I had a temporary opportunity to enter discussion at no charge while travelling. I have another opportunity at moderate cost so can reply now.
I was interested in replying but usually I must severely limit my involvement in this forum if I am to avoid spending too much on public internet access. I do not have a computer or internet.
Before I begin; may I again draw your attention to my arguments in the "time and entropy" post.
It is a curious demonstration of physics:
They say "entropy increases with passing of time".
We know the physics texts treat "entropy" as a "tendency to disorder" where this is taken as a breaking up of things into smaller pieces.
We know (and I hope Dr. Dick reads this because it has everything to do with his paper and his idea of "assignment of definitions") that (I'll put this key phrase in capitals):
TO EVEN TALK AGAIN ABOUT THE CATEGORY (OR CONCEPT) "ENTROPY" AND TO EVEN TALK AGAIN ABOUT THE CATEGORY (OR CONCEPT) "TIME" : SOMETHING YOU MUST DO TO COUNT THE MEETINGS OF THESE CATEGORIES AND THE CONTENTS OF THESE CATEGORIES: YOU MUST BE ABLE TO TELL THEM APART.
That is; you must be able to still see the difference between "entropy" and "time" to keep talking about them together and any change of one with respect to the other.
Now; I once saw Christopher Langan on Television; he is reputed to have the highest IQ in U.S.A. He has a website for discussing his "CTMU" or "Cognitive Theoretical Model Of The Universe".
As you know; Dr. Richard Stafford has written a paper "Foundations Of Physical Reality" where he claims much of modern physics is "true by definition".
In my opinion; although I can see there are circumstances where one might want to ask about someone's credentials in the course of wondering about the reliability of their work; I do not think one should have to pass up the opportunity to simply analyse what someone says and if it withstands honest investigation what does it matter if they have no reputation in their field?
If a toddler says something wise; why should I ignore it? We have the words of Chris Langan and of Dr. Richard Stafford and many others and we can investigate.
Now here is a curious thing:
You have this concept "entropy" which I might call "breaking up into pieces or into more groups".
You have this concept "time" which involves seeing a CHANGE in something.
To see a CHANGE in something surely MUST mean you end out with a big group: "the something before" plus "the something after" from a minimalist definition perspective.
But that involves breaking the WHOLE into groups?
Whatever it was that changed; that thing has a "SAME" (the "common background": the unchanged common factor) and a "DIFFERENCE" (the changed aspect.
It seems that to even talk of "time passing"; rather than "time stopped" requires a BREAK into two pieces ("before" and "after").
"Entropy" is "breaking into pieces". To even talk about "entropy" AGAIN; requires a "SAME" entropy (unchanged aspect) and a "DIFFERENT" entropy (the changed aspect of it).
Otherwise "entropy" would be stopped; you could not talk of "entropy" and "time passing" in the same breath?
To find your concept "entropy" AGAIN; to see what it looks like after "time passes" MUST REQUIRE THAT THE CONCEPT "ENTROPY" HAS BROKEN IN TWO?
And since "entropy" is "breaking into pieces"; BY THE VERY REQUIREMENT OF BEING ABLE TO TALK NOT ONCE: BUT TWICE: ABOUT "ENTROPY" AND "TIME" IN THE SAME BREATH (with a same background) means (doesn't it?) that in minimilistic definition terms: "entropy increases as time passes".
The very act of COUNTING has delivered a physics law by virtue of the way the concepts are defined and the minimal reqirements to be able to compare the concepts again.
What about COUNTING? Math says "1 = 1 = 2"; to even talk of "1 + 1" requires that there be a "SAME" background to the ones (called "2") and a DIFFERENCE between the ones (Or you couldn't count them).
Looking at Christopher Langan's work you can see he is on to this with his "conspansive duality".
Looking at Dr. Richard Stafford's work:
He talks of the minimum requirements for a "rule" the the universe might supposedly obey.
And what are they? A "rule" GROUPS things together; if it didn't; you would just have a "one-off"? So the essence of a "rule" is that it is a "SAME" background to a DIFFERENCE; a "2" for a "1 + 1".
A rule says that things MUST go together.
In my opinion; it is very likely that "M-theory" is "math re-discovered"; that Professor Stephen Hawking's "pea instanton" idea might be a rediscovery of "same-difference"; I think Dr. Richard Stafford and Professor Stephen Hawking have re-discovered mathematics INSIDE mathematics.
Chris Langan appears to uncovered a pre-math perspective on this.
Be interested in your finding if there are any flaws in my argument!
On to your comments:
Quote: "object X lies on plane P", if, and only if, "object X lies on plane P" actually expresses an object X lies on plane P as a mathematical abstract reality, and object X lies on plane P obtains in this mathematical abstract reality...
We have no way to specify what it means for an abstract object to 'lie' on a plane." We do? Chris Langan's "question and answer together". In "math world" we say "2 + 2 = 4" for each case? From a free association perspective; "object " "lie" and "plane" need only meet in a certain order?
I don't know who Chris Langan is? Throw a name at me who is recognized in the field of philosophy, like Hilary Putnam, or Michael Dummett, or Daniel Dennett."
I mentioned above who he is; and that I think reputation is not the only revelant factor in discussions; content is relevant too.
Quote: "This 'free association' is all based on human language and extends from human imagination. The point about defining truth in terms of abstract concepts is that they don't have any tangible meaning when talking about the actual words 'object', 'lie', 'plane', etc."
But...? You deliberately excluded "tangible meaning" by seeking to have math statements correspond to facts in a math world ????
Quote: " Without something tangible, we can only define our terms to a certain point, at which we have to work based on some kind of belief system."
What is "tangible"? Doesn't every situation give scope for "faith" in Existence?
Quote: "For example, if someone asked me what does it mean for an apple to lie on the desk, I merely have to take the apple and show them how the apple presses against the desk. Perhaps I can press the apple into the desk such that it starts to mash into the desk, all of which I am trying to convey a tangible meaning and thereby translate 'apple', 'lie', and 'desk' into a set of images and sounds that provide tangible meaning."
Doesn't an abstract concept like "government" still rely on a bedrock of world-experiences? Sophisticated concepts may look detached from the concrete but on closer inspection of the personal world-experience of the individual with the abstract concept; you might find it to be built out of experiences regarded more traditionally as "tangible"?
(continues in "reply part two")