This is in reply to our correspondence below:
***All I can say is that you sure have a compulsion to keep attention to peripheral issues! Reminds me of something Henry Ford said: "thinking things out is very difficult that's why most people don't do it!"***
I just reply to the issues as they are presented. I'm letting you control the flow of the discussion as you lay out your 'case'. I believed you made the argument about cataloging data, and this is where we had apparent disagreements.
***H: Yes, misunderstanding is an error, but not all messages are equal in terms of the possibility of them being misunderstood. Appearance is important in establishing confidence that a message was correctly understood. D: One of the fundamental issues of my position is that it is an *error* to believe that your confidence has any bearing on the issue of whether or not an error exists! It is always possible you have been stupid maybe you should take that into account in your thoughts. The real issue here is that I know how to do that and you do not.***
Hmm... You think it is an error to believe that confidence has a bearing on whether an error exists? How confident are you that you are correct on this position?
***H: What about Thales? D: So what about Thales? Clearly he didn't comprehend the problem I have solved (if he had, the whole scientific community would be aware of it). I have no idea what he did nor do I have any interest in it and I am certainly not going to take the time to find out. What I have done stands on its own merits and makes no claim on any authority other than the accepted rules of mathematics.***
Mathematics is a game (as Wittgenstein said). Mathematics says nothing about reality, so I don't see how you can think that mathematics is any authority on this subject manner. Where in mathematics do you have definitions of terms like: reality, senses, mental image, observation, etc.? This isn't mathematics.
***H: How do you know what you consider important is really a valid category to distinguish as meaningful D: My category is "information"! Now, you are going to tell me that "information" is not a meaningful category??? If information is not a meaningful concept, please explain to me what you consider to be meaningful!***
Okay, let me restate it. How do you know the terms that you consider important in your model are a valid category to distinguish? You are assuming that you have attached the right meaning of the variables in your equations (starting with 1.1, 1.2, etc). However, how do you validate those terms?
From what I gather in your paper, you validate the method by the end results (i.e., you have obtained many of the equations used in physics). But, this is not real validation (in a scientific sense) since you could just as well argue that the left side of equation 1.1 [X(n)=f(x(1), x(2), x(3),...,X(n-1)] means every possible hiccup. We could, I think, take all of your equations and reinterpret the meaning of every variable. What would stop us? What would restrict the meaning of any one particular variable? Yet, we would get the same mathematical results with a totally different meaning to your model.
***H: I am skeptical of any attempt that tries to be more fundamental than pragmatism. D: I have no idea what you have in mind! You are implying that my approach is not pragmatic! Either you do not understand what I am saying or you are operating with a definition which is not consistent with the common interpretation of the word. For that reason, I looked up "pragmatism". 1. Character or conduct that emphasizes practicality. 2. A philosophical movement or system having various forms, but generally stressing practical consequences as constituting the essential criterion in determining meaning, truth or value.
3. Archaic: a. officiousness; meddlesomeness. b. dogmatism; arrogance. This lead me to look up practical which appears to revolve around the idea that "it works". Certainly, since I am trying to show you something which (outside everyone's expectation) "works", I cannot comprehend why you regard what I am doing "more fundamental than pragmatism", unless of course you are using the word in its archaic sense.***
Pragmatism, as a philosophical system, is summarized in definition (2). It isn't as simple as a model 'working' (e.g., providing good math results), it is a matter of what the model actually does. For example, from a perspective of the worth of science a purely pragmatic view of science is the technology it provides. In terms of scientific research, the pragmatic view is more often called instrumentalism.
Your model is not pragmatic (or instrumentalist) since has no pragmatic value. It doesn't do anything. It merely states what we already know, and that's it. Nor does your model acknowledge where we really come to know what we know. For example, in your paper one of your opening suppositions is that: "In this presentation, I will attempt to construct a mental image of the universe without presumption and, thus, discover what it is we know and what part of what we think we know which is myth."
From a semi-pragmatist such as myself, this statement is off-base. We 'know' as a result of the benefits which are paid to those who accept certain concepts as true. The mental image of the Universe we hold is an accumulation of our accepting a whole series of ideas that benefit us. Like Pavlov's dog we are forever locked onto those schemes and way of thinking. You cannot construct a mental image non-tainted by those experiences that make us who we are. The same is true of math, you cannot eliminate the 'epistemological trail' of mathematicians that led them to the analytical 'truths' of math.
***H: Most intellectuals know the history of foundationalism. It has failed miserably over the course of the centuries and every attempt to revive it has also failed. D: ERGO all attempts will fail!! Is that the extent of your *proof*?***
No, the failure of foundationalism is centered around where knowledge arises. Where does knowledge arise? Why is it that we consider something as true? If you attempt to answer that question you will see the failure of foundationalist views. Mathematics is also not foundationalist as you will see if you ask the same question.
***H: I am not saying that you have cataloged errors, I am saying that whatever you catalog is based solely on appearance. If you catalog an appearance, then your cataloging is only as valid as the appearance of the thing in question. D: So something appears to be information and it turns out in the end to be "not a valid appearance"! Could you clarify that a bit for me?***
I'll give you an example. You defined observation to be 'a member of the set of examined subsets of reality'. You defined reality as a 'set of numbers'. So, an observation is 'a member of the set of examined subsets of a set of numbers'. Well, what if that appearance is wrong? What if it turns out that an observation isn't a member of the set of examined subsets of a set of numbers? What if it is actually a member of set of examined subsets of all that is 'out there'? In that case, what is 'out there' 'set of numbers'. How do you *know* that what is 'out there' is equal to a set of numbers? You are presupposing based on the appearance that everything that can be observed can be numerically represented. This *might* be a false presupposition.
***H: You are not depending on experiment, so the question becomes how do you know you have properly cataloged a valid appearance? D: See, right here you have the whole issue confused! I am not proposing to explain anything without experiment! All I am doing is organizing my thoughts so that when I do go to "examine the Universe", I do not make the insipid error of thinking something is real when it is in fact nothing more than a direct consequence of my definitions! Let us think about things a little bit before we go charging off with some half-cocked hypothesis!***
Okay, how do you know your organization of thoughts is a correct way to organize as to produce a correct interpretation of the Universe? What makes it true? Science says that experiment is what mostly validates the title of 'scientific truth'. What makes your model true? (and don't say math because math doesn't define terms like observation, time, reality, etc - these are all non-mathematical terms).
***Now, just because I happen to have discovered that most of what the scientists think are "laws of physics" are no more than consequences of their definitions, you presume I am saying experiment is unnecessary! I am not saying that at all! What I am saying is, let us first find some experiments which prove something!***
I'm not saying that you think experiments are unnecessary. I'm only saying that you don't have experiment to validate your choices used to give meaning to your equations (e.g., 1.1, 1.2, 1.3, etc).
***You are clearly confusing the issue of "definition" and "assignment". As you point out, the scientific community has done a very poor job of "defining" time ("It is one of the perplexing mysteries of science") but "assignment" of the concept absolutely permeates all the sciences. Now, I define it very specifically. It is almost beyond comprehension that something defined in such a simple way could be successfully assigned in a manner absolutely identical to theirs with no conflict with any conceivable experiment!***
Meaning is use (also something that Wittgenstein would say). When you use a assign a term to a variable you are implying a certain meaning (or definition) to the term. When you specify an assignment for time you are doing so in an unconventional manner. I am not concerned about your selection, I am concerned with the validation of that selection. Time is used in many different assignments within physics, but they are all acceptable (e.g., entropy, dimensions, etc). These usages are validated by experiment. You don't have experiment to validate your usage, so what does this validation in your selections?
***H: No, my position is that foundationalism is completely off base and that there are very general reasons why this is so. D: No one has ever managed to establish a valid general foundation for examining the Universe therefore it cannot be done! Reminds me of a joke. A businessman and an economist are walking down the street. The businessman says, "hey look, there's a twenty dollar bill in the gutter!" "No", the economist answers, "it cannot possibly be there, as, if it were, someone would have picked it up!"***
No, foundationalism isn't dead because of lack of effort, it is finished because it needs itself to substantiate itself. Unless you have a foundation you cannot establish a foundation, but it is the foundation that we are trying substantiate. We see this in your model in what substantiates the meaning of your variables. You are basically asking for people just to believe you. As I pointed out above, I can use the same equations and input totally different meaning into those variables. Nothing in math forbids it. So, where is the foundation?
***H: If you rely on mathematics, then how do you know that mathematics is merely a human invention? What if our evolution were different, how do you know that our mathematics wouldn't be different? I believe that mathematics couldn't be different for an alien species, but heck, mathematics was different between the Babylonians and the Greeks. D: Now here, your definition of "mathematics" and mine are very different (since you have made it clear in the past that you disliked my definition). As I said in my paper, I believe "mathematics" could be defined to be the creation and study of internally self consistent systems. If one takes that to be the definition of mathematics then there is no "different" mathematics, only mathematics you are not yet familiar with!***
Gödel's second incompleteness theorem shows that you cannot prove the consistency of axioms of a number of branches of math (e.g., set theory). So, you cannot even show that the body of mathematics is consistent (if you could, then according to Gödel they wouldn't be consistent).
***H: When we make assumptions based on appearances D: You are the one who keeps wanting to make assumptions based on appearances, not me! As I said in my paper, I don't want to make any assumptions (other than the fact that mathematics is valid - as defined above).***
Time, reality, observation, pattern, etc. Your assignments of variables to these concepts are all appearances. That's okay as long as you find a valid means to validate those concepts. In science this is accomplished by experiments. What does it in your model?
***H: not ontological proof of anything D: Tell me Harv, do you have any ontological proof of anything? I would like to see it just for the fun of it.***
No, I don't. But, I admit it openly and am a fan of pragmatic approaches. I openly admit that we come to know about the world through the benefits paid to those who make the most successful choices.
***So I return to the original issue: I would like to show you a way of cataloging arbitrary communications which yields some rather astounding relationships (which are true "by definition" when the information in the communications is so cataloged). In order to show that it is possible for those relationships not to be true, you need to show that there exists a communicable concept which cannot be represented as I propose to represent it.***
Not so. I am not the one with the burden of proof. The burden of proof is on the one wanting to show that something is true. You wish to say that certain relationships are yielded by cataloging arbitrary communications, but you have not demonstrated that your meanings are exclusive to the terms you used in your mathematics. You need to prove that no other meaning to a term is applicable, but how could you do that without violating your thesis (that you assume nothing in your accessments)? And, most importantly, you haven't answered the question as to why mathematics limits what is actually possible in the world.
Warm regards, Harv