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The Foundations of Reality

  1. Jul 11, 2006 #1
    The purpose of this thread is to explore Dr. Richard Stafford's paper 'The Foundations of Reality' in order that I (and anyone else who wants to try) can come to some understanding of it. I'll quote from some introductory essays written by the author and also by Paul Martin, who has spent some time getting to grip with Dick's ideas, and ask questions of the two essayists as they arise.

    These essays are available at http://paulandellen.com/ideas/tfor2.htm and are quoted with permission.


    Q1: How is 'self-consistent' defined here? Specifically, would quantum theory qualify as a self-consistent (mental or otherwise) model despite the contradiction at the heart of it?

    Q2: For 'explanation' my dictionary is not very helpful. It equates explaining with rendering comprensible. But the explanation of Nature given by physics is incomprehensible to us according to most physicists. Does this create a problem for the definition here or not? Is 'explanation' given a more precise definition later?

    I'm ok with the rest.

  2. jcsd
  3. Jul 11, 2006 #2
    Some clarifications needed, so we don’t go off in different directions.

    How is “knowledge” defined as used above? Should we assume the Justified True Belief (JTB) definition? (if so, then some of the above is incorrect).

    (4) presumes that we can arrive at the perfect explanation at the outset. This is not how progress in understanding is normally made – normally we start with one explanation and adapt and evolve it as more information is added (eg Newtonian Mechanics being replaced by Relativity) – that our explanations evolve and change as we understand more is something we should accept.

    Best Regards
  4. Jul 13, 2006 #3
    Sorry for dropping out for a while. We have a brand new grand daughter and there are more important things to do. At the same time, I kind of lost heart in the idea of reaching anyone when everyone seemed to want to understand the universe without understanding mathematics. Even Paul, who I know has a masters in mathematics, made the comment, "as far as we can get without 'going mathematical'" which bothered me quite a little considering the source. As you all should know by this time, I regard mathematics as a language constructed by people concerned with exact meaning; as such, I agree with Feynman that "mathematics is the distilled essence of logic. Essentially, Paul's comment had exactly the same impact on me as would the comment "as far as we can get without "being logical".

    Add to that the fact that another thread which I thought was at least developing a little interest on another forum encountered a rather extreme reaction and was terminated in a thread lock when I referred to their physics expert an http://www.scienceforums.net/forums/showthread.php?t=20615&page=3 [Broken]. Actually, his reaction was quite similar to most all professional reactions; I think they have too much invested in being right to think about any other possibilities.

    However, barring my declining interest in butting my head against a stone wall, I was surprised to find you all still at least a little interested in what I was talking about and thought I might answer your questions.
    As I said above, I regard mathematics as the only decently defined language. Mathematics consists of complex systems of defined objects and procedures which allow us to make large numbers of relational statements. Such a "mathematical" system is deemed "self-consistent" when the constructed statements within the system are not a function of the procedure used to arrive at the statement when multiple procedures leading to the same statement exist. If English were a well defined construct, then the concept self consistent would have meaning in English; however, in my opinion, English is far to vague to provide one with internal self consistency over any substantial range of logic.
    I define "An explanation" to be a method of obtaining expectations from given known information. That is my definition and I think it is quite precise. My entire presentation is based on that definition and my conclusions follow directly from that definition. If it is your intention to call my definition into question, I would appreciate your giving me an explanation which does not provide you with any expectations or a logical procedure for producing expectations which can not be seen as an explanation.
    As far as I am concerned, using that definition is fine; however, by bringing the question up you point out that you are missing perhaps the single most important aspect of the presentation: i.e., the deduction is not a function of the definition of "what is known" (the elements which go to make up C are intentionally undefined).
    You will need point out exactly what you are referring to before I can comment on that statement.
    I think that is a function of your point of view. From my point of view the assumption is that, if it is impossible to arrive at the perfect explanation, we will fail to find one: i.e., it can't hurt to look.
    And you are putting this forth as a reason for not looking at the big picture in a coherent manner? There are lots and lots of people attempting to understand the universe via the "normal" approach. I call it the "by guess and by golly" approach.

    My whole development began with an attempt to understand how the problem should be approached intelligently. I was actually quite surprised to discover that all the equations of modern physics were approximate solutions to my "fundamental equation". Clearly, since my development is nothing more than a tautology based on the definition of an explanation, it appears that the entire field of physics tells us nothing about reality. If their results are no more than the logical consequences of an internally consistent explanation how can there be any real content? Now that is an issue really worthy of serious discussion.

    I personally believe the resolution of this conundrum lies in essence of symmetry arguments. Paul has brought up Noether's theorem several times. Most scientists see Noether's theorem as the fundamental foundation of symmetry arguments but I think there is more there than they think. An excellent discourse on the common scientific view of Noether's theorem can be found on John Baez's website.

    Symmetry arguments are often referred to as the most powerful arguments extant. I have heard them referred to as the only arguments which can produce something from nothing. The general introduction to a symmetry argument begins by supposing a symmetry and then logically deducing the consequence. In general, little time is spent on the issue of a general definition of a symmetry. At least Baez tells us what he means by a symmetry: "Next, suppose the Lagrangian L has a symmetry, meaning that it doesn't change when you apply some one-parameter family of transformations sending q to some new position q(s)." He then progresses through a pretty standard deduction of the relevant conserved quantity.

    What I would like to point out is the fact that no mathematical deduction of any kind can produce a result which is not embedded in the axioms relevant to that deduction. That is, all proofs are tautological in nature as there is nothing in the result which was not stated in the original axioms: i.e., they amount to "saying the same thing twice", the essential definition of a tautology. To me it seems worthwhile to examine exactly how those conservation effects are embedded in the axioms. I think that the issue can be cleared up by examining the definition of symmetry carefully.

    Just for the fun of it, let's take shift symmetry as an example. Shift symmetry has to do with the case where the analysis of a problem cannot depend upon our selection of the origin. The symmetry argument then leads to conservation of momentum. The real problem here is that, if shifting the origin has no impact on the problem to be solved, then the solution of that problem cannot depend upon the selection of the origin. That being the case, if I give the problem to two different students (one of them could be God himself) if they can find a correct answer, their answers must be exactly the same no matter what origin I select when I hand them the problem. In fact, I should not even have to tell them what point I selected as the origin when I composed the problem.

    It should be clear to everyone that, under the description of the problem as I have given it here, any problem concerning the position of an object cannot be solved. It is absolutely necessary that the student make some selection of an origin before he can even express the position of the object. When he makes that selection, he is assuming something he cannot possibly know. But what he assumes cannot have any bearing on the solution thus the probability the object will be found at some position (x-a) (obtained by student number one, who's origin differs from mine by a) must be identical to the probability the object will be found at some position (x-b) (obtained by student number two, who's origin differs from mine by b). This means that P(x+c+d) must be identical to P(x+c) or the solution is an invalid solution (clearly c can be set to -a and d to a-b). As this relationship has absolutely nothing to do with what a or b is chosen, anyone familiar with calculus should see that the derivative of the probability with respect to the shift must vanish. (The derivative is simply defined to be limit, as d goes to zero, of the quantity (P(x+c+d)-P(x+c)) divided by d so it cannot be anything but zero.) All that is left is to define what we are going to call the differential. The concept "momentum" can be defined in terms of that differential and, by this means, one is able to obtain "conservation of momentum".

    So let's review exactly what has happened here. Essentially, the problem was unsolvable as given as any solution had to presume the existence of a meaningful (yet unknowable) concept called "the origin". Thus the statement of a symmetry is really a statement of an assumption in the representation of the problem which has no bearing on the real problem. The solution of the problem thus involves an unstated assumption. It is that assumption which is exactly equivalent to asserting that the specified derivative vanishes. As moving finger has stated many times, one cannot make any deductions without making some assumptions. What I have actually shown is that those assumptions must include assumptions which are equivalent to differential relationships.

    To put it another way, what I have shown (in my paper, http://home.jam.rr.com/dicksfiles/Explain/Explain.htm [Broken])
    is that you cannot solve the problem of explaining anything without making the assumption that my fundamental equation is a valid relationship; it is a pure consequence of your assumption of a basis of representation of your ideas. (Physicists have essentially made that very assumption and the assumption fundamentally constitutes the assumption that physics correctly explains the universe.) Now I find that a very interesting thing to think about.

    Have fun -- Dick
    Last edited by a moderator: May 2, 2017
  5. Jul 13, 2006 #4
    The position of a point, is as you say, dependent on establishing its origin.

    Saying the origin is unknowable, however, isn't necessarily true.

    The origin of all dependent points is an independent point with no location. It has no outside whatsoever (of or to itself). It is a literal point.

    Is this description logically accessible? Yes. Why? Because the point is invisible. We are allowed to look through it and see that it has no outside, and why. We can't, however, step outside of it to turn around and look.

    From the inside, however, we can see it has a quantity and quality. Its quantity is one and its quality is existence.

    Inside of a point with no location, there is only one possible literal postion – the center. The center is the only place, so it is everywhere.

    At the center is another literal point – zero. It has no inside whatsoever.

    Between these two literal points, which are both invisible and indivisible, is a relative "reality" of figurative points. These points "appear" to move from the center and take on dimension, but in fact, no matter how far they seem to move from center, they are always equally moving towards it, so they never actually do.
  6. Jul 14, 2006 #5

    Congratulations on the addition to the family.

    I take your point about mathematics. I agree it is a vital tool in studying the universe. However, not all of us can be mathematicians and I do not believe this entails that not all of us can understand the universe. For example, I have almost no understanding of Godel's mathematics, but this does not prevent me from having a reasonable understanding his results. Similarly, although I will not understand your mathematics, I may come to understand the form of your argument and your results.

    I wrote something earlier that I realised later you might misinterpret. Can I add then I have no interest in whether or not you are a crank, and certainly none in trying to prove it. I've no doubt at all that many people here think I'm a crank.

    I'm not going to object to your definitions. They are your definitions and as such are given. However, I would like to be clear about them, otherwise when I say 'explanation' I will not mean what you mean, which will cause chaos.

    Would you equate 'explanation' with 'theory' and 'description'?

    Is 'expectation' here equivalent to 'prediction'?

    I find the phrase 'given known information' a bit ambiguous. Do you mean information that is either known or assumed to be true?

    This may answer my previous question, but I'm not sure. Are you saying that your argument holds whatever the chosen axiom-set? (Does C represent the axiom-set?

    I couldn't agree more, although I get very confused when I consider this issue. It seems to relate to a recently published article (in New Scientist if I remember right) mentioned on another thread, in which the author argues the laws of physics are the same as the laws of nothing.

    That seems true to me.

    What about reductio proofs like Euclid's that there is no highest prime? In other words, what about proofs of the falsity of the axioms?

    Hmm. It probably doesn't matter here but I think there are exceptional cases in which this statement is not true. I certainly wouldn't want to move on leaving this as an assumption if it is going to be important later.

  7. Jul 14, 2006 #6
    My sincere apologies. I did not mean to bother or disparage you. I agree with you that we can't really understand reality without understanding the mathematics, but on the other hand, few of you are equipped to understand the mathematics. The rest of us have to do the best we can by understanding as much math as we can, and then trying to remain logical and consistent when we use language. Given the nature of language, this can't be achieved completely as I think you would agree.
    Sorry about the impact, but I think that the only change I would make would be to say "as far as we can get without being "completely" logical. I just don't think you can be rigorous in natural languages. Even in mathematics, I think rigor is achieved only with great difficulty.

    I applaud your approach of using mathematics to derive your result. That is why I insist on calling it a theorem. I am convinced that it deserves either recognition or serious refutation. It is either correct or incorrect and I wish someone qualified would confirm or deny its correctness.

    Warm regards,

  8. Jul 14, 2006 #7
    while almost everybody will agree that mathematics is of the utmost importance in studying reality i would like to remind us that the source of inspiration for the new direction in which this great investigative tool navigate comes harldy ONLY from mathematics/physics. This is especially true when we talk about physics and reality.

    Most of initial "gut" intuition (or whatever one wants to call it) to start working on certain problem certain way comes from metaphysics/philosophy.

    We may in our effort to root out any trace of metaphysics from science deprive ourselves of our very important source of inspiration. Even more so, there is great number of assumption in physics which when scrutinized do not come from known physics but from metaphysics. (a great book: "https://www.amazon.com/gp/product/1...26529/ref=sr_1_1/103-1867651-4576662?ie=UTF8"")

    So while i agree (as physics grad student) the crucial importance of mathematics in study of nature, i do not agree that its the only language to convey our understanding of it. Lets just look how we learn from childhood before we get to the level of mathematics of Ph.D, ie, the power of metaphors in study of physics and math......,(for example)

    Last edited by a moderator: Apr 22, 2017
  9. Jul 14, 2006 #8
    In my of thinking anyway, it might be more accurate to describe it as the figurative and the literal.

    Very important distinction in any discipline.
  10. Jul 15, 2006 #9
    I agree. I would not advocate eliminating metaphysics from science. You are correct that it provides us with inspiration to ask the right questions.
    I think you have the emphasis backwards. I think that our child-like wonder at nature, our experience at living in the world, and the reflections of metaphysical thought are all of crucial importance to the study of nature. But when it comes time to carefully formulate statements about how nature behaves, and in particular when it comes time to convey our understanding of it to others, then mathematics becomes crucially important. I think there is no other useful way.

    Poets and artists, for centuries, have tried to convey to others their understanding of nature. But their attempts, when compared against those of the scientists of the past two or three hundred years, have been nearly useless in solving any human problems.

    Warm regards,

  11. Jul 15, 2006 #10
    I think that very much depends upon your definition of "understand" and that is another issue which could require a lifetime to resolve.
    No, I don't think so. As I said, I define "An explanation" to be a method of obtaining expectations from given known information. A theory seems to qualify as such a thing as it provides one's expectations; however, the common concept of a description seems to be little more than a list of information: i.e., a way of representing something you think you know ("given known information").
    A "description of what you expect" seems to me to be quite similar to "predicting what you expect". The only real difference between the two concepts seems to me to be the issue of solidarity. "Predicting what you expect" seems to imply a static assertion whereas the idea of a "description of what you expect" implies a more dynamic assertion: i.e., your expectations can be seen as changing from moment to moment. But, as I say English is a rather vague mechanism for communication and I can not be at all sure that the same ideas cross your mind as cross my mind when I hear those words.
    Except for the mathematics presented (which I regard as a mechanism for communication established by others having nothing else to do with my presentation) C represents everything known which is absolutely true. D represents everything one thinks is true which may not be true. C + D represents everything thought to be true. As such, they would seem to include any axioms presumed to be valid. They are part of your explanation are they not?

    As I have said many times, there exists no way of separating C from C + D other than its failure to be yielded by the explanation: i.e., things which are eliminated via invalidity of expectations are certainly members of D and never members of C. The new explanation must continue to explain all of C. The fact that Solipsism can not be invalidated is no more than the fact that one cannot prove C does not vanish; however, it is just as true to state that you cannot prove C vanishes so, a rational statement of the circumstance needs to include both possibilities. That is exactly why the set C is included.
    Now, from my perspective, your confusion arises from your attempt to understand without understanding mathematics. Sans mathematics, your logic can carry you no farther than a few meager steps. You need to look at what I wrote to moving finger as to the difference between "logical thought" and what I like to call "squirrel thought". "Squirrel thought" (analogous to intuition or Zen) provides one with rational steps when the information relevant to the step is too complex to be processed logically (which is the most common situation one runs into).
    The fact that a set of axioms are false is contained in the set of axioms!
    It gets quite important later but not in the way you and/or moving finger comprehend the issue. We will perhaps get to that issue sometime later.
    Paul, you owe me no apologies and I did not take it as being disparaging in any way.
    I agree with you completely; that's why I always doge the issue: I will leave it to others much more brilliant than I. After all, I really don't use much difficult mathematics. None of what I use goes even close to the bleeding edge of mathematics development. Most everything I use is in common usage throughout the hard scientific fields. As I say, I use it for exact communication and little more.
    As I said to Canute, that depends very much on your definition of "understanding". If the only purpose of your "understanding" is to provide you with direction when the information relevant to the next step is too complex to be deduced logically from your circumstance (i.e., a rule of thumb useful to your current situation) then "gut" intuition or some convenient metaphor may be the most valuable thing you have. That's fine for a working system to obtain useful results applicable to a given circumstance but I certainly would not set that definition equal to "understanding the universe".

    The philosophical concept of "understanding the universe" is unachievable in the absence of mathematics as without mathematics, the extent of your logic is limited to the number of steps you have time to list and the universe is far to complex an entity to even begin to compile the relevant information. A philosopher without mathematics is analogous to a quadriplegic wanting to compete in an Olympic 100 yard dash, he can't even get out of the starting blocks.

    I don't think anyone here has any real concept of the complexity achievable from very simple propositions via what is commonly referred to as "emergent" phenomena. Only mathematics can easily develop such results: take a look at the Mandelbrot set. (Google Mandelbrot for a lot more information.) I have a rather simple geometrical proof which displays some rather astounding (and unbelievable) "emergent" phenomena which I am tempted to post. Next week I may just write it up for the fun of it. All you need to know is a little geometry and common trigonometry but you have to be able to understand and follow logic.

    Have fun -- Dick
  12. Jul 15, 2006 #11
    Let us look at it from this view. i can have dr. hawking and to him similar quenching math that is beyond me even to begin to phantom for me coming with some conclusions which (like 11 dimension and other "unbelievable" stuff) are not accessible to 99% of population living. Now, what good is it, if the 99% of population simply cannot appreciate, or even begin to understand it? Would not the 99% of population create their own understanding of universe/reality? Sure the would, and they do. 40% of US believes that earth is 6000yr old.

    Plus, scientists are dependent on funds. Well, what business is gonna support science which for them is magic? Just like i would not fund magic projects that would be telling me that they are really how universe works, the same goes for ordinary ppl who perceive it the same way.

    I think we got the point im trying to stress here. While we need precision of math to investigate universe, we have to be able to find a language and forms to convey the information to the 99% of ppl. Otherwise, we just have white coat "crazy” scientists who throw at themselves some Masonic jargon which is useless to rest of the world.

    As one may see, human begins have different interests and talents. If i spent my life time crunching math i must be able to intelligently narrate it to a poet or musician. Science should create bridge, not border around different group of ppl that will feel, naturally, hostility due to misunderstandings in their views about reality. Science (math) has its limits (talking about physical world), so does poetry, but those are two different domains.

    To summarize this, understanding i mean to talk about finding of science in other than math language, or approach ppl on their level of math thinking. Being falsely proud or rigid in thinking in one way limits our own understanding.
  13. Jul 16, 2006 #12
    That was rather unsubtle of you, Dr Dick. That’s not normally like you, is it?

    Then it follows that your statement “the future is completely unknown” is false. I can justifiably believe on July 4th that the statement “the sun rises on July 5th” is a true statement, and indeed “the sun rises on July 5th” may be a true statement, in which case by definition (the definition you accept) I know on July 4th that “the sun rises on July 5th”. Hence, the future is not completely unknown.

    See above.

    Your latter statement “if it is impossible to arrive at the perfect explanation, we will fail to find one” is an analytic truth, but this is NOT the same as “we must have the perfect explanation at the outset”.

    In other words, “having an imperfect explanation to start with” is compatible with “arriving at the perfect explanation in the end”. But “arriving at the perfect explanation in the end” does not entail “having a perfect explanation to start with”.

    Thus imho your (4) should read :

    (4) The perfect explanation can not change as more information is added. That is, the "perfect model" must be valid at all times past, present and future. But in striving to arrive at this “perfect model” we may need to pass through many “imperfect models”.

    No, I am not putting this forth as a reason for not looking at the big picture in a coherent manner. I am saying that the ultimate goal may be the “perfect explanation”, but our journey towards that goal will entail working with imperfect explanations on the way.

    Agreed. This is the definition of an analytic truth. All proofs by deduction fall into this category. Hence my point that we must first make assumptions before we can arrive at any meaningful understanding or meaningful explanation.

    It seems to me that all this shows is there is no such thing as an absolute position in space (which truth is actually a tautology). All positions are measured relative to some arbitrary (assumed) coordinate axes. Your conclusion that P(x+c+d) = P(x+c) is based on an argument with an invalid inference (the inference confuses two different and arbitrary coordinate axes, one x axis defined by you and one x axis defined by the student, and assumes they refer to one and the same axis), thus the argument is unsound.

    Best Regards
  14. Jul 16, 2006 #13
    Yes. But this comment applies equally to a mathematical understanding. Nobody has yet shown that mathematics provides the best way to understand the universe, or even that it is possible to understand it in this way. But this is an irrelevant issue here I think.

    That's fine. I will treat an explanation and a theory as the same thing. (However, I'll only do this here, because to me they are not necessarily the same thing.)

    Ok. I'll take expectation and prediction as equivalent.

    Fine. I'll assume C + D = axiom-set.

    Here I strongly disagree. However, I don't think this disagreement matters here, not yet anyway.


    If you are saying that C cannot include the truth or falsity of solipsism then I agree, It seems a very good point imo. (Although there are in fact three possibilites for solipsism, true, false and neither).

    No, this is not the case. It is not the mathematics that is confusing, it's the issues. Mathematics is an example of formal reasoning, not the only way of doing it. But again, this is a side issue.

    Sorry, but this remark is based on complete misunderstanding of Zen etc. But yet again, the issue is not important here.

    Oh yes.

    In your opinion.

    Except you, presumably. My feeling is that emergent phenomena are only complex if one does not understand the simple proposition from which they emerge. But again, I'm quibbling, this seems irrelevant to your mathematics so I'll back off.

    I'm ok to move on. Shall I post the next essay?

    (I get the impression that your proof is of the fact that the mathematical scheme of physics does not refer beyond itself and is thus tautological. Is this roughly it? If not just say no, I'll correct my impression as we go).

  15. Jul 16, 2006 #14
    Could you give us examples of these exceptional cases (apart from cases of tautology/analytic truths)?

    Best Regards
  16. Jul 17, 2006 #15
    Well, sometimes it is. I will admit that I am an opinionated old man and I sometimes get a little short with people who can't comprehend an alternate perspective on things; particularly when those people have sufficient education that one would expect a little more from them. One of my favorite quotes (it fact, it is framed over my desk) is: "Knowledge is Power" (in large capital letters) and then, is small letters, "and the single most popular abuse of that power is to use it to hide stupidity". Another framed quote I have consists of the three lines, "You can fool some of the people all the time and (new line) you can fool all of the people some of the time (new line) but you can't fool all of the people all of the time" with a red line through the third line and the comment "that requirement is never necessary!"

    In general, I tend to rub authorities the wrong way. I believe I am personally responsible for the authorities on this forum closing down the category thread "theory development". The people in charge actually used to refer to it as the "nuts are us!" forum (they closed it to outside posting and started using it as a place to move "crank" posts then finally moved it to the archives). That is where I first got the idea of writing that paper "A Universal Analytical Model of Explanation Itself". Take a look at the thread I started Aug 15, 04: "Exactly what is theory all about?"
    Ah, you and I are talking about two entirely different things here (again, problems with the vague nature of English). I thought you were referring to the definition of C+D not to my definition of time. My definition of time is simply that the past is what you know and the future is what you don't know (defined in terms of C). That has nothing to do with "justification". The only way which C differs from D is that C will absolutely never turn out to be wrong (see my comment to Canute on Solipsism). Again these are analytical truths, not hypothetical axioms. I don't think you can prove "absolutely" that the sun will rise in the future; there are lots and lots of scenarios (all quite possible circumstances) which would result in that statement being false.
    Well, as I remember, I never said the second. All I said is that I was looking for a route to it.
    So what! I don't comprehend your complaint.
    First, I should comment that I didn't write that. It's Paul's attempt to explain what I am doing and he seems to be a better communicator than I so I don't generally try to change his presentations. But, what is important to me is to get straight to the most important issues. I think you are merely bringing up the way "rules of thumb" are generally acquired: the issue of obtaining useful results applicable to a given circumstance. I am interested in cutting to the meat of the problem and not really concerned with the "guess and by golly" aspects of the common course. They can be seen as ways of cataloging what we have come to think we know.
    Then you don't agree that analysis of where we want to go is a worthwhile endeavor?
    Now that is where I would like to go. The problem is that I suspect you and I have quite a different concept of the word "meaningful". Again, I think the most worthwhile thing I might do is present that geometrical proof I commented about earlier; however, to do so will take me a little time and I am kind of busy with other things at the moment.
    No, I think you have missed the point entirely. The point is that they must refer to an axis before they can answer the question. This is an assumption which must be made prior to solving the problem and the solution of the problem cannot depend upon that assumption a subtly different fact. You might take a quick look at another post I made a year ago on the same subject (a post to one "saviormachine". Perhaps you might get a little better comprehension of what I am talking about.
    But at least I can expect better understanding of what I say than I can if I use English.
    As you already know, I complain almost daily on the vagueness of the English language so I won't argue with you; however, I am curious as to what you think the difference is.
    Now here I have to disagree with you. C+D being "everything you think you know" certainly cannot be constrained to an "axiom-set" as the concept is simply too constrained to express "everything you think you know" (unless you are a very strange individual).
    No, I think it is a very serious issue. It appears to me that you do not understand the nature of the sets C and D. All I am doing here is separating "what is absolutely true" from what you think is true which is only a requirement of your explanation. Unless you can show me a way of proving every thing you think you know is either "absolutely true" or "absolutely not true" (which, by the way, would be a proof that Solipsism is false) there is no way of separating C from C+ D.
    Then just take "Zen" out of the list. I am trying to point out the difference between logic and the other way we come to think we know things.
    Certainly; and, as I said to moving finger, I am an opinionated old man.
    I really will have to set up that geometric proof.
    Sure, why not?

    Have fun – Dick
  17. Jul 17, 2006 #16
    Oops! Hi Dick,

    You were a little too hasty.
    MF was referring to point (4) in
    which was written by you and unchanged by me. On my website I identified which of the five attempts were written by me and which by you. You helped me edit and change mine, but I didn't change yours at all.

    Warm regards,

  18. Jul 18, 2006 #17
    I expect this is an irrelevant issue, but what I meant was that a theory would be based on one or more assumptions, whereas an explanation may not be. But we can forget this, I'm going with your definitions.

    Ok. But if ones explanation is derived from C and D then would these not constitute ones axioms?

    If your requirement is that C be demonstrable truths or falsities then I agree. But knowledge is not usually defined in this way. As it is not possible to demonstrate that a proposition is absolutely true or false it seemed to me that by your definition C & D may as well be the same set.
  19. Jul 18, 2006 #18
    "The vagueness of the English language" might be contingent upon the words one chooses to use, based on the "attack" one chooses to take.

    If my memory serves me, it was John Archibald Wheeler who said "a complete theory might boil down to understanding the English language". (paraphrase)
  20. Jul 18, 2006 #19
    Sorry Paul, if you say I said exactly that then I must have as I certainly wouldn't argue with it. My comment to moving finger was more to the point that the quote is on your web site and not subject to my editing (I didn't realize it was a direct quote). Nonetheless, I will comment to moving finger as to exactly why that is stated the way it is.

    "4) Finally, the explanation can not change as more information is added. That is, the "model" must be valid, no matter what the future consists of."

    If that fact is not true, then we have failed to find a perfect explanation; it's as simple as that! :biggrin:
    The assumptions lie in D: i.e., my definition of "an explanation" includes the existence of assumptions. Again, one could admit the possibility that D could vanish (just as Solipsism presumes C vanishes) but, if D vanishes then only C remains and you are "all knowing": i.e., everything you think you know is absolutely true and nothing you will ever learn will violate your expectations: i.e., nothing will ever surprise you or change your opinions of anything. It seems to me that would be a "valid Religion": i.e., as unlikely as Solipsism. :wink:
    I think you would have to define your concept of an "axiom" for me to understand what you are trying to say. If you want to define an axiom to be "everything which you believe to be true" then I would have to agree with you but I don't think that is the common concept of "an axiom".
    First, I do not require that C be demonstrable truths or falsities: I simply define it to be that portion of "everything which you believe to be true" which is actually true; a subtly different thing. I do that for a reason which becomes very important down the line. Though you can not tell the difference between them they nonetheless obey a subtly different constraint. Since C constitutes what you actually know of the truth, all the elements of C must be available to your explanation and explained by that explanation. D, on the other hand, being a fictional construct (composed to make your explanation work) need not be so directly constrained: i.e., to have the existence of the elements of D implied by the explanation is sufficient. o:)

    Now I know you didn't understand that and I apologize. The issue is directly related to "Sub Problem number 1" in my presentation of http://home.jam.rr.com/dicksfiles/Explain/Explain.htm [Broken]. The tau axis was introduced solely to make sure that a representation of the elements of the explanation as points on the x axis would not limit expression of those elements. The elements of D need not be so constrained as they are fictitious constructs and need only serve the purpose of "making your explanation work". That difference has very important consequences when one goes to solve my fundamental equation; consequences having to do with evaluation of the impact of the Dirac delta function.

    Have fun -- Dick
    Last edited by a moderator: May 2, 2017
  21. Jul 18, 2006 #20
    That is correct, I cannot prove absolutely that the sun will rise in the future. But knowledge is not about “absolute” certainty, is it? Even some of the things we think we know about the past may (or even do) turn out to be false (hence not knowledge after all). The belief that we possess knowledge is a fallible belief, no matter whether that belief is about past or future events. Granted our inductive inferences about the past often tend to be more accurate than our inductive inferences about the future, but that’s as far as it goes. It does not follow from this that the future is “completely unknown” as you claim.

    Are you now saying that you do not agree with the JTB definition of knowledge? If so, may I ask you to define just what you do mean by “knowledge”?

    I think Paul has answered this one for me.

    Why would you think that? We seem to be talking past each other. I agree that knowing and analyzing where we (think) we want to go is “good” – but I believe that getting there will be in incremental steps – and that in doing so we may even adjust the idea of where we (think) we want to be.

    Indeed we might, because meaning is in the mind of the “meaner”. But explanation without a “meaner” is meaningless.

    I agree they must refer to an axis – but not to the same axis. This is the point. In your analysis you seem to treat them as if they both refer to the same axis.

    Best Regards
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