What can we know of reality?

Doctordick · 12-01-2007

Quote:

Originally Posted by Majik

You seem to be trying to make a distinction between ontology in the left hand and epistemology in the right hand.

Yes and No. I think you are putting the emphasis in the wrong place. The epistemology (the solution to understanding reality) is indeed in my right hand but so are the definitions of the ontology behind that epistemology. Think of it this way: I do not know what the solution is so, as far as I am concerned, when I go to consider that which is in my right hand, I must include absolutely every possibility. When I go to do that, in the abstract of course as the number of possibilities could be infinite, there are some subtle things I can be quite sure of.

First of all, each epistemological solution must be based on some ontology. Now, if I have the solution, then I also have the definitions of the ontological elements underlying that solution. So, if I look at all the possibilities, each one has embedded within it a finite set of ontological elements. (They must be finite because we cannot base our solution on an infinite quantity of information as we will never finish acquiring an infinite amount of information.) So, since the number of ontological elements is finite, the process of labeling them can be completed. That labeling constitutes an explicit ”what is”, is “what is” table associated with the specific epistemological solution being analyzed.

At this point, if we look at that entire collection of ”what is”, is “what is” tables (again, in the abstract as the number of possibilities could certainly be infinite) we will most probably find that there are a number of ontological elements which are required only by certain epistemological solutions. For example, the epistemological solutions of the form, “it's what the gods want” have ontological elements consisting of “gods” which are not necessarily embedded in some of the other possible epistemological solutions. Remember, these epistemological constructs are no more than mechanisms which yield our expectations and there is no constraint that requires our expectation to be correct. On the other hand, we can require they be flaw-free: i.e., that no known information invalidates them (the only reason I throw that in is because it is a pure waste of time to consider internally invalid epistemological constructs).

Now a very important issue here is that these epistemological constructs were created to “explain” reality. That presumes there is something to be explained: i.e., some of those ontological elements (the fundamental noumenons) must exist in every flaw-free ”what is”, is “what is” table. Those elements constitute the undefined ontological elements in my left hand. They are undefined because I have no specific epistemological construct in mind but they, nonetheless, stand as the basis for every possible flaw-free epistemological solution. It follows that reality, truth, whatever you want to call it, sits in our left hand and not in our right hand.

Quote:

Originally Posted by Majik

But what if our epistemology were derived solely from inescapable logic? Would we really then need to even look in our left hand?

You should rather say, “would we need to look in our right hand?” The answer would then be no, because we would understand the epistemological construct which provides our expectations. But our expectations are based upon our past (what we know) which is what we have in our left hand. That is why I expressed the opinion that what we are dealing with here is essentially a data compression mechanism. Do you realize just how much information is embedded in the concept “a college education”, “big” or say “difficult”. That information is not lost if we were to simply refer to those concepts as “concepts 234, 900 and 12”.

There is an interesting article in the December issue of “Scientific American” entitled “The Semantic Web in Action?

Quote:

... a common language for representing data that could be understood by all kinds of software agents: ontologies - sets of statements - that translate information from disparate databases into common terms; and rules that allow software agents to reason about the information described in those terms.

The whole purpose here is to generate expectations consistent with the entire body of information available. The major problem I see is that they want the “common terms” to be English expressions. A typical American approach: “let the other guy learn English”. Perhaps English is a far to limited ontological set to express all the information in these “disparate databases”. They need software which will generate the simplest set embodying the relevant information; a mechanism which allows the software agents themselves to develop their own representation of the pertinent concepts from the available information. I feel it will only begin to grow, “in a grass roots fashion”, after that piece of software is written: one needs the right data compression mechanism.

Quote:

Originally Posted by Majik

Would we really need to do experiments? If physics were derived from logic alone, wouldn't we "know" without even looking what IS real?

Without the basic information we couldn't “know” anything. All I am doing is pointing out that there exists some rather simple constraints on any flaw-free epistemological construct and those constraints should explicitly be taken into account.

Have fun -- Dick.

Majik · 12-01-2007

If any epistemologyical theory can only predict the probability of ontological data, then ontology will always be separate from epistemology. And only after observing many ontological data will we be able to confirm that the epistemological theory was correct. So the question is, can a theory predict with 100% certainty?

Doctordick · 12-02-2007

Quote:

Originally Posted by Majik

If any epistemologyical theory can only predict the probability of ontological data, then ontology will always be separate from epistemology.

What you miss is the fact that the epistemology must identify the ontological elements it is referring to in those predictions. Thus it is that the “definitions” of the ontological elements are embedded in the epistemology itself. In the absence of an epistemology, they are undefined.

Quote:

Originally Posted by Majik

And only after observing many ontological data will we be able to confirm that the epistemological theory was correct.

You can never confirm that an epistemological theory is correct; the only thing you can confirm is that it's predictions are consistent with what you know of the past. That is why I introduced the term “flaw-free” meaning that there exists no information that you are aware of which invalidates that epistemological construct. That does not make it true; all it means is that you do not posses any information which is inconsistent with it. Note, the moment you perform an experiment, that experiment lies in the past: i.e., it becomes part of the known information and, with regard to the current past (which includes that experiment) that epistemological construct is either still flaw-free or it is not. If it is not, then it is no longer a flaw-free epistemological construct. The predictions you are referring to (predictions which you credit with “confirming the epistemological theory”) all lie in the past. Each specific time in that past can be seen as a hypothetical present and, were the outcome of the experiment not known, one can ask, were the expectations (what you are calling "the prediction") consistent with what occurred. Consistency in that sense is what I call flaw-free.

Quote:

Originally Posted by Majik

So the question is, can a theory predict with 100% certainty?

Now right here we get ourselves deeply embedded in the ambiguity of the English language. Just exactly what do you mean by “predict with 100% certainty”? Do you mean that the expectations expressed by the theory are consistent with the past and future outcomes? From that perspective, any epistemological construct which yields the answer “the outcome is totally uncertain” is 100% consistent with any outcome. For example: "it occured because the gods wanted it to happen" is perfectly consistent with any outcome.

Thus it is that concern with never being wrong is not the central issue here. Rather, we are more concerned with the value of the prediction than we are with its infalability: i.e., does it provide us with any control over our personal future; that is, are those expectations of any benifit to us. We should never consider our expectations to be exact, that is why expectations should always be put in the form of probabilities. To do otherwise is to assure we will be wrong.

Have fun -- Dick

Majik · 12-03-2007

Quote:

Originally Posted by Doctordick

You can never confirm that an epistemological theory is correct

Actually, I'm not so sure this is correct. If a theory (epistemology) can be derived from some kind of logic alone, then it is not possible to deny it's correct. But what kind of logic would do this. I realize this opens up a whole new can of worm, but I've been working on such a theory. I wouldn't call it completely proved yet, but I think it is close enough to merit some serious attention.

Starting with the premise that all facts in realtiy (not concerned here with exactly what those facts are) are consistent, meaning no fact proves any other fact false, it is possible to derive the Feynman Path Integral formulation of quantum mechanics.

See my home page in my public profile.

The question here is whether this kind of derivation is actually part of science. Or is it more philosophy? I mean if such concerns yield the laws of physics, then physics is no longer based on observation but is based on phylosophical considerations alone.

Rade · 12-05-2007

delete message

Bombadil · 12-06-2007

Dr. Dick, all that you are describing here then is a mathematical definition of an explanation. That is, given any list of objects A and a second sufficiently large list of know objects B such that objects in B are somehow derived from A. Then a function exists that will give us expectations about the elements of list A. That is, it will tell us the likelihood of any particular element being in A. What you are giving is a set of provable requirements that any function that can be an explanation must obey.

Of the math what I don’t quite get is how the shift symmetry implies differentiation. I can understand how adding any number to every entry makes no effect on the explanation but I don’t see how this implies that the derivative exists. Obviously any solution to your equation must be an explanation but how do we know that all functions that are explanations have a derivative? I’m speaking of the existence of the limit necessary to have a derivative not a function that won’t satisfy shift symmetry.

Now I can understand that what we believe we know of reality (reality being list A) is nothing more then an explanation that we build off of experiences of real objects that we have experienced plus a second set of objects that are based off of these object (together these object make up list B) but not necessarily consistent with the list of real objects and hence we can never know that such a explanation is correct. But I’m getting confused when you start talking about ontological items and epistemological constructs. How I understand it an ontological item is anything on list A while an epistemological construct is anything on list B. Am I correct in this understanding?

Doctordick · 12-06-2007

Quote:

Originally Posted by Bombadil

Of the math what I don’t quite get is how the shift symmetry implies differentiation. I can understand how adding any number to every entry makes no effect on the explanation but I don’t see how this implies that the derivative exists. Obviously any solution to your equation must be an explanation but how do we know that all functions that are explanations have a derivative?

We don't! That is exactly the reason I continually refer to the fact that “an interpretation” of any explanation exists which will satisfy that differential equation.

The issue is that any interpretation of any explanation is based upon a finite amount of information. Now I proved explicitly that, if the information in your left hand is finite then there exists an interpretation of that information (the valid ontological elements) together with a presumed set of invalid ontological elements under the rule that no two labels may be exactly the same, which is totally consistent with the presumed information (the collection of valid and invalid ontological elements) exists. I then point out that symmetry and the fact that the labeling procedure demands that

$\vec{\psi}(x_1+a,\tau_1,x_2+a,\tau_2,\cdots, x_n+a,\tau_n,t)=\vec{\psi}(x_1,\tau_1,x_2,\tau_2,\cdots, x_n,\tau_n,t)$

is valid so long as the number of elements in the presumed information is finite. This means that it must be true no matter how large that finite number is. Since our “theoretical” case is, “the possibilities go to infinity”, if follows that we are interested in what that relationship looks like in the limit where the number of elements in the known information goes to infinity (the history of events we need to match are infinite). It is no more than a mathematical consequence that if the relationship being stated is always consistent (as we go to infinity) it drops directly into the fact that the definition of a derivative of $\vec{\psi}$ with respect to a must vanish. The rest is ordinary mathematics.

Have fun -- Dick

AnssiH · 12-09-2007

Quote:

Originally Posted by Doctordick

No problem at all. I am fully aware that your first priority is earning a living and I wouldn't want you to think there is anything more than enlightenment to be found here. But enlightenment can be fun. All in all, I think you are doing an excellent job of picking up the mathematics.

Thanks, it's just too bad that last months I've seldom had large enough chunk of free time at once to really concentrate on learning the math. The end of the year is going to be like that for me too (will be busy and then away from home)

None of this is a waste of time for me though, since just learning the math is useful for me. And of course it's an interesting topic

[unit vectors in the definitions of $\vec{\alpha}$ and $\vec{\nabla}$ ]

Quote:

Their use allows us to write “vector” equations. The symbol $vec{nabla}$ (which you will often also see represented as a bold $nabla$ ) is the vector representation of a partial derivative. Being a vector in the $(x,tau)_t$ plane, the representation has an x component (which is the partial with respect to x) and a tau component (which is the partial with respect to tau).

Okay I think I understand that. And those partials are the partials of $\psi$ , yes? I suppose that's what you mean by (from post #89):
"The term being summed is $\vec{\alpha_i}\cdot \vec{\nabla_i}$ and each “i” yields a different term in that sum but every term is operating on the same $\vec{\psi}$ ."

[Expansion of $\sum_{i=1}^n \vec{\alpha_i}\cdot \vec{\nabla_i}$ ]

Quote:

Your interpretation here is erroneous. In vector relations, there is a thing called the “dot” product (or often, the “inner” product).

Oh I see, the dot product again, had forgotten all about that by now :P Thank you for the explanation of dot product. I took a look at dot product Wikipedia entry as well and now I understand that expansion of the sum.

Quote:

The reason this inner or dot product is defined the way it is, is that it turns out that the result is independent of the orientation of the coordinate system.
...
which is exactly $vec{A}cdotvec{B}$ expressed in the (x,y) representation. The only reason I went through all of that was to convince you that the dot or inner product is indeed something defined by the vectors themselves and not by the particular coordinate system chosen to represent those vectors.

I didn't go through that proof very carefully since you say it is not very important at this point of the analysis yet. Nevertheless, thinking about the geometric interpretation of the dot product, I would certainly expect it to be independent of the orientation of the coordinate system.

So I followed the math from post #89 through and understand how you get:
$\alpha_{qx}\sum_{i=1}^n \vec{\alpha_i}\cdot \vec{\nabla_i} = \left\{\sum_{i=1}^n \vec{\alpha_i}\cdot \vec{\nabla_i} \right\}(-\alpha_{qx}) +\frac{\partial}{\partial x_q}$

Next I suppose its the latter parts of posts #42 and #83 I should concentrate on?
---from post #83:---
$\left\{\sum_i \alpha_{qx}\vec{\alpha}_i \cdot \vec{\nabla}_i + \sum_{i \neq j}\alpha_{qx}\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \right\}\vec{\Psi} = iKm\alpha_{qx}\vec{\Psi}$

->

$\left\{\sum_i -\vec{\alpha}_i \cdot \vec{\nabla}_i \alpha_{qx}+ \sum_{i \neq j}-\beta_{ij}\delta(x_i -x_j)\delta(\tau_i - \tau_j) \alpha_{qx}\right\}\vec{\Psi} +\frac{\partial}{\partial x_q}\vec{\Psi}= iKm\alpha_{qx}\vec{\Psi}$
-------
I think I understand the sign change on those terms now, but the next step on that post is little bit of a mystery so far... :I But then, I haven't had much time to stare at it yet either

Thank you for the patience once again.

-Anssi

AnssiH · 12-09-2007

Quote:

Originally Posted by Majik

You seem to be trying to make a distinction between ontology in the left hand and epistimology in the right hand. But what if our epistimology were derived solely from inescapable logic? Would we really then need to even look in our left hand? Would we really need to do experiements? If physics were derived from logic alone, wouldn't we "know" without even looking what IS real?

I would like to make a comment here.
I took a quick look at your home page, and while I don't understand almost any of it, I can see there are some similarities to the topic on this thread. I.e. you are looking for constraints that must be true for any valid worldview, and the consequences that such constraints would have.

You are concerned with "all facts in reality are consistent, meaning no fact proves any other fact". That is what has been referred to as "self-consistent worldview" in this thread, i.e. that the mental idea you have about reality cannot contain self-contradictions for it to be taken as valid.

You seem to be equating a worldview/model with reality itself, and that's a stretch you should not make. Instead you should be concerned with the possibility that there are many valid ways to describe reality. For example, we are free to define different features of reality as "entities" (say they are things with temporal identity, i.e. we refer to them as the "same thing" when we see them at different times).

Anyway, not to get into that discussion again (you can look at my older posts for clarification if needed), what I'm getting at is that your treatment - like Doctordick's - doesn't say as much about reality as it says about our ways of describing reality. That is NOT to say it is insignificant. On the contrary, it is very significant.

In a nutshell, if you can derive quantum mechanics from logical constraints that are general to ANY possible valid worldview, that says something about the QM-models that we built, but not necessarily so much about reality itself.

Think about that

-Anssi

Turtle · 12-09-2007

Quote:

Originally Posted by Majik

Actually, I'm not so sure this is correct. If a theory (epistemology) can be derived from some kind of logic alone, then it is not possible to deny it's correct. But what kind of logic would do this. I realize this opens up a whole new can of worm, but I've been working on such a theory. I wouldn't call it completely proved yet, but I think it is close enough to merit some serious attention. ...

This comment stirred up my affinity for Kurt's hammers, that is Gödel's incompleteness theorems, and I don't think I or any others have yet have brought this up with the good Dr. Dick in any of our earlier discourse on his work. Consider it brought up I guess. Thoughts?

What can we know of reality?

Hypography?

Share the love!

Sponsors

Friends