Hi Harv,

Regarding the "significant fallacy" in my reasoning:

"set A is problematical for applying to reality."

[b]1. A is a set!![/b] That set is the set of those elements (elements of A) which we wish to explain! Fundamentally, there is nothing here defining A to be "reality".

You claim that "(1) if set A only represents reality, then the representation is also a subset of set C (since set C is equivalent to an explanation of reality by implied definition)…" That inference is entirely in your mind and is impossible to justify logically. It is a direct result of your presumption that the information you are trying to explain is correct. C is in no way equivalent to an explanation of reality, it is no more than an abstract representation of what you have to work with, whatever that may be. Your interpretation is equivalent to saying "reality is a subset of your interpretation of what you know". That is putting the horse entirely on the wrong side of the cart.

Your claim continues with "in which case your set logic is flawed since if set A is a subset of set C then set C cannot be a subset of set A". In my presentation A cannot possibly be a subset if C for two very clear reasons: First, the suggestion that A is a subset of C implies that there is nothing you don't know about reality which seems to me to be a dogmatic contention unworthy of argument and second, the character of the elements of C are not even of the same form as the elements of A.

[b]2. B is a set, defined to be an unordered finite collection of elements of A!![/b]

As a matter of fact, B is not guaranteed to be a subset of A as, "a collection of elements of A includes the possibility of multiple copies of an element in A whereas it is entirely possible A contains no multiple copies of any of its elements.

[b]3. C is defined to be a finite collection of sets B!![/b]

Under that definition, the elements of C cannot be elements of A unless all possible sets B consist of single lone elements of A and, if that were the case, I would not have used the phrase "collection of elements" in my definition of B.

With regard to your second complaint, "if set A is reality, then you have erred by suggesting an equivalence relationship with what cannot be known", that is why I titled the paper "An Analytical Model of Explanation Itself". I am not modeling "reality", I am modeling an "Explanation". If that explanation happens to be an attempt to explain reality, the so be it.

Your comment, "For example, we have no way of knowing with any certainty if sets are valid concepts with regard to reality", has utterly no bearing on what I am doing. More to the point, I think any theorists who tried to publish an explanation of reality without including any labels on his concepts (think "words" or "letters" Harv) would have a very difficult time publishing. In fact, you might consider the difficulty of carrying on this debate without using a set of labels for your concepts.

Your last comment includes the condition "if set A is completely undefinable"! That is simply not what I said. What I said is that I have not defined A; quite a different statement. Essentially, what I claim is that my deductions are valid for any definition of A and you have not even considered that question.

Finally, since I am basing my "probability on the human perspective which must take into account human perception and human cognition - which the science of each is vastly incomplete to form any probability matrices as to what a human is likely to perceive of undefined set A considering their environment, personal history, beliefs, etc", my presentation must remain quite abstract: i.e., what I can prove is very limited. All I can prove is that any explanation of anything must agree with modern physics.

Applying it to philosophy is a vipers pit! I don't disagree with that at all! Why do you think I am trying to talk to you?

Have fun -- Dick