Reference & Existence

OK it seems that all that explosion of reading and ideas boils down to the issue of reference and existence.

The issue is what is "a thing"? If for example we refer to a box A we are "referring" but we are not handling the real thing, only a reference or name to the real thing. If on another case we say that we are holding box A, on one hand we are reffering to the act of holding this box (as written in fact in this blog) but on the other hand we are actually holding the box, and event that we can refer to but which is in existence. It is through the act of refering that we can lie and play all those games of reference, like telling a story like just done here without ever actually handling the box A. The symbols have a life of their own regardless of the actual events.

Now with set theory it is a similar situation. Let us take a set {1,2,3}. What we are saying is that we have a collection of numbers 1,2,3. Now consider what the set of arabic symbols for 1,2,3 looks like... {1,2,3}. But the first case is a collection of counting numbers while the second is a collection of symbols. Thus {I,II,III} are the counting numbers 1,2,3 expressed in roman numerals, so it is identical with the first case, but different from the second case. Each symbol has several uses:

1- the level of its actual existence as a mark on the page (in which case A and A are different examples)
2- the level of its place in a symbol set (where "A" = "A")
3- its level as a reference (where if A=5 then A=A because 5=5)

This is explicitly found in computers where referencing is common place.

A variable has 3 meanings. the symbol as understood by the compiler within a namespace (1) so that variables with the same name in different namespaces are different, the memory location linked to that name (2) and the value at that location (3)

In computers the human programing interface often uses symbols from the ASC set to code for variables. At run time these are converted into actual memory locations and the name becomes linked to an address. Into each address data can be stored.

While all data in a computer is simply binary numbers the destination of code is of two fundamental types. If the data in loaded into the instruction register of the CPU then it is used to control the CPU at the next clock cycle, if it is loaded into the data registers of the CPU then it is processed. Thus for every symbol that we may type in at a key board its fundamental meaning is augmented by where that will go. If the symbol "A" with a binary value of 65 or 01000001 is directed through the data part of the CPU as this has just been then it is processed, in this case to appear as a symbol on the screen and data for a file to be sent over the internet to update the blog program. If on the other hand I could direct that code into the instruction register (which I can't through this blog program) then it would instruct the CPU to perform some operation (I don't know Intel assembly language so don't know which operation 01000001 is).

So we have 3 flavours to symbols and then another 2 types of symbols on top of that. An example...

"=" is well known as the symbol for equality in maths. It is an operator so in computing terms it would go to the instruction register to tell the CPU to compare the values in its data registers.

However "=" can also be data as it is in this file since its simply a word processor and = is just a symbol in fact symbol #61.

In some esoteric language you might be able to write "= ? 5" where = is a variable and ? is understood as the equality operator i.e. it translates to "A = 5". Its just numbers at the end of the day and what we are conditioned to understand from the symbols need not apply.

So in set theory the statement A = {1,2,3} is a complex system. Firstly A,1,2,3 are references to things, but are not to be taken as what they are, otherwise we would thing that the letter A was the set of symbols 1,2,3 when in fact we are supposed to be saying that A stands for a set of numbers. The equality operator is a reference to the idea of an assignment operator telling us to take A as a reference to this set from now on.

Now there are a lot of complications possible here. How might be assign a reference to the assigment operator "= = what" ? Can a set really hold an actual thing?

A = {1} could hold this symbol 1, in which case A = {1} is a new assigment rather than a repeat of the same assigment. Or if we take A and 1 to be in the same name space, then is A = the symbol 1 (i.e. the set containing the symbol 1) which is also false since A is the symbol A! unless we mean that A refers to the set containing the symbol 1 which is a mix up of contexts. Or finally we take the whole thing as a reference to the set idea of containing a number.

Now with that in mind when we talk of self-reference we are very much in the world of thoughts where lying and many other unrealities are true. The set T = {T} is a system of self-reference where while T is an existent in its own right it can occur in multiple places and each refers to the same things namely a set which contains another set by the same name, i.e. itself. This is not a real event, but a thought made possible by multiple entities referring to the same thing. Obviously such a state of affairs cannot be done in reality, you have an infinite regress.

This issue of reference and object/existence, and also operators and data are the two dualisms which i need to resolve to bring this flurry of exploration to a close.