series of mappings, between different sets of information).

Best Regards

 

[Canute]

Moving Finger

What paradox?

Metaphysical paradoxes. I would include the 'hard' problem of consciousness as one of these.

There is plenty of literature supporting both yes and no. The real problem is that first one must define precisely what one means by “free will”.

Yes, I agree. My point was just that the arguments supporting yes or no both fail. (Which is why the debate is ongoing). The suggestion is that truth about it is subtle, in such a way that the yes and no arguments are both flawed. This would explain why the debate is ongoing.

The problem with “wave-particles” is that most of us want to call a quantum object either a particle (it has definite position) or a wave (it has definite momentum) – the fact is that it is neither particle nor wave. We need to start thinking “outside the box” of waves and particles.

I couldn't agree more. Now try applying the same principle to metaphysical questions, such as the whether we have freewill, whether the universe begins with something or nothing etc. This is what Brown means by using imaginary values in our reasoning.

Paul – sorry, but your ideas sound more and more like religion or mysticism than philosophy……

I feel it would be best to call it an esoteric philosophy. But I don't know if Paul would agree.

Unfortunately, it seems to me that you, Canute & Dr Dick are closer to agreeing with each other than I am to agreeing with any of you. My personal philosophy is directed at explaining the world with the minimum of assumptions, and to me the assumption of the PC (or any other fundamental conscious entity) doesn’t seem to explain anything useful, but instead wraps up within itself so much that is not explained.

But if a single assumption explains everything else, and does not produce a reductio argument against the assumption, then would this not be a reasonable strategy to make the assumption? Still, I half agree with you, since the result can only be a theory.

I think you need to be clear about your definition of “knowledge” – can you clarify what you mean when you talk of “knowledge”? (I suspect when you talk of knowledge you are thinking of “certain knowledge” – which imho would be a mistake).

Yes, I distinguish between certain knowledge and provisional or relative knowledge. Why would it be a mistake to talk about certain knowledge?

Do we know anything with absolute certainty?

Only you can answer that. I'm certain of one or two things. The unfalsifiabilty if solipsism is the nearest I can get to knowledge that is certain and communicable. The knowledge that I'm hungry is certain, but I can't demonstrate it.

Which is why the notion of “no beginning” is appealing.
If there is a beginning to time, then we need an explanation for that beginning. If there is no beginning to time, then no explanation for any beginning is needed.

This seems true to me also. However, the idea of an eternal substance is paradoxical, so this view still leaves a question begging.

Could you give an example of an imaginary statement which is neither true, false, nor meaningless?

Well, not an imaginary statement, but I know what you mean. The statement 'the universe arises from nothing' is true or false in metaphysics. The statement 'the universe arises from something' is true or false likewise. However, in the esoteric or 'advaita' view both these statements are neither quite true nor false. The truth would be that the universe arises in a sense and in a sense does not, and that it arises from nothing in a sense but in a sense arises from something. Hence this comment by Robin Robertson about Brown's calculus.

"Anyone who thinks deeply about anything eventually comes to wonder about nothingness, and how something (literally some-thing) ever emerges from nothing (no-thing). A mathematician, G. Spencer-Brown (the G is for George) made a remarkable attempt to deal with this question with the publication of Laws of Form in 1969. He showed how the mere act of making a distinction creates space, then developed two "laws" that emerge ineluctably from the creation of space. Further, by following the implications of his system to their logical conclusion Spencer-Brown demonstrated how not only space, but time also emerges out of the undifferentiated world that preceeds distinctions. I propose that Spencer-Brown’s distinctions create the most elementary forms from which anything arises out of the void, most specifically how consciousness emerges."

Proof by deduction tells us nothing new about the world (ie nothing that is not already logically contained within the assumptions). All proofs by deduction are either analytic truths (truths by definition) or are tautologies.

Agreed.

Your “proof by abduction” is essentially a form of proof either by induction or deduction (unless you can come up with an example of proof by “abduction” which is neither induction nor deduction).

Abduction is generally considered to be a third form of inference. C. S. Peirce takes this view, as do most dictionaries. I agree that it is a form of deduction, but still feel the distinction is useful. A deductive proof would normally be more certain than a abductive one. But at the limit, say in the case where all explantions of a phenomenon except one had been eliminated, they would be effectively the same thing.

Proof by direct experience is effectively a form of proof by induction (with the single possible exception that experience tells us, by definition, that there is “something rather than nothing” – this may be the single “proof by experience” which is deductive rather than inductive).

I don't agree here. If I am experiencing pain then this is direct knowledge, not an inference. It is not possible to be mistaken, even if the pain is in a phantom limb it is being experienced.

Thus the only useful method of proof we have boils down to proof by induction – and all inductive truth is probabilistic and not certain.

This is not the case. You can see this if you consider how it is possible to prove (to yourself) that you are conscious. Still, I wouldn't object to calling this verification instead of proof.

The only “absolute” knowledge (imho) is “something exists”. What this something is, we do not necessarily know. All we know for certain is that something (as opposed to nothing) exists.

Hmm. Believe it or not I don't agree. The stament 'something exists' is not true according to many people. Mind you, the statement 'nothing exists' would also be not true. Here we meet another of Brown's complex values. There are a few proofs around that nothing really exists, although not everyone agrees they are successful.

I prefer Dr Dick’s interpretation of “explanation” – an explanation is simply a way of describing one set of information in terms of another set of information (or : an explanation is a mapping, or series of mappings, between different sets of information).

I'm ok with that, depending on how 'information' is defined. But I think this falls within my definition. The question arises of whether everything that can be known and understood can be explained.

Cheers
Canute

 

[Paul Martin]

Paul – sorry, but your ideas sound more and more like religion or mysticism than philosophy……

The way you speak of PC sometimes suggests Creationism to me, that PC creates universes by intention and lays down the laws by which they will evolve. But if spacetime universes follow directly from what is, then no intention or will can be involved.

Yes, I'm afraid my ideas do sound "religious". And I am sorry about that too. My ideas sound religious because they include intention and consciousness as operative functions in the development of the universe prior to the appearance of brains or even biological organisms. I am sorry that these ideas have the taint of "religion" because of the awful baggage accumulated by religious precepts and notions as they have developed over the millennia.

We need to start thinking “outside the box” of waves and particles.

Agreed. And with respect, I suggest we need to start thinking "outside the box" of science and religion. In my view, religion has done virtually nothing with whatever "truths" it has apprehended to help solve human problems if you net out the harm from the good. Science, on the other hand has produced astounding and wonderful solutions to most human problems even after netting out the harm from the good.

But as I see it, there are still some "gaps" in the explanations of science which naturally and traditionally fall into the purview of religion. In my humble opinion, science may be able to close some of these gaps by extending their boundaries, methods, and assumptions. I think they need to think "outside the science box". In the case they are successful, it will only extend science and diminish religion; it will not necessarily make science "religious".

What confuses me is that you agree with me far more often than I agree with you.

Unfortunately, it seems to me that you, Canute & Dr Dick are closer to agreeing with each other than I am to agreeing with any of you.

This reminds me of the duelist who was concerned because his opponent was a better shot than he was. He offered the following solution in order to make the duel fair: He said, "How about if I stand twice as far from you as you stand from me?" Maybe dualists can do the same?

I think that the reason I seem to agree with each of you more than you think you agree with me is that I can interpret most of what each of you says to make sense in my "PC scheme". To the extent that each of you accepts my PC notion, you might agree with me, otherwise my ideas probably seem like nonsense to you. As I have said before, if you can show me where my ideas are nonsensical, I will gladly abandon them. Merely labeling them as "religious", or "nonsense", however, doesn't convince me -- not that any of you do that.

This shows simply that we cannot answer all possible questions about the naïve idea of the set of all sets (ie some questions are unanswerable). Naïve set theory was superceded by various axiomatic set theories (of which Zermelo-Fraenkel (ZF) set theory is the most well known) which avoid Russell’s paradox. Godel later showed that no system of set theory can be shown to be both consistent and complete, but even this does not entail paradox. It entails only that the set of all logical possibilities cannot be shown to be complete if we also wish it to be consistent. What does this mean? It means simply that the set of all logical possibilities cannot be a complete set.

You seem to know more mathematics than you let on. I'm glad of that because maybe you can help me -- again. I have a problem with the foundations of mathematics which I tried to spell out in my thread at https://www.physicsforums.com/showthread.php?t=49732 . I was not satisfied with the response I got there so I decided that I need to go back to school at some time and study the foundations to see if I can't resolve my problem. Maybe you can help me before I do that. If you wouldn't mind, take a look at that thread and see if you can help me out.

It is my understanding that the Axiom of Choice is one axiomatic way of getting an infinite number of integers defined with only a finite number of axioms. By adding the Axiom of Choice (C) to ZF set theory, producing ZFC set theory, the infinite set of integers can be defined. Does ZF contain the infinite set of integers? If so, how are they defined? If not, then is there a largest integer in ZF?

One cannot legislate against the question that Russell asked. One cannot simply say “we will prohibit consideration of infinite sets” and then blindly hope the paradox goes away. The problem highlighted by Russell remains – there are some questions which cannot be answered. Even if legislation is introduced to exclude infinity from mathematics, one can still ask the question “is the class of all classes that are not members of themselves a member of itself?”, and the question is still unanswerable.

We can legislate however we like; we must, however, live with the consequences. If we prohibit consideration of infinite sets, by providing no way to define them in our axioms, then IMHO the paradox does not appear in the first place. Russell's approach with his Theory of Types, on the other hand, prohibits consideration of certain sets in some propositions, i.e. different rules for "classes" than for "sets", and IMHO represents the "blind hope that the paradox goes away". I would really appreciate your shedding whatever light you can on this.

I have my own thoughts about the paradoxes introduced by the concept of infinity in conventional number theory – it has to do not with the concept of infinity itself, but with the rather strange notion that mathematicians seem to have of an integer. For some strange reason, in conventional number theory we choose to define an integer as an arbitrarily large number, with every integer representable by a finite string of digits.

I'm not aware of that definition. In what axiomatic system are integers defined that way?

But it is impossible to uniquely identify every member of an infinite set with finite strings, which implies that an infinite set of integers must contain members of infinite length, which in turn contradicts the definition of an integer.

I agree with this (intuitive) conclusion. I think similar arguments can be brought to bear against Cantor's definitions and I think they also apply to Goedel's proof.

I think Feynman was trying to express the same thought when he told his nephew (I think it was) that, "There are more numbers than numbers."

No because now you must define "a mapping", various sets of information and, explain these things. They cannot be more basic than the concept of an explanation.

And your definition of explanation is “a method of obtaining expectations from given known information” – can you define “method”, “expectations”, “given”, “known” and “information” without either tautology or infinite regress?

With respect, I agree with MF here, Dick. I think you are mixing up two different methods of investigation. You want to stick to the logico-mathematical methods, but you are forced to get into an English vernacular dialog here for those of us who can't follow your math completely. And, you will have to admit, even in your paper, you include many non-mathematical English sentences which have been a source of aggravation and disagreement for many of your readers.

I think the limitations we need to keep in mind are these:

In formal mathematical development, we must start with undefined primitives, unprovable axioms, mysterious and non-specific rules of logic, a portion of some natural language in which propositions can be stated, an assumption that someone else might read the language expression of the development (This one is not absolutely necessary unless the development is to be useful at all), and an assumption that you, the developer, has enough continuity and coherence of thought to produce a sensible development. (This last assumption is, in your case Dick, your familiar assumption of the two types of mentality available to you: formal logic and squirrel logic.) That's a lot of assumptions and each one suggests some reason to question the veracity of any conclusions drawn.

In vernacular English conversation, such as we are doing in this forum and which is the primary method of philosophy, the ambiguities are not collected together in the primitives and axioms of formal systems, but instead are rife throughout the lexicon and even the grammar. With the severe limitations of natural language it is a wonder to me that we ever come to agreements on anything more significant than questions like, "Do you want fries with that?"

I am pleased and amazed that we come as close to agreement as we do here. As I have said before, I think that nearly all of our disagreements are semantic. I think we just need to be careful to realize that in our discussions here, we are involved in a vernacular conversation, not in the development of a formal system. I think we get into trouble when we talk about the formal systems of Russell, Cantor, Zermelo, Spencer Brown, Dr. Dick, etc.

A case in point is Dick's insistence that the concept of 'explanation' is fundamental to his argument. It probably is in his formal development, but it certainly isn't in our vernacular conversation here.

I think there are two approaches we could take. We could try to rigorously establish what we think are the primitive, or fundamental terms we want to use, and rigorously define the rest in terms of these, and then proceed in our discussion. But then we would be doing mathematics, and we might make better progress by studying Spencer Brown, Goedel, Schroedinger, or someone else who has already taken this approach and gained some ground.

The second approach is to continue to probe the differences in our respective understandings or connotations of the words and phrases we use, in an attempt to discover whether the differences are only semantic or whether they constitute some significant conceptual disagreement. I think that we are making some substantial progress with this approach, and I am delighted.

For example,

...experience tells us, by definition, that there is “something rather than nothing”

I consider this to be equivalent to the proposition that "thought happens". Now, to figure out whether or not we disagree on this, let me ask you, MF, do you think that the "something" that exists could be thought? Could you accept a definition of 'thought' that makes it something? Or would you prefer to consider thought as nothing?

In my humble opinion, I think that there are no iron-clad answers to those questions. I think it is simply a matter of opinion about how to express concepts in language in a way that is first satisfactory to us and secondarily has a chance of conveying that concept to another. It is "simply" that, but that is far from simple. I think we're doing the best we can.

(more to follow)

Paul

 

[Paul Martin]

Yes. I am convinced that Dr. Dick has proved this to be the case.

I haven’t seen it myself.

You can see it at http://home.jam.rr.com/dicksfiles/reality/Contents.htm .

OK, so the PC makes a choice, and thereafter the PC is constrained by the laws of mathematics and physics, yes?

Yes.

Apart from “making the choice to be consistent”, the PC does not actually create these laws, the laws follow on as a necessary consequence of the PC’s consistency decision?

No. I think that at some point PC actually "does mathematics" by choosing primitives, axioms, and definitions, which then imply, or "create" the laws. Yes, this imbues PC with a lot of anthropomorphism, but the capability to do math, IMHO, developed after a long stretch of time prior to the Big Bang. PC evolved and advanced to a huge degree beyond its extremely rudimentary, simple, fundamental primordial condition. I think this is the point you miss when trying to understand my ideas. I think there was probably a huge amount of trial and error before the precise conditions for an interesting universe like ours were stumbled upon.

This indeed seems to confirm that the PC does not actually create the laws, the laws follow on as a necessary consequence of the PC’s consistency decision. Correct?

Almost. The laws follow on as necessary consequences of the PC's consistency decision and the particular choices of primitives, axioms, definitions, and boundary conditions.

OK, so the first thing the PC did was in fact NOT that it chose to be consistent. It first had to experiment with many different possibilities, until it gained enough information about the world to then make a rational decision to be consistent?

YES! I'm sorry I didn't make that more clear earlier. That is what I was trying to say when I said that PC was extremely rudimentary and limited at the outset and that PC underwent an extremely long evolution of acquiring the capabilities and knowledge necessary to pull off a Big Bang.

It seems that your PC is becoming less and less primordial as we go along.

It seems that way to you because PC is becoming less so as we go along in this conversation and you are beginning to see what I have been trying to say all along. And, in my view, PC did indeed become less and less primordial as reality developed from its initial primordial and extremely simple and limited condition.

We are already now speculating about some kind of background environment in which the PC learns (about logic, consistency etc), and we also seem to think that the laws of logics, mathematics and physics are constrained to be necessary by virtue of consistency, quite independent of the experimentation by the PC.

Yes, exactly! I am absolutely delighted that you used the pronoun 'we' here. I have been doing exactly the speculation you described for quite some time. I am happy to learn (or at least hope) that you are beginning to entertain the same speculations. The next step is to ask you whether these speculations make any sense to you, or are they nonsense? I am sincerely eager to hear your opinions.

If the PC supervenes on, and does not create, the laws of logic and of mathematics, then it follows that these laws EITHER exist prior to the PC coming along, OR that they spontaneously come into existence at the moment of creation of the PC. Which?...
But you have just said that the PC supervenes on the laws of logic and mathematics. Now it seems you are saying the reverse.

I'm sorry that I don't understand the word 'supervene' well enough to use it in a sentence, and as a result I may be misunderstanding your questions. But here's how I see it. When PC was truly "primordial" it had no capability of contemplating laws, logic, mathematics, or anything else. These capabilities developed over a long period of time as we have discussed above. It would be a fair question to ask in what exact sequence did the various capabilities appear, such as the recognition of the notion of consistency, the rules of inference for logical deduction, the idea of logical consequences, particular choices of primitives and axioms, the ability to grind out the results of algorithms operating on specific sets of numbers, etc.

The question is fair, but I think not trivial. In my opinion, this is exactly the question that Spencer Brown and Chris Langan have attempted to answer. I think it is essentially the same question that Whitehead and Russell attempted to answer with their Principia Mathematica. I'm not sure at this point if anyone has yet come to a conclusive answer, but I do suspect it is within our reach, if not our grasp yet. I think it is possible to demonstrate logically how all of reality could have developed from nothing but the ability to know of some distinction.

But to give you my guess at the answer to your question, I'd say, Neither. The laws of logic and math did not exist prior to the existence of PC. The laws did not spontaneously come into existence "at the moment of the creation of the PC", which I take to mean the initial or primordial appearance of PC, however that came to be. The laws spontaneously came into existence the moment that rules of logical inference were adopted by PC as a deliberate choice. This is just like the fact that a bishop cannot occupy a square of a different color spontaneously comes into existence the moment the chess board and the rules of chess are defined. The fact did not pre-exist the definition of the game in any sense, and the fact is a logical consequence of the rules for the initial placement of the bishop and the rules for its legal moves.

What comes first – the constraint imposed by the rule, or the making up of the rule?

The making up of the rules of logical inference comes first. The constraint then applies to any further rules that are chosen and which conform to the rules of logical inference.

But this implies that the rules (of logic and mathematics) supervene on the PC, not the other way about (which is the reverse of what you agreed above).

I don't understand the word 'supervene', so I can't comment any further.

OK, I shall try to avoid reference to time by using supervenience instead. Do the rules supervene on the PC, or does the PC supervene on the rules? (you seem to have claimed both so far).

Well, here we have a problem we can work on. You seem to need the word 'supervene' in order to make your point, and I don't understand the word. I need to use the notion of time in order to explain exactly how I see the pre-BB evolution of reality and you want to avoid that discussion. I hope you are willing to work on one, or preferably both, of these problems.

IMHO PC "creates" by thinking that it creates, as you seem to imply.

That is interesting. Perhaps the PC only thinks that it is inventing as well?

I'm not sure how to interpret your question, but I'm glad you find my statement interesting. You taught me to ask whether PC, being the ability to know, really knows or only thinks it knows. I think that is a profound question and I have thought about it a lot. It is reminiscent of the recent question someone here asked of whether free will requires awareness. In my PC scheme, the questions of this type, in the context of humans are answered as follows: Humans only think we are conscious, know things, and have free will. We are usually aware (really think we are aware) of our thoughts only in the context of our human existence. But in cases usually labeled as "altered states", we can sometimes become aware of a higher level of existence, from which perspective, "we" know that the human "mind" is an illusion caused by PC vicariously using or driving the brain and thus limiting its attention and awareness to the physical human environment and situation. So the human mind thinks it knows things, but it really doesn't. PC (and add considerable amount of complexity here with the multiple levels of reality with their respective PC-driven vehicles, or Natural Individuals) ultimately is the only knower who really knows. But, if you go up the entire hierarchy asking exactly who (which natural individual) knows exactly what, the answer is that all the lower levels only think they know, and it is only the top level PC who actually knows anything.

But here is where the notion of time comes into play. If time is only a parameter marking PC's progress in attending to the world line of a Natural Individual, then there is no time at all when we consider what PC knows at the very highest level. So it is hard to conceive how PC can or does know anything at all at that level. Maybe PC only thinks it knows anything and there is really nothing known at all in reality. Who knows?

That's probably more than enough for now.

Very sorry to hear that – my condolences and best wishes

Thank you.

Warm regards,

Paul

 

[PIT2]

And, in my view, PC did indeed become less and less primordial as reality developed from its initial primordial and extremely simple and limited condition.

Do u also think there was a beginning to the PC? And did time exist during PC's pre-bigbang evolution?

Obvious questions, but i couldn't resist asking them.
(also forgive me if uve already mentioned it, i didnt read all the giant posts here)

If time is only a parameter marking PC's progress in attending to the world line of a Natural Individual, then there is no time at all when we consider what PC knows at the very highest level. So it is hard to conceive how PC can or does know anything at all at that level.

Im not sure what u mean with that PC doesn't know time at the highest level. Is this something like: 'when one is omniscient then nothing is relative, so time disappears'?

 

[Paul Martin]

Hi PIT2,

Sorry for being so lengthy in my posts. Thanks for reading what you do.

Do u also think there was a beginning to the PC?

I don't really have an opinion on that question. Maybe PC (the bare ability to know) sprang at once out of nothing. Maybe there always was a PC and all at once it noticed some distinction for the first time. Maybe something else accounts for its appearance. But I'd say that the starting point for reality involved a rudimentary PC regardless of how it got there.

And did time exist during PC's pre-bigbang evolution?

I'd say, Yes. I think time existed as soon as PC began pondering any sequence of anything. (Of course the only candidates for "anything" are concepts.) A dimension of time arises simply as any mark or measurement of the progress of PC's attention as it ponders elements of a sequence of concepts. The really interesting sequences are the events in the vicinity of the world line of a natural individual, but I see no reason (except for a way for PC to get the information) why PC couldn't ponder the sequence of positions of some inanimate object like a photon or a galaxy.

But...and maybe this is the question you really meant to ask, time did not exist prior to PC noticing that first distinction, because "prior" to that, there was no sequence for PC to ponder, and indeed, there was not even any pondering.

Im not sure what u mean with that PC doesn't know time at the highest level. Is this something like: 'when one is omniscient then nothing is relative, so time disappears'?

I wouldn't put it that way. First of all, I don't think there is any such thing as omniscience; in particular I don't think PC is omniscient. It's more like if PC is pondering the highest level, then there are no constructs of concepts to ponder, so there is no pondering, and thus time does not appear. It's not like it was there and then disappeared, it just isn't there at all. All concepts, and thus all time, appears only in the lower levels of the hierarchy.

I hope that helps.

Paul

 

[Canute]

Paul

Great post. By the way, when I said your ideas sounded suspiciously like creationism I didn't mean to criticize them for sounding religious. I couldn't care less whether they are religious, scientific or philsophical or none of these. My point was rather that I have a problem with the idea that the universe was created by intention.

This extract from MF interests me, and seems crucial.

Godel later showed that no system of set theory can be shown to be both consistent and complete, but even this does not entail paradox. It entails only that the set of all logical possibilities cannot be shown to be complete if we also wish it to be consistent. What does this mean? It means simply that the set of all logical possibilities cannot be a complete set.

I agree with all of this except for the final sentence. I may be misunderstanding it but it seems to assume that ordinary logic (ordinary equation theory, Boolean algebra) is the only sort there is. But we do not use this logic in quantum theory, we make use of complex values.

This may seem a small point but I feel it's central to the discussion. Suppose that PC (not my choice of term but no matter) is a contradiction in ordinary logic? Suppose it is something that is logically equivalent to a wave-particle? In this case the true 'explanation of everything' would be inconsistent and complete. It is this get out clause that prevents Godel's proof from being a disproof of the cosmology of Taoism, Buddhism etc. The structure of these cosmologies is isomorphic with quantum theory, two contradictory but self-consistent explanations of the same self-contradictory explanandum. It is this curious property of the Tao and Brown's void that I feel is missing from Paul's PC theory.

This relates to MF's point about Godel and Russell directly, since it is precisely by adopting the logical scheme of quantum theory that Brown overcomes the need for Russell's 'Theory of Types' (as Russell acknowledged) and avoids logical paradoxes in his calculus (which is a model of his cosmology). This is undoubtedy the hardest thing to understand about Brown's view (and the Buddha's, Lao Tsu's etc).

On the issue of language I agree with most of what Paul wrote. But this passage is worth some thought. It's taken from Werner Heisenberg's Physics and Philosophy(1959).

"The vagueness of this language in use among the physicists has therefore led to attempts to define a different precise language which follows definite logical patterns in complete conformity with the mathematical scheme of quantum theory. The result of these attempts by Birkhoff and Neumann and more recently by Weizsäcker can be stated by saying that the mathematical scheme of quantum theory can be interpreted as an extension or modification of classical logic. It is especially one fundamental principle of classical logic which seems to require a modification. In classical logic it is assumed that, if a statement has any meaning at all, either the statement or the negation of the statement must be correct. Of ‘here is a table’ or ‘here is not a table’, either the first or second statement must be correct. ‘Tertium non datur,’ a third possibility does not exist. It may be that we do not know whether the statement or its negation is correct; but ‘in reality’ one of the two is correct.

In quantum theory this law ‘tertium non datur’ is to be modified. Against any modification of this fundamental principle one can of course at once argue that the principle is assumed in common language and that we have to speak at least about our eventual modification of logic in the natural language. Therefore, it would be a self-contradiction to describe in natural language a logical scheme that does not apply to natural language."

If this is understood then the self-contradictory language of mysticism can be understood. This connects directly to the notion of 'nonduality' or 'advaita' that lies at the heart of the mystical doctrine. In logical terms it is the suspension of the tertium non datur rule.

Armed with this notion the problems relating to creationism, intention and so on that are IMHO problematic in Paul's view can be resolved.

Hope some of that made sense.

regards
Canute

PS. Paul - I was waiting to hear from Dick before starting a thread on your essays, but I'll go ahead anyway, just as soon as I can disentangle myself from all the different arguments I've stupidly got myself into and freed up some time to do so.

 

[selfAdjoint]

This extract from MF interests me, and seems crucial.

Godel later showed that no system of set theory can be shown to be both consistent and complete, but even this does not entail paradox. It entails only that the set of all logical possibilities cannot be shown to be complete if we also wish it to be consistent. What does this mean?

Only problem is that Goedel did not say this! He said that any logical system capable of developing arithmetic from axioms had this property. That's a big restriction because there are a lot of systems, like segments of real analysis, that don't fall under it and cannot be called undecideable.

 

[Canute]

Yeah, you're right to pick up on some sloppiness. Still, I think the general point holds once a couple of provisos are added.

 

[moving finger]

Only problem is that Goedel did not say this! He said that any logical system capable of developing arithmetic from axioms had this property. That's a big restriction because there are a lot of systems, like segments of real analysis, that don't fall under it and cannot be called undecideable.

I'm happy to stand corrected - because if anything this reinforces my point that the notion of a set of all logical possibilities does not entail contradiction.

Best Regards

 

[Canute]

What exactly do you mean by 'a set of all logical possibilities'? Do you mean the set of everything that is the case? Or do you mean that if two facts are possibly true they cannot contradict each other? Or something else?

 

[moving finger]

What exactly do you mean by 'a set of all logical possibilities'? Do you mean the set of everything that is the case? Or do you mean that if two facts are possibly true they cannot contradict each other? Or something else?

In modal logic, a proposition may be :

True in all possible worlds - ie logically necessarily true
True in some, but not all, possible worlds - ie logically contingent
False in all possible worlds - ie logically necessarily false (ie impossible).

Note that "possible worlds" refers to all logically possible worlds (ie we are not considering ourselves constrained here by physical possibility).

The set of all logical possibilities would be the set of all propositions which are either logically contingent or logically necessarily true.

Best Regards

 

[Canute]

Does this mean that the set of all logical possibilities is the set of all propositions that are tautologically true (e.g. all bachelors are single) or that may be either true or false?

 

[Canute]

Paul

I've started a thread in Metaphysics titled 'Foundations of Reality' and kicked off with a couple of questions. See you there I hope.

 

[moving finger]

Does this mean that the set of all logical possibilities is the set of all propositions that are tautologically true (e.g. all bachelors are single) or that may be either true or false?

The set of all logical possibilities is the set of all propositions, each one of which is true in at least one logically possible world.

 

[Canute]

Ok. I see what you're getting at. I wonder though. Are you not asuming that all logical possibilities can be stated as true or false propositions? What about the proposition that not all logical possibilities can be stated as true or false propositions?

 

[moving finger]

Ok. I see what you're getting at. I wonder though. Are you not asuming that all logical possibilities can be stated as true or false propositions? What about the proposition that not all logical possibilities can be stated as true or false propositions?

No, I need not assume that all logical possibilities can be stated only as either true or false propositions.

Would you care to propose a different form of logic to 2-valued (true/false) logic? We could then discuss the implications for the set of all logical possibilities (the notion of such a set does not necessarily assume 2-valued logic).

As we discussed (in another thread, or this one?), one cannot arrive at any understanding or explanation unless one makes assumptions.

One may assume 2-valued logic (in which case all meaningful propositions are either true or false), or one may assume some other valued logic.

Which logic would you like to assume for the purpose of this discussion?

(Granted that meaningless propositions may not have a truth value)

Best Regards

 

[Canute]

Yes, that's what I'm getting at, that reality may not accord with the dualism inherent in ordinary logic. In my view it does not. My suggestion is to use the modification to ordinary logic that physicists make use of in quantum theory.

(I know what you think about the necessity of assumptions, but don't forget that I haven't agreed with you yet).

 

[moving finger]

What paradox?

Metaphysical paradoxes. I would include the 'hard' problem of consciousness as one of these.

I’ve responded to the so-called “hard problem” in another thread (which, even if it were a problem, is hardly a paradox – it would be just something in need of explanation).

Are there any other paradoxes you had in mind?

The suggestion is that truth about it is subtle, in such a way that the yes and no arguments are both flawed. This would explain why the debate is ongoing.

I agree that part of the problem is defining exactly what we mean by free will. But even if we do agree what we mean by free will, the reason why the debate is ongoing (imho) is because one side insists on holding incoherent beliefs which at the same time they deny as being incoherent.

I couldn't agree more. Now try applying the same principle to metaphysical questions, such as the whether we have freewill, whether the universe begins with something or nothing etc. This is what Brown means by using imaginary values in our reasoning.

Nope. It doesn’t work (or perhaps I should say – imho one can delude oneself into thinking that one has found the answer to everything by answering nothing).

But if a single assumption explains everything else, and does not produce a reductio argument against the assumption, then would this not be a reasonable strategy to make the assumption? Still, I half agree with you, since the result can only be a theory.

Are you looking for just a single assumption? That’s called God isn’t it? Doesn’t that explain everything we need to know?

Yes, I distinguish between certain knowledge and provisional or relative knowledge.

Then how do you define “knowledge”?

I'm certain of one or two things. The unfalsifiabilty if solipsism is the nearest I can get to knowledge that is certain and communicable.

That’s an example of an analytic truth or a tautology (a truth by definition - like the certainty that “all bachelors are unmarried”) – yes one could claim it is certain knowledge, but it doesn’t tell us anything useful about the world.

The knowledge that I'm hungry is certain, but I can't demonstrate it.

Are you hungry? Or do you just think you are hungry (ie you just think that you have hunger pains, when in fact you don’t really have them)? Perhaps you are hallucinating, perhaps you have been drugged or hypnotized to think you are hungry, perhaps you are a brain in a vat which an evil scientist is experimenting with, sending signals to your brain.

This seems true to me also. However, the idea of an eternal substance is paradoxical, so this view still leaves a question begging.

Why paradoxical? Because you assume there must be a beginning?

Well, not an imaginary statement, but I know what you mean. The statement 'the universe arises from nothing' is true or false in metaphysics. The statement 'the universe arises from something' is true or false likewise. However, in the esoteric or 'advaita' view both these statements are neither quite true nor false. The truth would be that the universe arises in a sense and in a sense does not, and that it arises from nothing in a sense but in a sense arises from something. Hence this comment by Robin Robertson about Brown's calculus.

Then the question is ambiguous. It is all too easy to avoid giving “yes” and “no” answers (as many eastern philosophies do) by claiming “in one sense it is yes, in another sense it is no” – all this means is that one’s understanding of the question is ambiguous. Imho to claim that one possesses “knowledge” or “understanding” by simply uttering meaningless statements like “the universe arises in a sense and in a sense does not” (without further qualification) is to delude oneself.

In what “sense” does it arise from something?
And in what “sense” does it arise from nothing?

Anyone who thinks deeply about anything eventually comes to wonder about nothingness, and how something (literally some-thing) ever emerges from nothing (no-thing).

This explanation assumes that the “something” did emerge from “nothing” – perhaps the “something” has existed for all time (in which case there is no “emerging”)

I propose that Spencer-Brown’s distinctions create the most elementary forms from which anything arises out of the void, most specifically how consciousness emerges.

Nice “proposition” – but hardly a detailed explanation.

Abduction is generally considered to be a third form of inference. C. S. Peirce takes this view, as do most dictionaries. I agree that it is a form of deduction, but still feel the distinction is useful. A deductive proof would normally be more certain than a abductive one.

Proof by deduction is 100% certain (assuming the premises are true). Note that I am saying proof by abduction is either a proof by induction or by deduction (I am not saying that all proofs by abduction are proofs by deduction).

But at the limit, say in the case where all explantions of a phenomenon except one had been eliminated, they would be effectively the same thing.

Agreed the distinction may be useful – just as it is useful to distinguish between men and women – but they are all humans. The important point however is that (I believe) any proof by abduction is also either a proof by induction or a proof by deduction. The point I am trying to make is that fundamentally all proofs are either by induction or deduction – and only the latter provides certainty.

I don't agree here. If I am experiencing pain then this is direct knowledge, not an inference. It is not possible to be mistaken, even if the pain is in a phantom limb it is being experienced.

Pain is not knowledge – pain is a phenomenal interpretation that your conscious mind places on certain states that seem to occur within your brain. What “knowledge” do you think your phenomenal experience of pain is giving you (apart from the tautological knowledge that “experience of pain means I am experiencing pain”)?

Whatever “knowledge” you think you have from the experience of pain (apart from tautological knowledge), how do you know it is not possible for you to be mistaken? You may be a brain in a vat, with an evil scientist stimulating various parts of your brain to make you think that you are experiencing things when in fact you are not experiencing those things at all. When you feel a “pain in your foot” you don’t believe that you feel that pain in your brain – you believe that you feel the pain in your foot. But if you are a brain in a vat, you have no feet, and the stimuli that the evil scientist is providing to your brain are (perhaps) simply low-voltage electrical signals which your brain interprets as “that is a pain in my foot”.

This is not the case. You can see this if you consider how it is possible to prove (to yourself) that you are conscious. Still, I wouldn't object to calling this verification instead of proof.

How would you go about proving to yourself that you are conscious? (suggestion : first you need to define consciousness)

Hmm. Believe it or not I don't agree. The stament 'something exists' is not true according to many people

Would you care to defend this position?

Mind you, the statement 'nothing exists' would also be not true. Here we meet another of Brown's complex values. There are a few proofs around that nothing really exists, although not everyone agrees they are successful.

Would you care to support your claims with some examples?

I'm ok with that, depending on how 'information' is defined. But I think this falls within my definition. The question arises of whether everything that can be known and understood can be explained.

Absolutely everything may be explained – the real question is whether the proffered explanation is true or not (the easiest way to explain everything, which requires very little effort or thought, is the way that theists do it).

(continued in next post)

 

[moving finger]

I think that the reason I seem to agree with each of you more than you think you agree with me is that I can interpret most of what each of you says to make sense in my "PC scheme". To the extent that each of you accepts my PC notion, you might agree with me, otherwise my ideas probably seem like nonsense to you. As I have said before, if you can show me where my ideas are nonsensical, I will gladly abandon them. Merely labeling them as "religious", or "nonsense", however, doesn't convince me -- not that any of you do that.

Paul - I don’t claim that your ideas are nonsensical – they constitute (imho) just unnecessarily complex assumptions. Your ideas seem to wrap up a lot of complexity within their assumptions; complexity which I believe is emergent rather than primordial.

You seem to know more mathematics than you let on.

Naaah, I’m just an experienced bullsh**ter, who knows a lot less than he thinks.

I'm glad of that because maybe you can help me -- again. I have a problem with the foundations of mathematics which I tried to spell out in my thread at https://www.physicsforums.com/showthread.php?t=49732 . I was not satisfied with the response I got there so I decided that I need to go back to school at some time and study the foundations to see if I can't resolve my problem. Maybe you can help me before I do that. If you wouldn't mind, take a look at that thread and see if you can help me out.

It is my understanding that the Axiom of Choice is one axiomatic way of getting an infinite number of integers defined with only a finite number of axioms. By adding the Axiom of Choice (C) to ZF set theory, producing ZFC set theory, the infinite set of integers can be defined. Does ZF contain the infinite set of integers? If so, how are they defined? If not, then is there a largest integer in ZF?

Axiom of Choice, or Axiom of Infinity?

See http://en.wikipedia.org/wiki/Axiom_of_infinity

A (positive) integer is (allegedly) a number which can be obtained from adding 1 to itself a *finite* number of times.

The problem is, I have no idea how one can generate an infinite set of integers (ie a set with infinite cardinality) using this procedure. Do you? (see below)

We can legislate however we like; we must, however, live with the consequences. If we prohibit consideration of infinite sets, by providing no way to define them in our axioms, then IMHO the paradox does not appear in the first place.

But it does. Russell’s paradox has nothing to do with infinity – it has to do with unrestrained self-referentiality. Even in a finite number system, one can still ask “is the class of all classes that are not members of themselves a member of itself?”

Russell's approach with his Theory of Types, on the other hand, prohibits consideration of certain sets in some propositions, i.e. different rules for "classes" than for "sets", and IMHO represents the "blind hope that the paradox goes away". I would really appreciate your shedding whatever light you can on this.

Remember I’m a bullsh**ter. Russell’s Theory of Types did not exclude infinity (as you seem to wish to do), it excluded (as you point out) the conflation of “classes” and “sets” – this was an attempt to draw a distinguishing line between naïve sets on the one hand, and the consideration of “self-referential sets of sets” on the other hand (which latter ultimately leads to his paradox). Thus, Russell’s paradox is not a consequence of infinity, it is a consequence of unrestrained self-referentiality. THIS is why I said that legislating against infinity does not make the problem go away.

I'm not aware of that definition. In what axiomatic system are integers defined that way?

I had a long battle with the Maths geniuses on this forum a couple of years ago, in which I was basically told that I was an ignoramus for suggesting such a thing as an infinite integer –

They aren't integers. Go learn some maths

A (positive) integer is a number which can obtained from adding 1 to itself a *finite* number of times.
The strings you wrote out are not elements of the integers, nor R, with any reasonable interpretation of them.
They are elements of a p-adic system, though.

Integers in base 10 with the usual rules of presentation have only a finite number of non-zero digits. You should possibly hold back from telling some people who all have degrees or higher in mathematics or related areas things like that.

There is no such thing as an infinite integer.

There exist infinitely many integers, each of which is a finite number.

The set of integers has infinite cardinality, but each individual integer has finite magnitude.

My question (still unanswered) : If each and every integer is constructed by “adding 1 to itself a finite number of times” (this is the argument that leads to the conclusion that every integer is finite), then how is it possible to produce a set of integers with infinite cardinality?

But it is impossible to uniquely identify every member of an infinite set with finite strings, which implies that an infinite set of integers must contain members of infinite length, which in turn contradicts the definition of an integer.

I agree with this (intuitive) conclusion.

Amazing – we agree! Unfortunately, most conventional mathematicians think this is nonsense.

In formal mathematical development, we must start with undefined primitives, unprovable axioms, mysterious and non-specific rules of logic, a portion of some natural language in which propositions can be stated, an assumption that someone else might read the language expression of the development (This one is not absolutely necessary unless the development is to be useful at all), and an assumption that you, the developer, has enough continuity and coherence of thought to produce a sensible development. (This last assumption is, in your case Dick, your familiar assumption of the two types of mentality available to you: formal logic and squirrel logic.) That's a lot of assumptions and each one suggests some reason to question the veracity of any conclusions drawn.

Hey, at least someone agrees with my belief that we must make assumptions if we are to arrive at any explanation or understanding!

In vernacular English conversation, such as we are doing in this forum and which is the primary method of philosophy, the ambiguities are not collected together in the primitives and axioms of formal systems, but instead are rife throughout the lexicon and even the grammar. With the severe limitations of natural language it is a wonder to me that we ever come to agreements on anything more significant than questions like, "Do you want fries with that?"

I agree wholeheartedly with this. I believe one of the reasons that we usually believe we agree with each other is because our normal language is based on such ambiguity and uncertainty in meaning that there is plenty of room for “overlap” in both intended and non-intended meaning that we just “happen” to be able to communicate ideas with each other (sometimes more by luck than by judgment).

I am pleased and amazed that we come as close to agreement as we do here. As I have said before, I think that nearly all of our disagreements are semantic. I think we just need to be careful to realize that in our discussions here, we are involved in a vernacular conversation, not in the development of a formal system. I think we get into trouble when we talk about the formal systems of Russell, Cantor, Zermelo, Spencer Brown, Dr. Dick, etc.

OK.

A case in point is Dick's insistence that the concept of 'explanation' is fundamental to his argument. It probably is in his formal development, but it certainly isn't in our vernacular conversation here.

Understood. But even in his formal development, it seems to me that an explanation is a mapping (a series of vectors if you like) which provides a translation from one set of points in his 3D space, to another set of points in the same space. Whether the points are more fundamental than the vectors which map between them, or vice versa, is arguable. Imho the reason why I think Dick wants to believe his “explanation” is more fundamental is because he can identify a mathematical and quantum mechanical analogy in the wave equation (whereas there is no quantum mechanical analogy for the sets of points).

I consider this to be equivalent to the proposition that "thought happens". Now, to figure out whether or not we disagree on this, let me ask you, MF, do you think that the "something" that exists could be thought? Could you accept a definition of 'thought' that makes it something? Or would you prefer to consider thought as nothing?

It “could be” thought – but first (bearing in mind your very insightful words about semantic disagreement) I think we need to agree on a definition of “thought”. What do you mean by “thought”?

No. I think that at some point PC actually "does mathematics" by choosing primitives, axioms, and definitions, which then imply, or "create" the laws. Yes, this imbues PC with a lot of anthropomorphism, but the capability to do math, IMHO, developed after a long stretch of time prior to the Big Bang. PC evolved and advanced to a huge degree beyond its extremely rudimentary, simple, fundamental primordial condition. I think this is the point you miss when trying to understand my ideas. I think there was probably a huge amount of trial and error before the precise conditions for an interesting universe like ours were stumbled upon.

Sorry, Paul, but this doesn’t seem to answer the question. You seem to be saying that the PC creates the laws of mathematics, as in “the laws of mathematics do not follow on as a necessary consequence of the PCs consistency decision”.

You say that the PC “does mathematics”, but then so do most humans. But humans do not create the laws of mathematics by “doing mathematics”.

Allow me to re-phrase the question. Given the choice by the PC to be consistent, did the laws of mathematics then follow as a necessary consequence of this (independently of the PCs wishes)? Or are the laws of mathematics contingent (the PC created the laws, and could have created different laws of mathematics if it had so wished)?

The laws follow on as necessary consequences of the PC's consistency decision and the particular choices of primitives, axioms, definitions, and boundary conditions.

OK. This is true of all mathematical laws. Thus (to take an example) given a right-angled triangle in a 2-dimensional plane conforming to Euclid’s 5 postulates of geometry, the law that the square of the hypotenuse is equal to the sum of the squares of the other two sides is a necessary mathematical law. There is no way that the PC could have “created” a universe in which this law (given the postulates and definitions) would have been false. Thus in a very real sense, this law (given the postulates and definitions) “exists” independently of the PC.

Yes, exactly! I am absolutely delighted that you used the pronoun 'we' here. I have been doing exactly the speculation you described for quite some time. I am happy to learn (or at least hope) that you are beginning to entertain the same speculations. The next step is to ask you whether these speculations make any sense to you, or are they nonsense? I am sincerely eager to hear your opinions.

I have never said your ideas are nonsense (at least I don’t think I have). I think I can understand your ideas – but I’m afraid that your ideas do not appeal to me as being “reasonable”, for the reasons already explained. My philosophy is based on making the simplest and smallest number of assumptions possible, and deriving complexity as emergent phenomena from these simple assumptions. One such emergent phenomenon (imho) is consciousness. Consciousness is an exceedingly complex phenomenon, and knowledge is predicated on consciousness – your theory posits that this complexity is somehow “built-in” to the boundary conditions of our universe; my theory posits that the boundary conditions are exceedingly simple, and that both consciousness and knowledge emerge as natural but complex phenomena when the circumstances are right.

But to give you my guess at the answer to your question, I'd say, Neither. The laws of logic and math did not exist prior to the existence of PC. The laws did not spontaneously come into existence "at the moment of the creation of the PC", which I take to mean the initial or primordial appearance of PC, however that came to be. The laws spontaneously came into existence the moment that rules of logical inference were adopted by PC as a deliberate choice. This is just like the fact that a bishop cannot occupy a square of a different color spontaneously comes into existence the moment the chess board and the rules of chess are defined. The fact did not pre-exist the definition of the game in any sense, and the fact is a logical consequence of the rules for the initial placement of the bishop and the rules for its legal moves.

The analogy fails because the rules of chess are contingent, not necessary – they could have been different. But the laws of mathematics are not contingent, they are necessary. No matter what the PC does or does not do, given consistency and given a right-angled triangle in a 2-dimensional plane conforming to Euclid’s 5 postulates of geometry, it follows necessarily that the square of the hypotenuse is equal to the sum of the squares of the other two sides. This law is “true” before the PC discovers it to be true (this law always was true, right from the beginning of time), whereas the law that a bishop may only occupy certain coloured squares on a chessboard is neither true nor false until someone determines what the (contingent) rules of chess are to be.

Maybe PC only thinks it knows anything and there is really nothing known at all in reality. Who knows?

It’s important to clearly define what we mean by knowledge. When you say that the PC knows, how do you define knowledge?
(one possibility : knowledge = justified true belief, but maybe you have a different definition)

This may seem a small point but I feel it's central to the discussion. Suppose that PC (not my choice of term but no matter) is a contradiction in ordinary logic? Suppose it is something that is logically equivalent to a wave-particle?

Are you suggesting that a “wave-particle” is a contradiction in ordinary logic? Could you explain?

Armed with this notion the problems relating to creationism, intention and so on that are IMHO problematic in Paul's view can be resolved.

Can they? Could you explain the resolution?

Yes, that's what I'm getting at, that reality may not accord with the dualism inherent in ordinary logic. In my view it does not. My suggestion is to use the modification to ordinary logic that physicists make use of in quantum theory.

OK – over to you. If you don’t want to assume that any given meaningful proposition is either “true” or “false”, then what exactly do you want to assume?

(I know what you think about the necessity of assumptions, but don't forget that I haven't agreed with you yet).

I don’t know whether you agree or disagree, it seems hard to pin you down.

Best Regards

 

[loseyourname]

Canute, what is the proposition with an indeterminate truth-value that you are identifying from the theories of quantum physics?

 

[Canute]

I'm not suggesting that propositions can have indeterminate truth-values. Rather, I'm suggesting that we need to modify the tertium non datur rule in metaphysics just as we do in physics (e.g. for wave-particles and for the background-dependence problem).

 

[loseyourname]

I'm not suggesting that propositions can have indeterminate truth-values. Rather, I'm suggesting that we need to modify the tertium non datur rule in metaphysics just as we do in physics (e.g. for wave-particles and for the background-dependence problem).

I don't think that's the rule you're proposing we get rid of. Excluded middle simply asserts that
(p\vee \negp) is true, meaning either p is true, \negp is true, or both are true. It is the law of noncontradiction, \neg(p\wedge \negp), that states the third option cannot be true.

Both laws can be satisfied in any number of different logics, but remember, neither is actually an a priori law of logic, they are simply tautologies that arise as a consequence of the rules of logic being applied, which are simply the formal syntax and semantics, basically just the definitions of how logical connectives operate and what truth-values are available for use. In bivalent logics only the truth-values 'true' and 'false' are available for use. It seems you want to use another logic that is not bivalent, one that is used by quantum physicists because of a paradox brought about by wave-particle duality. So my question is what proposition regarding the wave-particle duality is it that you believe bivalent logic cannot properly deal with and what kind of logic is it that you believe quantum physicists use to deal with this proposition?

 

[moving finger]

It seems you want to use another logic that is not bivalent, one that is used by quantum physicists because of a paradox brought about by wave-particle duality. So my question is what proposition regarding the wave-particle duality is it that you believe bivalent logic cannot properly deal with and what kind of logic is it that you believe quantum physicists use to deal with this proposition?

I understand what I think you mean, but I think the expression "paradox brought about by wave-particle duality" is unfortunate and misleading. There is no paradox, as long as we remember that a quantum state is neither a wave nor a particle - it is something for which we have no classical analogy. A quantum state contains complementary position and momentum information "wrapped up together" as it were, so that it is false to think of it as having both a definite position and definite momentum at the same time. In trying to label it as either a particle or a wave, we are ignoring one or other of it's properties.

I don't see that any of this requires rejecting the law of the excluded middle.

Best Regards

 

[loseyourname]

Well, that's exactly the point I'm trying to make. I don't personally see any reason that bivalent logic cannot be used to make true statements about quantum physics, so I'm wondering why Canute feels this way. Quantum entities certainly behave in a strange way, counterintuitive to say the least, but they don't do anything I can think of that results in a contradiction when we try to talk about it. Certainly all of the math involved is still derivable from ZFC set theory, which relies on bivalent logic.

The only thing I can think of is, as you point out, we can only speak of position and momentum probabilistically, but the statements of probability are still either true or false.

 

[moving finger]

Well, that's exactly the point I'm trying to make. I don't personally see any reason that bivalent logic cannot be used to make true statements about quantum physics, so I'm wondering why Canute feels this way. Quantum entities certainly behave in a strange way, counterintuitive to say the least, but they don't do anything I can think of that results in a contradiction when we try to talk about it. Certainly all of the math involved is still derivable from ZFC set theory, which relies on bivalent logic.

The only thing I can think of is, as you point out, we can only speak of position and momentum probabilistically, but the statements of probability are still either true or false.

OK, agreed. (it's just that I could just envisage Canute latching onto the notion of "paradox in QM" and using this as a lever to argue for 3-valued logic).

Best Regards

 

[Canute]

I don't think that's the rule you're proposing we get rid of. Excluded middle simply asserts that
(p\vee \negp) is true, meaning either p is true, \negp is true, or both are true. It is the law of noncontradiction, \neg(p\wedge \negp), that states the third option cannot be true.

You almost certainly know more about formal logic than I do. However, I am always careful not to say anything I haven't heard someone who is an expert saying. Here is Heisenberg on the topic, from his Physics and Philosophy.

"The vagueness of this language in use among the physicists has therefore led to attempts to define a different precise language which follows definite logical patterns in complete conformity with the mathematical scheme of quantum theory. The result of these attempts by Birkhoff and Neumann and more recently by Weizsäcker can be stated by saying that the mathematical scheme of quantum theory can be interpreted as an extension or modification of classical logic. It is especially one fundamental principle of classical logic which seems to require a modification. In classical logic it is assumed that, if a statement has any meaning at all, either the statement or the negation of the statement must be correct. Of ‘here is a table’ or ‘here is not a table’, either the first or second statement must be correct. ‘Tertium non datur,’ a third possibility does not exist. It may be that we do not know whether the statement or its negation is correct; but ‘in reality’ one of the two is correct.

In quantum theory this law ‘tertium non datur’ is to be modified. Against any modification of this fundamental principle one can of course at once argue that the principle is assumed in common language and that we have to speak at least about our eventual modification of logic in the natural language. Therefore, it would be a self-contradiction to describe in natural language a logical scheme that does not apply to natural language."

This seems clear and straightforward to me, but is there an objection I'm unaware of?

Both laws can be satisfied in any number of different logics, but remember, neither is actually an a priori law of logic, they are simply tautologies that arise as a consequence of the rules of logic being applied, which are simply the formal syntax and semantics, basically just the definitions of how logical connectives operate and what truth-values are available for use.

Yes, I agree. This was my point. The universe need not be constrained by these man-made rules.

In bivalent logics only the truth-values 'true' and 'false' are available for use. It seems you want to use another logic that is not bivalent, one that is used by quantum physicists because of a paradox brought about by wave-particle duality. So my question is what proposition regarding the wave-particle duality is it that you believe bivalent logic cannot properly deal with and what kind of logic is it that you believe quantum physicists use to deal with this proposition?

They use a modification to the tertium non datur rule as I understand it. Here is Spencer Brown from 'Laws of Form' describing the logical scheme I'm proposing we should consider.

"The position is simply this. In ordinary algebra, complex values are accepted as a matter of course, and the more advanced techniques would be impossible without them. In Boolean algebra (and thus, for example, in all our reasoning processes) we disallow them. Whitehead and Russell introduced a special rule, which they called the Theory of Types, expressly to do so. Mistakenly, as it now turns out. So, in this field, the more advanced techniques, although not impossible, simply don’t yet exist. At the present moment we are constrained, in our reasoning processes, to do it the way it was done in Aristotle’s day."

[However, says Brown, we need not be so constrained].

"What we do … is extend the concept to Boolean algebras, which means that a valid argument may contain not just three classes of statement, but four: true, false, meaningless and imaginary. The implications of this, in the fields of logic, philosophy, mathematics, and even physics, are profound."

To see what he means here consider any metaphysical question. Take the something/nothing question of cosmogony for example. It contradicts reason that the universe arises from something or nothing. In other words, this question is undecidable in ordinary logic. The cause of the problem, according to Brown (and me) is that the universe did not arise from something or nothing. Rather, this distinction is ultimately innapropriate when considering such ontological questions.

Would this not be a rather neat explanation of why metaphysical questions are undecidable?

 

[loseyourname]

The application to metaphysical cosmology would be interesting indeed, though I do have to say there is a certain aesthetic dis-ease I feel at the thought of the truth values for the answers to the great questions simply being "imaginary." Even if that allowed us to use the statements computationally, it just doesn't seem very 'satisfying,' so to speak.

Heisenberg hasn't really answered my question, though, which is why a polyvalued logic would need to be used in quantum physics. I understand the problem he points out of assigning definite positions to entities. The statement 'X is in position Y' has no truth value in the quantum world. My objection is still that the statement 'X has p probability of being in position Y' does have a definite truth value. So it seems they could either choose to invoke some notion of fuzzy sets and make computations using statements of the first kind, or use ordinary bivalent logic and make statements of the second kind.

What they actually do, I have no clue, but I imagine we have quantum physicists somewhere around here that would know. That's the great advantage of being on a physics board, though I often hesitate to ask questions like this lest I get laughed at.

As far as the application of noncontradiction to reality, it agree that it does not place any absolute constraint. It seems to apply to some statements and not to others. 'X is in the bedroom,' for instance, it does not apply to. If X is standing in the doorway straddling the boundary, the statement is both true and false. They say in basic logic texts that such a statement is not truth-functional, but they can be when we use non-bivalent logics.

 

[selfAdjoint]

Heisenberg hasn't really answered my question, though, which is why a polyvalued logic would need to be used in quantum physics. I understand the problem he points out of assigning definite positions to entities. The statement 'X is in position Y' has no truth value in the quantum world. My objection is still that the statement 'X has p probability of being in position Y' does have a definite truth value. So it seems they could either choose to invoke some notion of fuzzy sets and make computations using statements of the first kind, or use ordinary bivalent logic and make statements of the second kind.

The statement 'X has p probability of being in position Y' does not always have a definite truth value in the quantum world. This is precisely where quantum physics bids adieu to classical probability just as it does to classical physics.

The properties of position and momentum are complementary. This means they cannot be measured at the same time. And in fact, the more accurately you measure one (the smaller the variance in your probability distribution for it) the less you can know about the other (broad variance; the product of the variances is a constant). If you pin down the position of something accurately, the momentum becomes completely undefined It doesn't have a probability distribution; it just doesn't exist as a measurable property. And the same thing happens if you accurately pin down the momentum - no position information AT ALL!.

For example the momentum of a photon is proportional to the frequency of the light it carries; if you find out the frequency exactly, the position becomes an undefined property.

Stick with this fact (it is as well established as any fact in physics) and you won''t go wrong about quantum physics.