Let me reply to your second post firstly, since this will probably help you understand my reply to your first post.
****After I made the post above, I was soaking in the bath and realized that maybe I can prove the set is empty! I have never considered myself as a great at proving theorems but this seems logical to me. Let us consider the existence of a "thing" which is impossible to refer to. Let us call this thing "A". Given that, what can we say about "A"?
Whoops, I just referred to it! Well clearly since we have referred to it, it certainly is not a member of the set of "things" which cannot be referred to. It follows that any "thing" which cannot be referred to is not a member of the set of those "things" which cannot be referred to! The only possibility is that the set of "things" which cannot be referred to is empty.***
You have referred to A, but not necessarily 'A'. Remember, 'A' is a label used to designate something about Ultimate Reality, but what that something is we cannot say. Perhaps that something cannot accurately be labeled as a number. For example, if I asked you to label the largest even number, we might label that number as 'infinity'. However, if I asked one to show me that number (as if I were asking you to show me the number 9), then obviously there label 'infinity' has no reference to a specific number. It is a concept without any specific numeral reference. However, it would be wrong to say that 'infinity' is part of an empty set of 'things'. It (the concept of infinity) simply cannot be referred to like you would refer to the number 9.
***First, I do not understand what the term "non-referring" means! With regard to "a dead horse" in category 1, you have just referred to such a thing and I can immediately transform your reference to a number (just for the fun of it, pick the ASCII representation of your entire sentence read as a number). Thus a number can be attached to what you are referring to. Anything you can refer to, I can label with a number! Now, anything which exists can either be referred to or it cannot be referred to.****
You are referring to a human concept of 'things'. However, you are not referring to 'things'. Using my example above, you can refer to the human concept of 'infinity', but you cannot refer to infinity itself since whatever number you use to refer to infinity would be incorrect (i.e., you can add 1 to that number showing that whatever number you labeled to infinity did not meet the requirements of infinity by being the largest number).
***To quote you, "existence has to be defined, and causal connection with our physical universe is one of the key attributes for something to be considered to exist". Just what is a "causal connection" if it cannot be referred to?***
As far as I know, there is nothing wrong for an infinite causal connection. That is, you can never refer to the first or last causal 'thing' as a thing, but you might be able to refer to it as a concept. For example, the cause of the universe might be a 'original condition' which has an infinite causal connection to our world. In such a situation, we can never refer to the 'original condition' as a thing since whatever condition we refer to must have a prior causal connection to something else in order to be infinitely causally connected. However, this doesn't change the fact of the matter that it is causally connected with our world (even though it is an infinite causal connection).
***By the way, the term "a dead horse" is usually used to reference something not worth discussing or something considerably over discussed and has no connotation at all of "can not be referred to".***
I choose the name 'dead horse' because it is part of those things which you don't want to discuss. I can only imagine that the reason that you don't want to discuss such concepts is because they cannot be included as part of (6). I realize the connotation is different than the common phrase, but I think the concept works since you cannot accept the existence of dead horses - especially since they are an exception to (6) as I have defined them.
****Your use of the word seems to indicate that when I say "can not be referred to" you think I mean it as some sort of choice. I do not! When I use the phrase "can not be referred to", I mean literally that reference to it is impossible: reference to it has never occurred and will never occur by anybody at any time 'forever' because such can not occur.***
This, in a nutshell, best exemplifies your misunderstanding of your whole approach. In short, you are saying that because you cannot conceive of something as possible that it becomes impossible. Based on what? Based on logic that you learned from childhood? What a short span of time is that? What if your experience is wrong? You admit no fallibility in your knowledge. This is a problem.
***I suspect very strongly that nothing which truly exists can be thought of as fulfilling that requirement: i.e., I think it is an empty set; however, I will still include it as a possibility anyway, that is exactly why I put the constraint "communicable" on the "reality" which is to be modeled.***
I did not see the words 'communicable' in the original collection of (1) thru (6). [More about your revision to (6) and addition of (7) later].
***Exactly what do you mean by this property of "reference"?
Reference means to a thing. For example, if I see a calculator, I refer to it, I am referring to a thing. On the other hand, if I see a cloud that is intertwined with another cloud (i.e., from my perspective), then it might be unclear to another person where my reference of "that cloud" is different from someone else's reference of "that other cloud". I might have to pin point exactly what I mean when I refer to "that cloud" versus "that other cloud". If I gave "that cloud" with a numeric label of '1' and "that other cloud" as '2', then someone should clearly understand what '1' refers to and what '2' refers to. What if someone comes along and thinks there are three clouds and not two? Obviously, we need some criteria of identification which allows anyone to know what I consider a separate cloud. I wouldn't want my criteria to allow other people to identify five clouds when I said there are two. That would mean that my criteria was not specific enough. If, after many hours, I gave up and said "I'm sorry, but I just can't communicate with you the criteria that I am using to identify only two clouds", then my reference to only two clouds is without any substance. What if Ultimate Reality is like this situation? What if we cannot identify criteria for object identities simply because there is no such firm criteria that exists? I think your whole approach from (1) - (6) assumes that criteria exists even if you do not know what that criteria happens to be. This is a bad assumption. You help yourself, by limiting the criteria to being communicable. Otherwise, we could not continue.
***What I accept is that "things which can not be referred to" are omitted; however, I state that any "thing" which can never be referred to (that means it cannot be discussed Harv) can have little impact on any explanation of anything! If you disagree with the reasonableness of that statement, you need to make your reasons clear to me.***
It depends on what you are trying to explain! If you are trying to find as close fit of explanation to Ultimate Reality as humanly possible, then if Ultimate Reality did in fact have 'dead horses', then it would be far more satisfactory in our explanation of Ultimate Reality to mention 'dead horses' since they do in fact exist. On the other hand, if 'dead horses' are not even possible (let's say that they are not and we somehow can know this), then we should remove them from any explanation.
***H: We have no direct experience of category 1 items... D: Now that seems to me to be a rather all encompassing far reaching declaration of fact with no defense at all that I can see! I would like to see your defense of the fact that we have "no" direct experience of anything which is part of ultimate reality! In my opinion that is a rather bold assumption indicating little serious thought.***
Let me re-word this. We have no known direct experience of category 1 items. That is, everything we experience might be direct experience of category 1 items, but we have no way of knowing it. It could be, as far as we know, only a human approximation to what is actually 'out there' (or just completely false altogether). We do not know.
***6. It is possible to label all of these "things" (which have ever or could ever be discussed) with numbers.***
7. Anything which can never be discussed is not worth talking about.****
I can happily agree as long as (7) applies only in the sense of our scientific theoretical understanding for pragmatic purposes. That is, I can see benefit about talking about 'dead horses' as a philosophical concept (i.e., as part of a philosophical theory about 'Ultimate Reality'), but I see no benefit of bringing up 'dead horses' as part of a scientific theory where pragmatic purposes are at stake. It does very little good to end each scientific statement with "these concepts could all be attached to 'dead horse' things...". Rather, we should ignore 'dead horses' and proceed to talk only within communicable concepts.
However, that is not to say that certain concepts cannot be entertained that imply non-communicable aspects. For example, Chaitin first created diophantine equations whose output is an uncomputable number. These kind of equations, including one's implying the existence of infinite numbers, complex numbers, etc, certainly have no physical analogues, but we can still use these equations. We just can't talk about the full meaning of these equations at a scientific level (of course, they are fair game for discussion as far as philosophical musings).
So, for the record (1)-(7) is as follows:
1. It is possible that some specific thing (or perhaps several specific things) may exist.
2. It is possible that some of those things which exist have no direct consequences in the physical universe available to my studies.
3. Some of those things described as having no direct consequences in the physical universe available to my studies may have consequences in the future.
4. At all times, from the ancient past to the far flung future, any rational person's idea of the universe will be based on things they think exist.
5. Those "things" which are not part of "Ultimate Reality" can be absolutely anything.
6. It is possible to label all of these "things" (which have ever or could ever be discussed) with numbers.
7. Anything which can never be discussed is not worth talking about.
***You seem to think that the sole act of identifying a "thing" proves that it is not a category 1 "thing".***
No. That is not my view. Rather, as far as we know we lack full knowledge about category 1 'things', therefore we cannot talk in terms of category 1 'things' without admitting fallibility (or potential fallibility) in our understanding.
*** My only contention is that, only if I did knew exactly what constituted ultimate reality, could I say which category any particular "thing" would fall into: i.e., that the categories themselves exist.***
I would agree.
***What I am saying is that "things which cannot be referred to" cannot be part of any explanation of "ultimate reality".***
This caveat wasn't originally part of (1) - (6).
***The subject of my paper is the abstract idea of logically constructing a rational explanation, period. If the explanation is to be an explanation of "ultimate reality", so be it! What I am saying is that any explanation of anything cannot contain things which cannot be referred to!***
This is not true. As I mentioned above, our explanation might refer to infinite numbers, complex numbers, and even uncomputable numbers. That doesn't mean that we cannot use these 'explanations' even though they refer to these non-referring physical things.
Warm regards, Harv