The bliss of a final resting place

The goal in life is to have those experiences where we want for nothing more.

Baby you'll all that I have
when I'm lying here in your arms
I'm finding it hard to believe
We're in Heaven.

As Brian Adams would say. But that is it, the experience of being found, or of finding what we are looking for, of being at home, and the journey complete, with no need anymore to search and no sense at all that we have to journey more. We have arrived at ourselves, in peace and there is nothing else to say.

Words are the currency of desires, just as money is the currency of getting. We talk of those things we have not got, and think of how we might get them. But when we finally arrive at ourselves, at home with ourselves then we have no need of thought we have no need of currency.

The problem of course is that these earthly experiences no matter how "found" and "home" they may feel are illusions because the outsider can see it is doomed to a short term.

The goal is that experience of being found, of being at peace with oneself, but after having found nothing and after having gone no-where.

It is odd however that within the realm of Earthly experiences, the experience of finding a resting place (especially in someones arms) is so completely satisfying. To people in such a state it is very hard to argue that this is just a stop on the journey, because it is not over yet.

Being over (the Enlightenment) is quite extraordinary then for it is being home but the final unshakeable one, no doubt anymore that the morning will rise on lovers bliss and carry their beloved away.

I'm not in a position to say whether I'm right or wrong!

Well if I could determine if I was right or wrong, then how do I know that this itself is right or wrong? ad infinitum!

So what are the conditions that allow right and wrong?

Babies prefer alturistic agents!

http://www.guardian.co.uk/science/2007/nov/22/humanbehaviour
http://www.agi.it/world/news/200711221004-cro-ren0007-art.html

Self-Reference is impossible!!

There is a problem with T= {T} but not under that disguise.

Consider the universal set U = {A,B,C} where

A = {10}
B = {1,2}
C = {3,4}

Now construct the set D = {x : x = 2} i.e. the set of all set with 2 members.

D = {B,C}

But D has 2 members so,

D = {B,C,D}

but now it has 3!

Either way D is an exception to it own rule. There is something wrong with the set construction.

There was no problem up to defining D = {B,C} but then we noticed that D was a new set which was an exception to its rule. Exactly! D is a "new" set and not a member of the Universal U = {A,B,C}. D is created from the universal U and creates a new universal in the process U* = {A,B,C,D}. So correctly its like this...

U = {A,B,C}

A={10}
B={1,2}
C={3,4}
D = {x : x e U & x = 2} (where e means "a member of")

Which also creates a new universal U* = {A,B,C,D}

Thus T = {T} is a trick of language because it should be written T = {x : x e U & ... } and T is not a member of the universal U.

The only way around this is to leave an unbound floating symbol in the universal definition...

i.e. U = {A,B,C,D} where D = nothing i.e. it is unbound and we reference it later ... but that is the point: a system requires an empty symbol to refer to itself - which doesn't become bound to the system until AFTER it picks up its reference. Self reference is indeed impossible.

This also solves a similar problem...

U = {A,B} where

A = {1,2,3}
B = {4,5,6}

now construct
C = {x : x = 3}

there are 2 answers

C = {A,B}
or
C = {A,B,C}

Now C refers to the same set i.e. {x : x = 3} but the axioms of set theory state that 2 sets are only the same when they have the same members and clearly

{A,B} /= {A,B,C}

However

C = {x : x e U & x = 3} solves it neatly.

Hypothesis: Self reference is only apparently possible if the symbol space/solution space/universe/etc is not properly defined.

===

Just a start but if self reference is impossible then that opens up the whole world. The limit cannot be expressed within the limit. Thus returning to the start the ideas of "materialism" cannot account or refer to itself (obvious really since ideas are not material). And, 2 sided positions fail because such dualistic argument works on the basis that "I am correct" and "you are wrong" but if no system can refer to itself without expansion then no such self-assured "I am x" is possible. War for one can never be justified since ultimately a "self" consistent argument would have to expand indefinitely to include the enemy at least! (And, G-d is out of the picture 4 sure - originally there was no symbol for Him)

Firstly note that a set construction involves the assigning of a reference

A = {1,2} = {x : 0 < x <3}

The character A, the set name, is not usually part of the symbols that build the set. If however we did used the symbols {1,2} as a name then the statement

{1,2} = {1,2}

does not mean that the set {x : 0 < x <3} contains the number 1 and 2, but rather that {1,2} is a name that - meaningless in itself - will now refer to the set {x : 0 < x <3}. It could be expressed like this for clarity:

"{1,2}" = {1,2}

1.0) Now consider a universal set containing three sets U = {A,B,C} where,

A = {10}
B = {1,2}
C = {3,4}

2.0) Now construct the set D = {x : x = 2} i.e. a set whose members are sets with 2 members, and call it D

2.1) D = {B,C}

But D has two members. If D is not included in itself then D is not the set of "all" sets with 2 members because it is the exception. We are thus inclined to include D to give the set

2.2) D = {B,C,D}

However now D has 3 members and so should not be included. How ever we try to build D we end up with a contradiction. Where is the problem?

Up until step 2.1 everything was good. It was only "after" constructing D that we noticed it became an exception to its own rule.

Step 2.1 suggests statement 2.2 but something goes wrong in building it. Let us recreate the process without assigning any names or references (beyond the basic elements i.e. 10,1,2,3,4}

supposing we write statement 2.1 as {{1,2},{3,4}}

We notice that it contains 2 members and so should be a member of itself so we try to write the self-referential statement without using reference:

{{1,2},{3,4}, itself} = {{1,2},{3,4}, {{1,2},{3,4}, {{1,2},{3,4}, {{1,2},{3,4}, itself}}}}

it cannot be done. This expression cannot be resolved into "definite" sets. The process of attributing a reference D to the unresolved set in 2.2 hides the fact that we don't yet know for sure what the set is. Writing D looks like a definite answer but actually it is an "unbound" reference. By "unbound" I mean we is unsure what it refers to.

The statement D = {B,C,D} is a formula for the answer. B and C are bound references because we know clearly what they are, but exactly what D refers to is uncertain. When we ask what D refers to we get another formula containing D. It resolves to nothing, a trick of language without reference, meaningless. Creating formulas is easy. g = 4*Hg¬K but until we know what these refer to it is meaningless.

"The unicorn in my garden is eating grass" is meaningless because "the unicorn" is an unbound reference, it is a formula we might use in the event of a unicorn being in the garden. When asked "which unicorn?" we cannot simply answer the unicorn eating grass (q.v. what is D it is {B,C,D}).

Predicate logic resolved this issue with: Ex: x = unicorn & x = eating grass. It is false because there is no unicorn (and it certainly then can't be eating grass) but the issue of reference is implicit.

Quick addition on reference. Reference is not the linking of "physical reality" to symbols and words, because objects in the world can only be referred to with symbols i.e. what do we mean by "physical reality" since that itself is a reference! mystery!

So we are stuck with D = {B,C} but it is unsatisfactory because it becomes an exception to its own rule.

The solution might be that D = {x : x = 2} creates a new Universal. Remember that U = {A,B,C} so the construction of D creates a universal U* = {A,B,C,D}

D = {x : x e U & x = 2}

And that is the point about self-reference. The reference to oneself cannot be in the same universe as onself.

It is the +1 conjecture again that a system needs to expand by 1 to take a useless entity and use it to reference the self.

===

Can we get from this position to the general situation that the self cannot contain itself.

And is this the same as the situation where the rules of a game (like war) can only occur because they try to reference themselves within themselves i.e. we Allies without understanding the requirement to see the Enemy and the Allies are part of the same game.

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.

clarification of ideas

Let us take a set of symbols where S is {A, B, =}

Now take the set of all combinations of any number of these symbols, which is the inifinite set of all possible sentences containing these symbols where S* is

{A, B, =, AA, BB, ==, AB, A=,B=, AAA, BBB, ===, AAB, AA=, ABA, ABB, AB=, ..., A=B, ..., B=A, ... }

Now a logical system will adopt certain of these sentences and ignore the rest.

We might for example have a system with only two sentences

A=B
B=A

or we might have a Lindenmayer system

A=AB
B=A
A=AB=ABA=ABAAB=ABAABABA (http://en.wikipedia.org/wiki/L-system)

where = means "goes to" and the symbols A and B get replaced according to the two rules.

In the Lindenmayer system if A=AB and B=A is the general rule then an infinite subset of S* can be included in the system. So that the sentence:

A=ABAABABA could be considered a member of the L-system because it could be considered a short hand of the sentence above.

Another version of the L-system might be freedom to apply any of the rules, more like logic:

A=AB
B=A
A=AB=ABB=ABBB=ABBA

In such an odd system ABBA,ABAB,AABB could all be derived by applying rule 1 three times and then rule 2 on any of the B symbols.

The point here is to avoid "thinking" outside the system of symbols and simply to see them as sentences.

Now when we say that the sentences "A=AB=ABA=ABAAB=ABAABABA" and "A=ABAABABA" are in the L-system clearly our inclusion of them is quite arbitrary according to the set of sentences. The meaning and use we ascrive to these sentences is not present within the sentence, any more than the game of rugby can be deduced from the rugby ball.

Two sketched point to work on...

If a sentence A is included in a system and two sentence B and C which are not included in the system are derived from changing two different symbols, can we express non inclusion within the system itself?

A is a member of the system if conforms to some rules say (not not present in the system itself for how else would we decide if those rules were present in the system ad infinitum). B and C are not members if they do not conform to rules, if they cannot be derived from the axioms, i.e. proven. However if they cannot be proven then they are outside the system and yet we know that they were derived by changing two symbols.

Explore this firstly by creating a system in which arbitrary symbols can be changed at will.

Point 2... Godel theorem in short...

If a function was present in a system which could determine if a sentence was provable, i.e. could be derived from the axioms and rules, i.e. was in the system then would sentences containing that function themselves be part of the system. i.e. could they be derived from axioms? there is a problem here but I need a bit more brain power to get over the hurdle...

What does a set contain?

Let us take the set of colours again...

{red, orange, yellow, green, blue, indigo, violet}

This clearly does not contain actual colours. "green" is not actually green.

It contains instead symbols that refer to colours.

If we have the set A = {1,2,3} and B = {4,5,6} we can easily see the process of setting symbols the mean things. A can be used instead of {1,2,3}.

1,2,3,4,5,6 are symbols that refer to numbers, they are not numbers themselves. In roman numerals we would write A = {I, II, III} and B = {IV, V, VI} to mean exactly the same.

So we make a distinction between the symbols that we see and the things they refer to.

So what of the rest of the symbols that we use to construct a set: { } , = what do they represent?

The basic idea in set theory is "containing" and we express containing in symbols by understanding that the brackets enclose the objects to be contained { } and each object is separated by a comma , and the whole set can be called something by using the = sign.

Obviously { } does not by itself "contain" anything without us knowing what the symbols mean, or how they are used. It would appear impossible then to construct the axiom within symbols and the question is raised how do we come by the concept of "containing"? This is running very close to what Wittgenstein was looking at and which he knowingly said he would never complete saying in his lifetime.

Returning to sets. On paper they are sequences of references, or symbols with specific uses. Thus { } we understand in the context to evoke the notion of containing, and the names that follow separated by spaces and commas we understand to evoke the things they are naming. The whole symbol system isolated and by itself is meaningless, but connected with the greater world of maths takes on the usual meanings and use. There is no containing at all within the symbols, indeed no meaning.

So let us turn to the reality of symbols and see if we can create a kind of existential self reference.

{x: x is a symbol for a counting number y & 0 < y < 4}

certainly gives us the set {1,2,3} but the context is different. This is a set of symbols, while A above is a set of numbers.

Furthermore there is a trickly problem... the entire expression is a sequence of symbols {, }, 1, 2, 3 so { and } are being used to articulate the notion of "containment" while 1, 2, 3 are not articulating anything ... they are just themselves... now sets contain references while this set is containing "real things". is that possible?

consider the following (none of this is new from recent posts I'm just seeking a clear expression of it)

The set of all symbols used in the expression for A

{A, =, {, ,, }, 1, 2, 3}

Clearly the symbols have become inadequate because in one place they are performing their function to construct the set, and in other places they are being operated upon.

Now this requirement of a system to be both subject and object is the question... does this have to be so? and why?

Self - containing systems again

Have made some progress...

the general argument from Godel to Logical Positivist school goes like this...

Some statement about the world... what if that statement apply to itself? and it always leads to "paradoxes".

So with the LP principle of verification, one asks what empirical evidence leads to the VP?

Especially this is true of truth itself. If a system can encode truth then you can get the absurdities of true statements that say they are false.

Godel showed that in numerical systems a wff can be formed which is unprovable. Provability is thus not the same a truth, and truth lies outside the system of provability. Systems are either incomplete - where unprovable statement exist or are inconsistent.

This is more obvious when one considers the "truth" of axioms. Clearly they are true "outside" a system since the system relies upon their truth. Such Judgement one must assume as a condition for the system.

Other fundamental conditions also exist like the education of users of a system, reason, existence, thought etc a pro pos Kant. There is a hermeneutic circle of given conditions which must be present before any system can be constructed. To construct that hermeneutic circle would require a position outside itself, and presumably another hermeneutic circle. The question formally that these speculations are true.

The implications are that there is no "fundamental" system with which to construct the world. That indeed the world is at root indefinable, and that is a construction of a notion of absolute Liberty.

So can this process be generally shown?

From Wittgenstein let us assume that the "meaning" of a statement is its "use".

To know the use of something we can simply create a set of all the possible uses of that statement.

A system of axioms and logic is thus a "compression" of the set of all possible statements but extracting the information to simply show that it can be reconstructed.

Thus in a logical system we could have a number refering to the sequence of rules applied to generate a statement, which would be identical with all the statements, and that set of numbers would constitute the meaning of the system.

The difference between that set and the normal expression of axioms however would be that the axioms no longer have a meaning outside the system from which the set of possible statements can be constructed, instead the set of possible statements becomes its meaning.

consider further....