The argument is a form of John Searles famous Chinese Room argument. Here he argues that humans following rule books blindly (like machines do) do not understand the rules so how can computers be said to?
The argument proposed here is: the output of human minds, (i.e. in the form of symbols (like this email), or in the form of computing machines, or even paintings or music) cannot be understood in isolation from the mind.
Consider: if something could be understood "as independent from the mind", then you would not need a mind to understand it. Conversely if we need a mind to understand things, then things cannot be considered independent from the mind.
This has wide implications as has already been discovered and I expand below.
In advance: by "mind" I am not referring to a "thing", it is simply undefined so far. The form of the argument is natural language. The issue is one of processes.
What I was trying to show previously was the processes of the mathematician processing symbols. The symbols cannot process themselves so I was hoping to find evidence of the "mathematician" in the symbols. In particular the evidence that systems are incomplete and that this implies work outside the system. That has been done by Godel.
I'll reconstruct a similar argument.
If we define a set A = {x : x <= 3, x in N} = {1,2,3}
Now it is true that A is a subset of itself. But that doesn't mean that the definition of A can "write" itself. Clearly the mathematician has done work to understand the set constructor notation and ensure the equality. For example I've had to learn how to do this.
So let us define B = {x: x is in set constructor notation} this is like a set of all sets that can be constructed.
Unlike the precise x<=3 above, there is no formal set constructor notation that I know to define set constructor notation, I'm relying upon the reader to understand that informal set definition.
What Godel would do here in essence is to give each set-constructor a number so that he could refer to it within itself. That way you can construct the set constructor {x : x is this constructor, x is not in constructor notation}.
That is a member of the set which is a member by virtue of saying it is not a member. Thus the member can be seen to be a member (because of its form), but you try and prove within the system you get a contradiction. This shows for my purposes (and has been identified elsewhere) that "truth" cannot always be proven within the system and relies on something else.
This is the liar paradox which is expressed well like this:
The Liar Paradox. "Truth" for English sentences is not definable in English.
Proof. Suppose it is. Then so is its complement "False". Let s be the sentence "This sentence is false" . Since the phrase "This sentence" refers to s, we have s iff "This sentence is false" iff "s is false" iff not s. A contradiction.
There are many oddities all very similar: consider Richard's Paradox which I quite like.
It all points to systems not being self-sufficient and I am taking that to point to the fact that if they were then why are minds needed to work on them?
Turing machines again find limitations in the halting problem (same link as Liar Paradox is good). I am trying to write a Turing machine on a Turing machine, its proving hard - any one know if it is possible? Obviously Turing machines carry the name Turing because of the work "He" did not the machines themselves.
Another paradox comes about like this:
Take a simple set system, we must define 2 things.
The Universal set (U), e.g. the colours = {red, white, blue, green}
A subset of U obeying some rule, A = {x: x is in the Union Jack, x in U}
So A = {red, white, blue}
The Universal is a special type of set which allows the complement: A' = U - A = {green}
Now the Universal set is "the universe of discourse", or "all the things we are talking about", or the "context". A new Universal set arises whenever we change subject, clearly that is the choice and work of the operator (mind).
Let me change subject to U1 = {x: x is four letter words} and define the set B = {x: x words beginning with "b", x in U1}
So we can see that "blue" is now a member of B. What has become of "green" in this universe? it doesn't exist. This is well documented in some philosophy esp. Buddhism that the mind creates existence, or that things have no existence outside the "field of discource".
Now if we can refer to the elements under discourse U, can we also refer to the "elements not-under discourse" for example {green} in this example. Well if we did then it would be under discourse and therefore part of U which contradicts U's definition, and if we don't then what is the meaning of "changing subject". Clearly the person using the set theory must be free from the field of discourse in order to define the U from the many elements which are not in U.
That is the more general paradox that we know that there are things outside our field of "view" or discussion, but if we try to refer to them they come under our field of view or discussion. So it is impossible to refer to things outside the field of view, or discussion, even while knowing they are there. How is that possible? i.e. there are things in the room next door that I can't see, but I know they are there... so what do they look like? we sort of imagine ghostly things that are both what they would look like if they were here, but which aren't here. Well I suspect in general that is called God to some, and I call it mind. Its the unbounded limits beyond the discourse which can't be in the discourse, but we know are there anyway.
The implications:
Materialist theories posit existence as a fundamental starting point. As seen above, existence is a product of mind or at least the field of discourse. Thus any theory trying to explain mind in terms of existences is flawed. I just had a "discussion" with a American neuro-scientist on the web and the unquestionable faith he put in existence was extraordinary. On one hand he says that the brain creates our world-view, on the other hand he says that world creates our brain. Well I pointed out if the world exists already what is the brain doing? He says it is creating a "representation" of the world. I said then what you call "the world" is only a "representation" since you are your brain, a representation of what? He didn't understand. Daniel Dennett is in the same camp, as is Dawkins and their hard materialist ilk.
AI etc runs into the same problems. Clearly we could make a human, women make humans every day. Its that this would not give us insight into mind. Mind is not brain because brain is only a field of discourse of mind.
Physics. There are a lot of quantum theories to explain mind and world. Again minds must be used ultimately to operate these theories and so these theories only posit a field of discourse. If machines could be made to operate these theories (like Deep Thought of Hitch Hikers fame) they would fall foul of the same problems surely?
Sunday, 30 September 2007
Thursday, 27 September 2007
Self-organising systems
Self-organising systems are dynamic systems which show stable emergent properties. i questioned already whether the emergent properties are really part of the under-lying dynamics - that is a question from Buddha!
In humans there are self-organising systems (basically the series that form societies structures, and also a large part of the processes that underlie all group formation). People may believe that they can create political parties and societies but unless the dynamics are already there it won't happen. Plus it is maybe rather egotistical that one person believes that by their own power they can influence so many people!
But as seem with the Nazis such self organising groups can put the individuals who are part of the self organisation in bizarre circumstances and make them behave in ways which alone they might disagree with.
It is precisely because social self-organisation can be so dangerous that it is something we should shy from, and remain personally conscious and responsible for everything we do. That is a repeat of the arguments against society and for Anarchy before.
In humans there are self-organising systems (basically the series that form societies structures, and also a large part of the processes that underlie all group formation). People may believe that they can create political parties and societies but unless the dynamics are already there it won't happen. Plus it is maybe rather egotistical that one person believes that by their own power they can influence so many people!
But as seem with the Nazis such self organising groups can put the individuals who are part of the self organisation in bizarre circumstances and make them behave in ways which alone they might disagree with.
It is precisely because social self-organisation can be so dangerous that it is something we should shy from, and remain personally conscious and responsible for everything we do. That is a repeat of the arguments against society and for Anarchy before.
Some problems from Physics
I don't have a formal understanding of this yet but as much as I understand: firstly Godel's incompleteness theorum states that in systems that correspond with maths it can be shown that some theorums cannot be proven from axioms. But we may be able to show they are true by computer process. Turing non-computability theorum indicates that some problems cannot be computed.
Disregarding those problems, the issue of where did all the data (information) in the universe come from? Now we might be able to determine equalities and equations, and we might be able to write comptable processes but upon what data can we work?
The possibility from the Quine investigation is that we could work on those theories themselves. If a theory could be created which produced which working on itself created itself this is a good step forward.
Disregarding those problems, the issue of where did all the data (information) in the universe come from? Now we might be able to determine equalities and equations, and we might be able to write comptable processes but upon what data can we work?
The possibility from the Quine investigation is that we could work on those theories themselves. If a theory could be created which produced which working on itself created itself this is a good step forward.
Constructing a Quine
I'm a bit annoyed with myself that I gave up too quick and had a glimpse of a quine which gave me the way forward. But I can construct the argument, and the sticking point, since I only gleened a small part of the problem.
A quine is a program which outputs (prints) itself. I'll use QBasic which is free and simple. It uses " for quotations and can't print " direct u need to use CHR$(34). I'm going to use ' for simplicity, so to use the program this will need be corrected.
We know then that it must include an output function that is 'PRINT' which sends whatever follows to the output screen. So our starting program is:
PRINT
it does nothing. So we know we need to print itself so we get
PRINT 'PRINT'
which produces an output of: PRINT. But putting new PRINTs in the code while it does produce a new PRINT in the output, also puts a new PRINT in the code so we never solve the problem.
What we need to do is add a PRINT to the output without typing it directly in the program. The easiest way to do this is to put the PRINT in memory (like a second screen) and then copy that twice to the output. That way you have 2 prints in the program (like the example above) and two in the output. Thus the problem has been solved and the backbone of the quine is done.
convert PRINT 'PRINT' to
a$ = 'PRINT': PRINT a$ a$
This was the sticking point for me last night, I was stuck on the approach of thinking that the a$ must include the program so I was starting like this:
a$ = 'a$ = ': PRINT a$ a$ -- This creates another problem of the type above. You need to mix data/code between the two parts of the equation ... it will be explained.
So given the basic structure above all we need to do is fill in the syntactic details. Firstly let us get the PRINT statement right so that it outputs as close as we possible to the above. In other words lets take the program elements of the first part and feed them into the data element of the PRINT statement in th second part.
: PRINT 'a$ = '' + a$ + '':' + a$
This outputs: a$ = 'PRINT': PRINT
So now take the program code of the second part (after the :) and feed that into the a$ data of the first part.
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' :
Stick those together and you got a quine
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' : PRINT 'a$ = '' + a$ + '':' + a$
However this does not work because on each line the data is enclosed by " marks, while the representation of " as data is '. If they were the same the program does not know whether to treat them as string delimiters or just parts of a string. If you then start filling out CHR$(34) then the code just keeps expanding endlessly.
This method does not work.
Trying to code delimiters and then enclode them within other delimiters is bound to fail because you will always have that problem we started with of a highest level delimiter which cannot be encoded.
A brute force method to solve this is to not use delimiters at all. The CHR$(34) method suggested above is the only way in QBasic to PRINT a " symbol since the " symbol is recognised by the language so we PRINT CHR$(34). We will have to use this method anyway somewhere.
So convert the whole string into ASC codes. There is a standard method in the language using READ to assign a variable with data from a DATA list.
Simply write the READ, DATA block with a line to print the CHR$ of each number, and another line to collect the list of data. Then once the data has all been read it prints the collection of data.
So the quine program reads its own data. Turns this into character output and then prints the data that it constructed itself from.
What the program could do is find its own place in memory and read itself into another memory location. Not that amazing really.
In the Quine though I've done that work already creating the data list. Using a recursive algorithm to write the program block, then encode it, then see how big it is and adjust the program and the code parameters until they match.
To note then: obviously the program gets written first. Without the engine nothing happens. This is a general solution to the problem of outputting data. Then just get it to print the data again to produce the data block at the end of the program. Then put in the data specific to itself and voila.
Its not as neat or intriguing as the first approach and I write endlessly here trying to find a way into the problem of "encoding itself". This second solution simply avoids the problem completely ... but how?
===
blurb from the first draft of this entry...
Now I'm interested in this process analogously because what I am having difficulty with, and the basis of my proof if such exists, is the implication of dualisms. For example where someone presents a limit to knowledge then this limit must be different from the knowledge itself. This is analogous to the data / program distinction. Other examples are subject / object. However if arguments of the Quine type can be constructed we have a way of expressing the "back breaking" job that dualisms create and find a way of overcoming the division.
Maybe then this investigation does not lead to a disproof of limits, but rather an personal understanding of how to construct limits within themselves, so that we can have something which full represents itself.
It is interesting that to do this we need to construct 2 copies of the partial structure, and that partial structure "represents" that dual creation. This if we were a "quine" only processing data we would know that our theorum on which we worked had two copies.
Q: how could a quine ever know that it was a quine? The process of comparing program and output is done by the user?
Q2: Next task a binary quine.
Q3: Is there a self-organising automaton version of the quine using recursive processes like above? Thesis/Anti-thesis -> Synthesis.
A quine is a program which outputs (prints) itself. I'll use QBasic which is free and simple. It uses " for quotations and can't print " direct u need to use CHR$(34). I'm going to use ' for simplicity, so to use the program this will need be corrected.
We know then that it must include an output function that is 'PRINT' which sends whatever follows to the output screen. So our starting program is:
it does nothing. So we know we need to print itself so we get
PRINT 'PRINT'
which produces an output of: PRINT. But putting new PRINTs in the code while it does produce a new PRINT in the output, also puts a new PRINT in the code so we never solve the problem.
What we need to do is add a PRINT to the output without typing it directly in the program. The easiest way to do this is to put the PRINT in memory (like a second screen) and then copy that twice to the output. That way you have 2 prints in the program (like the example above) and two in the output. Thus the problem has been solved and the backbone of the quine is done.
convert PRINT 'PRINT' to
a$ = 'PRINT': PRINT a$ a$
This was the sticking point for me last night, I was stuck on the approach of thinking that the a$ must include the program so I was starting like this:
a$ = 'a$ = ': PRINT a$ a$ -- This creates another problem of the type above. You need to mix data/code between the two parts of the equation ... it will be explained.
So given the basic structure above all we need to do is fill in the syntactic details. Firstly let us get the PRINT statement right so that it outputs as close as we possible to the above. In other words lets take the program elements of the first part and feed them into the data element of the PRINT statement in th second part.
: PRINT 'a$ = '' + a$ + '':' + a$
This outputs: a$ = 'PRINT': PRINT
So now take the program code of the second part (after the :) and feed that into the a$ data of the first part.
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' :
Stick those together and you got a quine
a$ = "PRINT 'a$ = '' + a$ + '':' + a$' : PRINT 'a$ = '' + a$ + '':' + a$
However this does not work because on each line the data is enclosed by " marks, while the representation of " as data is '. If they were the same the program does not know whether to treat them as string delimiters or just parts of a string. If you then start filling out CHR$(34) then the code just keeps expanding endlessly.
This method does not work.
Trying to code delimiters and then enclode them within other delimiters is bound to fail because you will always have that problem we started with of a highest level delimiter which cannot be encoded.
A brute force method to solve this is to not use delimiters at all. The CHR$(34) method suggested above is the only way in QBasic to PRINT a " symbol since the " symbol is recognised by the language so we PRINT CHR$(34). We will have to use this method anyway somewhere.
So convert the whole string into ASC codes. There is a standard method in the language using READ to assign a variable with data from a DATA list.
Simply write the READ, DATA block with a line to print the CHR$ of each number, and another line to collect the list of data. Then once the data has all been read it prints the collection of data.
So the quine program reads its own data. Turns this into character output and then prints the data that it constructed itself from.
What the program could do is find its own place in memory and read itself into another memory location. Not that amazing really.
In the Quine though I've done that work already creating the data list. Using a recursive algorithm to write the program block, then encode it, then see how big it is and adjust the program and the code parameters until they match.
To note then: obviously the program gets written first. Without the engine nothing happens. This is a general solution to the problem of outputting data. Then just get it to print the data again to produce the data block at the end of the program. Then put in the data specific to itself and voila.
Its not as neat or intriguing as the first approach and I write endlessly here trying to find a way into the problem of "encoding itself". This second solution simply avoids the problem completely ... but how?
===
blurb from the first draft of this entry...
Now I'm interested in this process analogously because what I am having difficulty with, and the basis of my proof if such exists, is the implication of dualisms. For example where someone presents a limit to knowledge then this limit must be different from the knowledge itself. This is analogous to the data / program distinction. Other examples are subject / object. However if arguments of the Quine type can be constructed we have a way of expressing the "back breaking" job that dualisms create and find a way of overcoming the division.
Maybe then this investigation does not lead to a disproof of limits, but rather an personal understanding of how to construct limits within themselves, so that we can have something which full represents itself.
It is interesting that to do this we need to construct 2 copies of the partial structure, and that partial structure "represents" that dual creation. This if we were a "quine" only processing data we would know that our theorum on which we worked had two copies.
Q: how could a quine ever know that it was a quine? The process of comparing program and output is done by the user?
Q2: Next task a binary quine.
Q3: Is there a self-organising automaton version of the quine using recursive processes like above? Thesis/Anti-thesis -> Synthesis.
Tuesday, 25 September 2007
random jot about consciousness
remember that a flat worm trained to do a maze and fed to another flat worm somehow passes on the knowledge. Examine that because information must be encodeable in flatworm matter!!
Don't forget music and consciousness. Frequences seem important, n music has been taken as a higher state of reality than text by quite a few!
Don't forget music and consciousness. Frequences seem important, n music has been taken as a higher state of reality than text by quite a few!
Notes as I read...
In other words true autopoesis is impossible.
Ok an autopoetic system supports itself, like butter is needed to make more butter. But you get chicken and egg because the first system must have been formed by other means. So it can't really "create" itself, only "support" itself
Alternatively its simply emergent property (almost epi-phenomalism), whereby an underlying dynamic system produces a stable property. But such a property is not involved in the system! Its a higher order.
An interesting possibility then is a system which creates an emergent property which is involved in the autopoesis. i suspect category mistake, but very interesting if this exists. i think immediately of group fitness versus individual fitness in behavioural ecology... however while these 2 levels can be studied i don't see yet how they interact.. if at all. Interesting way forward...
V. INTERSETING actually because this would test absolutely whether structure or "scale" was a product of perception or a reality. The world can be described in the level of atoms. It can also be described on the level of humans. But can it be described on both levels at the same time! This collection of atoms "died" thus leading to rapid dissipation. Does that make sense?
Just to state at this time, I've failed to see any "substance" in ideas of emergent properties. It seems to me to be simply a feature of "classification". Shall determine that belief for sure in this on going...
Just adding... regarding the old question about how remarkable it is that the world makes sense to humans... i wonder what the logical implications of it not making sense would be? What does this sentence really mean? Are we imagining a world that does not make sense? How about a world that makes more sense and in what sense. Obviously predicting the future is the test, and science does well. So in a world where we could not predict the future, or a world where the future was always known what are the logical implications? Well if the future was always known then it wouldn't be th future, and there would be no time (i suspect) and in a world where we simply could not predict the future and every moment was a complete suprise ther would be no memory or past (cos everything would be new). So time itself entails being slap bang in between the two!!! So why maths? That's the other big question... no thoughts yet...
self-organising -> basically decreasing entropy at one level, increasing at another.
Quines. Linked to compression. but first...
Compression a simple proof. If every binary sequence encodes a number, then there are as many binary sequences as N (natural numbers).
Now in compression we are saying that a number can be mapped to a smaller number and back again. In other words it is a 1 to 1 mapping within N. (btw The set of such mappings is the same size as N.) So given a number and a compression algorithm we need a bit of information to know whether the number is meant to be decompressed or not. ok that is not the proof just following a tangent, the proof was that each number by itself might or might-not be useful so compression is not an elimination of useless numbers, but rather a mapping and so it requires an algorithm to compress/decompress and that algorithm effectively generalises the information lost by compression. To develop an algorithm we extract the general information from the code, so that the code is smaller and the algorithm bigger. (We don't usually include the algorithm in the size of the result, but we should to be honest ... something need to just test with zip).
anyway the point and the relationship with Quines is that the code while producing itself is a cheat, because the binary exection code is not reproduced. A machine language Quine would be cute!! i.e. one that truely reproduced itself. And that is in Turing territory cos I need to write a Turning machine which first of all runs a set of Turing tables, and then writes itself. That would be exceptionally cute!!!
Same logic as the Turing machine on a Turing machine, consider a self interpreter... i.e. a compiler compiled by itself. Chicken and egg.
probably useless but tuppers self ref formula : http://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula
note: an argument I used against Dawkins Memes thus: has a weakness. He says that ideas evolve like genes (I had the idea of viruses). The problem tho is that Memes is an idea so if follows that it has evolved like a gene. Now the fitness of the Meme meme is not what Dawkins is meaning by its truth. I can't see the idea catching on, while it might be true. So we return to truth as a measure of fitness rather than population. Its not a strong argument against it, but it shows up the fact it can't be taken to totality, cos if the Meme meme was floated and then went extinct it loses any notability. This argument needs to be strengthened cos I suspect its a form of a general argument that could be applied to all formualtions including itself!
End. brain ache! off to eat.
Ok an autopoetic system supports itself, like butter is needed to make more butter. But you get chicken and egg because the first system must have been formed by other means. So it can't really "create" itself, only "support" itself
Alternatively its simply emergent property (almost epi-phenomalism), whereby an underlying dynamic system produces a stable property. But such a property is not involved in the system! Its a higher order.
An interesting possibility then is a system which creates an emergent property which is involved in the autopoesis. i suspect category mistake, but very interesting if this exists. i think immediately of group fitness versus individual fitness in behavioural ecology... however while these 2 levels can be studied i don't see yet how they interact.. if at all. Interesting way forward...
V. INTERSETING actually because this would test absolutely whether structure or "scale" was a product of perception or a reality. The world can be described in the level of atoms. It can also be described on the level of humans. But can it be described on both levels at the same time! This collection of atoms "died" thus leading to rapid dissipation. Does that make sense?
Just to state at this time, I've failed to see any "substance" in ideas of emergent properties. It seems to me to be simply a feature of "classification". Shall determine that belief for sure in this on going...
Just adding... regarding the old question about how remarkable it is that the world makes sense to humans... i wonder what the logical implications of it not making sense would be? What does this sentence really mean? Are we imagining a world that does not make sense? How about a world that makes more sense and in what sense. Obviously predicting the future is the test, and science does well. So in a world where we could not predict the future, or a world where the future was always known what are the logical implications? Well if the future was always known then it wouldn't be th future, and there would be no time (i suspect) and in a world where we simply could not predict the future and every moment was a complete suprise ther would be no memory or past (cos everything would be new). So time itself entails being slap bang in between the two!!! So why maths? That's the other big question... no thoughts yet...
self-organising -> basically decreasing entropy at one level, increasing at another.
Quines. Linked to compression. but first...
Compression a simple proof. If every binary sequence encodes a number, then there are as many binary sequences as N (natural numbers).
Now in compression we are saying that a number can be mapped to a smaller number and back again. In other words it is a 1 to 1 mapping within N. (btw The set of such mappings is the same size as N.) So given a number and a compression algorithm we need a bit of information to know whether the number is meant to be decompressed or not. ok that is not the proof just following a tangent, the proof was that each number by itself might or might-not be useful so compression is not an elimination of useless numbers, but rather a mapping and so it requires an algorithm to compress/decompress and that algorithm effectively generalises the information lost by compression. To develop an algorithm we extract the general information from the code, so that the code is smaller and the algorithm bigger. (We don't usually include the algorithm in the size of the result, but we should to be honest ... something need to just test with zip).
anyway the point and the relationship with Quines is that the code while producing itself is a cheat, because the binary exection code is not reproduced. A machine language Quine would be cute!! i.e. one that truely reproduced itself. And that is in Turing territory cos I need to write a Turning machine which first of all runs a set of Turing tables, and then writes itself. That would be exceptionally cute!!!
Same logic as the Turing machine on a Turing machine, consider a self interpreter... i.e. a compiler compiled by itself. Chicken and egg.
probably useless but tuppers self ref formula : http://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula
note: an argument I used against Dawkins Memes thus: has a weakness. He says that ideas evolve like genes (I had the idea of viruses). The problem tho is that Memes is an idea so if follows that it has evolved like a gene. Now the fitness of the Meme meme is not what Dawkins is meaning by its truth. I can't see the idea catching on, while it might be true. So we return to truth as a measure of fitness rather than population. Its not a strong argument against it, but it shows up the fact it can't be taken to totality, cos if the Meme meme was floated and then went extinct it loses any notability. This argument needs to be strengthened cos I suspect its a form of a general argument that could be applied to all formualtions including itself!
End. brain ache! off to eat.
Fine tune the form of argument
i just picked up off Wikipedia an excellent argument. If we were to prove that reason was flawed then that would flaw the proof since reason is flawed. Of course that would flaw the counter proof... its a mess.
My aim is not this. It is to show that for any symbolic system to be meaningful it must imply a non-symbolic "higher" heirachy, but obviously not be able to encode it. The "God" (or Mind) in the system so to speak.
Alternatively by reductio ad absurdum, if we were to assume that no non-symbolic realm was entailed, then a symbolic system would be able to entail itself. I seek to find out if this is the non-sense it seems to be.
Infinite heirachies, rather than a finite system, is the way to go.. at least it will keep the human race busy indefinitely!
My aim is not this. It is to show that for any symbolic system to be meaningful it must imply a non-symbolic "higher" heirachy, but obviously not be able to encode it. The "God" (or Mind) in the system so to speak.
Alternatively by reductio ad absurdum, if we were to assume that no non-symbolic realm was entailed, then a symbolic system would be able to entail itself. I seek to find out if this is the non-sense it seems to be.
Infinite heirachies, rather than a finite system, is the way to go.. at least it will keep the human race busy indefinitely!
An argument against materialism +
Just posted to a discussion board... but I have doubts
let me restate that another way in more depth if u don't mind reading it. You talk as though the table exists independent of the brain which percieves it, or the laws of physics under pin a reality which is independent of the brain which undertands them.
From a first person perspective you must admit you don't see 2 tables (the real one, and the perception) there is only 1 and that one is the perceived one. So what happened to the "real" one? Bad dualism steming from the materialist axioms we started with.
Lets start again (phenomenologically). There is only one table, that which you perceive. That is the thing you were calling "real". Your thoughts about it, which are not perceived, are just that "thoughts". when you think that the table is "real" actually that is a thought, not a state of existence! Hence how we can talk endlessly about it!
Now when you state in the 1st person that the perceptions are identical/product/what-ever of a "material brain" there are problems. Firstly that statement is an idea and has no "reality" - it's fantasy, like God. Secondly you are saying that your -now only - table (the perceived one i.e. the real table in your senses) is now not real but the result of this fantasy. Its very shakey territory, it will drive you mad, I hate this thought (for that is all it is).
The only escape is to reassert the primary status of the perception (the real table in the sense), for that is where all this thinking came from! Even if we think later it was an illusion, that is a thought, the "reality" is the "given".
Now that is true non-dualism, and strangely the notion of the "given" leads straight into notions of Pure-Mind, the Absolute and true-God. Ironic eh?
Doubts
=====
I'm still not done personally with the idea of the "given". Certainly I can be unconscious, and certainly i will die, losing all sense and thought. It seems that my ideas can gain knowledge of the "given" in a way that seems to transcend the "given".
Another example would be touching my own brain and watching not only the finger touching the tissue (in a mirror or something) but also the hallucinations it would create. My thoughts would be that the finger presses were causing the hallucinations. In other words the "given" was caused by finger presses to the brain, and that sets off all the thoughts about the brain being the cause of my experience.
Now I could take that a stage further and say that the finger press had caused a given and then caused all the thoughts themselves. That is the problem though isn't it because if the thoughts were caused by the finger press then the finger press is primary, and the thoughts simply entailments of that.
That does bring us back to the given being the primary cause, because it was the given "data" about the finger press, and the "given" hallucinations, that then caused thoughts.
If I fall asleep and wake from unconsciousness that sets off thoughts also. Thoughts about being conscious and thoughts about being unconscious. Interesting then that consciousness is a thought then brought on by unconsciousness. Is consciousness a "given"? that is the question!!
i have assumed to this point that consciousness was the arena of the "given". The "given" being the objects in consciousness. But if consciousness itself is a given, something to be distinguished from unconsciousness only by thought I finally get the bigger picture. The "Given" as transcending even consciousness and that is what I have personally struggled for, for ages.
Now returning to recent posts in the investigation of a proof of the finiteness/incompleteness/indefinite nature of thoughts it is actually accademic! The post made on meditation is the true path, but I wanted to leave a legacy at this cross roads, one that I could return to which clearly summarised the reason for turning away from "thoughts". s it worth continuing? Its still exciting work for the thinking mind, especially making a Turing machine, and learning set theory and logic enough to construct Cantor/Godel/Von Neuman proofs with confidence and following the science of consciousness and mind.
However it seems clear that whatever these branches discover it doesn't change anything, that the mysterious immediacy of Mind, the true Given, cannot be investigated because from it all things come, even the thoughts and theories that fill the pages of science books. Are these devils sapping my energies?
I was reminded last night of the Other World. Particularly vivid after a few weeks of intense "thought". The experience when i was 14 of jhana, that transcendent state of mind brought on by many weeks of hard work and concentration at school and home as i sort to be the best I could be. Totally different from anything I have talked about in these pages, complete unimaginable peace and purity of knowing. I saw the infinity of space within my Mind. I remember especially being aware of the space behind my head. This was not visual space. It came from contemplation of the darkness that surrounding the spot of light cast by the lamp on my desk. That light I realised was created by the darkness, and at once my mind filled the space of darkness - which is all around in a dark room. I may have mentioned this in previous posts ( a failure of my memory). It struck me last night how special and unexplored that experience was, quite different from the arena of play recently.
let me restate that another way in more depth if u don't mind reading it. You talk as though the table exists independent of the brain which percieves it, or the laws of physics under pin a reality which is independent of the brain which undertands them.
From a first person perspective you must admit you don't see 2 tables (the real one, and the perception) there is only 1 and that one is the perceived one. So what happened to the "real" one? Bad dualism steming from the materialist axioms we started with.
Lets start again (phenomenologically). There is only one table, that which you perceive. That is the thing you were calling "real". Your thoughts about it, which are not perceived, are just that "thoughts". when you think that the table is "real" actually that is a thought, not a state of existence! Hence how we can talk endlessly about it!
Now when you state in the 1st person that the perceptions are identical/product/what-ever of a "material brain" there are problems. Firstly that statement is an idea and has no "reality" - it's fantasy, like God. Secondly you are saying that your -now only - table (the perceived one i.e. the real table in your senses) is now not real but the result of this fantasy. Its very shakey territory, it will drive you mad, I hate this thought (for that is all it is).
The only escape is to reassert the primary status of the perception (the real table in the sense), for that is where all this thinking came from! Even if we think later it was an illusion, that is a thought, the "reality" is the "given".
Now that is true non-dualism, and strangely the notion of the "given" leads straight into notions of Pure-Mind, the Absolute and true-God. Ironic eh?
Doubts
=====
I'm still not done personally with the idea of the "given". Certainly I can be unconscious, and certainly i will die, losing all sense and thought. It seems that my ideas can gain knowledge of the "given" in a way that seems to transcend the "given".
Another example would be touching my own brain and watching not only the finger touching the tissue (in a mirror or something) but also the hallucinations it would create. My thoughts would be that the finger presses were causing the hallucinations. In other words the "given" was caused by finger presses to the brain, and that sets off all the thoughts about the brain being the cause of my experience.
Now I could take that a stage further and say that the finger press had caused a given and then caused all the thoughts themselves. That is the problem though isn't it because if the thoughts were caused by the finger press then the finger press is primary, and the thoughts simply entailments of that.
That does bring us back to the given being the primary cause, because it was the given "data" about the finger press, and the "given" hallucinations, that then caused thoughts.
If I fall asleep and wake from unconsciousness that sets off thoughts also. Thoughts about being conscious and thoughts about being unconscious. Interesting then that consciousness is a thought then brought on by unconsciousness. Is consciousness a "given"? that is the question!!
i have assumed to this point that consciousness was the arena of the "given". The "given" being the objects in consciousness. But if consciousness itself is a given, something to be distinguished from unconsciousness only by thought I finally get the bigger picture. The "Given" as transcending even consciousness and that is what I have personally struggled for, for ages.
Now returning to recent posts in the investigation of a proof of the finiteness/incompleteness/indefinite nature of thoughts it is actually accademic! The post made on meditation is the true path, but I wanted to leave a legacy at this cross roads, one that I could return to which clearly summarised the reason for turning away from "thoughts". s it worth continuing? Its still exciting work for the thinking mind, especially making a Turing machine, and learning set theory and logic enough to construct Cantor/Godel/Von Neuman proofs with confidence and following the science of consciousness and mind.
However it seems clear that whatever these branches discover it doesn't change anything, that the mysterious immediacy of Mind, the true Given, cannot be investigated because from it all things come, even the thoughts and theories that fill the pages of science books. Are these devils sapping my energies?
I was reminded last night of the Other World. Particularly vivid after a few weeks of intense "thought". The experience when i was 14 of jhana, that transcendent state of mind brought on by many weeks of hard work and concentration at school and home as i sort to be the best I could be. Totally different from anything I have talked about in these pages, complete unimaginable peace and purity of knowing. I saw the infinity of space within my Mind. I remember especially being aware of the space behind my head. This was not visual space. It came from contemplation of the darkness that surrounding the spot of light cast by the lamp on my desk. That light I realised was created by the darkness, and at once my mind filled the space of darkness - which is all around in a dark room. I may have mentioned this in previous posts ( a failure of my memory). It struck me last night how special and unexplored that experience was, quite different from the arena of play recently.
Is the Mind a Turing machine?
Well there is an easy answer to that: can a human do calculations that are non-computable. What does mean also?
Monday, 24 September 2007
Physics, Consciousness & summary
change of direction. News this week that Oxford studies show that "parallel worlds" significantly solves a number of quantum problems.
http://www.channel4.com/news/articles/science_technology/parallel+universes+exist++study/838052
So i'm off looking at this side of the equation. Consider though that Dennett has shown that Consciousness does not give either a spatially or temporarily coherent picture of brain processing. There is no direct match, rather that space and time seem to be constructs within a Turing machine modelled within the brain. A level of removal. So anyone looking for direct relationship leaves a lot of evidence out.
A learned friend (i.e. i wouldn't dismiss his ideas, and I don't fully understand them) believes (I think) that human choice can determine quantum states, so that we effectively chose which parallel universe we occupy. However (and I will find the experiments) this does not account for the fact that quatum states can be shown to be short lived even without human interference. i.e. it doesn't have to be a human instrument that checks on Shroedingers cat. Now u could argue that the whole system remains in quantum uncertainty until any human observation is made... and i don't know the difference but that is to be rechecked.
In the background I have my own take on this all which is that Mind is prior to all investigation, so putting the cart before the horse will create all kinds of problems. I also challenge the assumption that Mind is a product of Brain. Expect: Mind escapes any attempt at its classification, explanation, or replacement in any way by "thought" which is a product of Brain. I'm feeding in my understanding of Buddhist insights into Mind's unlimited nature. The true reality "just is" and from that comes everything else. Afterall if it "just wasn't" what are we investigating?
p.s. the maths stuff, and computing stuff, is leading - I see - toward an understanding of non-computable which is what I will be scratching around with for a while. Damn i've wasted time. But the naive work i did in 1996 at least put me in the opinion that machines that work on their own data set, recursively, churn out non-sense. That links meaningful work to the environment and intelligence can't be an inner product. Consciousness as we know is outside the brain for how else can we see things? hehe. OK Todo: fully understand proofs of non-computable so I can see if i can either find the right one or construct it. Keep up the effort to show that all textual/symbol work must be done in conjunction with a historical Brain (these marks on the page while having low entropy) are meaningless without a trained human to read them, and that this Brain can't be a "finite state machine" whose output could be totally put to paper. That is what I am doing, but I'm not dumping my training cos u can't learn to read by reading!
Check these names: Hameroff, Penrose in connection with work after 1992 on microtubules and consciousness. http://findarticles.com/p/articles/mi_m1511/is_n6_v15/ai_15447461/pg_1
btw in the smart language I'm learning i can frame the arguments thus: Thought is non-computable because there are issues with recursiveness. It would be like trying to think a thought. Consciousness even more so. And Mind is beyond all frames of reference. Investigate...
p.p.s. the issue of compression shows up too... because finding patterns in data is kike finding meaning too! and if there was a general algorythm then there would be a fixed way of getting meaning and then a machine could replace the human brain... a multiplicity of algorithms is the point and the mysterious (karmic) glue which determines which ones we use at any given time!
http://www.channel4.com/news/articles/science_technology/parallel+universes+exist++study/838052
So i'm off looking at this side of the equation. Consider though that Dennett has shown that Consciousness does not give either a spatially or temporarily coherent picture of brain processing. There is no direct match, rather that space and time seem to be constructs within a Turing machine modelled within the brain. A level of removal. So anyone looking for direct relationship leaves a lot of evidence out.
A learned friend (i.e. i wouldn't dismiss his ideas, and I don't fully understand them) believes (I think) that human choice can determine quantum states, so that we effectively chose which parallel universe we occupy. However (and I will find the experiments) this does not account for the fact that quatum states can be shown to be short lived even without human interference. i.e. it doesn't have to be a human instrument that checks on Shroedingers cat. Now u could argue that the whole system remains in quantum uncertainty until any human observation is made... and i don't know the difference but that is to be rechecked.
In the background I have my own take on this all which is that Mind is prior to all investigation, so putting the cart before the horse will create all kinds of problems. I also challenge the assumption that Mind is a product of Brain. Expect: Mind escapes any attempt at its classification, explanation, or replacement in any way by "thought" which is a product of Brain. I'm feeding in my understanding of Buddhist insights into Mind's unlimited nature. The true reality "just is" and from that comes everything else. Afterall if it "just wasn't" what are we investigating?
p.s. the maths stuff, and computing stuff, is leading - I see - toward an understanding of non-computable which is what I will be scratching around with for a while. Damn i've wasted time. But the naive work i did in 1996 at least put me in the opinion that machines that work on their own data set, recursively, churn out non-sense. That links meaningful work to the environment and intelligence can't be an inner product. Consciousness as we know is outside the brain for how else can we see things? hehe. OK Todo: fully understand proofs of non-computable so I can see if i can either find the right one or construct it. Keep up the effort to show that all textual/symbol work must be done in conjunction with a historical Brain (these marks on the page while having low entropy) are meaningless without a trained human to read them, and that this Brain can't be a "finite state machine" whose output could be totally put to paper. That is what I am doing, but I'm not dumping my training cos u can't learn to read by reading!
Check these names: Hameroff, Penrose in connection with work after 1992 on microtubules and consciousness. http://findarticles.com/p/articles/mi_m1511/is_n6_v15/ai_15447461/pg_1
btw in the smart language I'm learning i can frame the arguments thus: Thought is non-computable because there are issues with recursiveness. It would be like trying to think a thought. Consciousness even more so. And Mind is beyond all frames of reference. Investigate...
p.p.s. the issue of compression shows up too... because finding patterns in data is kike finding meaning too! and if there was a general algorythm then there would be a fixed way of getting meaning and then a machine could replace the human brain... a multiplicity of algorithms is the point and the mysterious (karmic) glue which determines which ones we use at any given time!
Friday, 21 September 2007
The Transcendental Set
Propositon: a set cannot be a member of itself
Using c to mean is a subset of, ¬c to mean not a subset of, e to mean is a member of, and ¬e mean not a member of, n to mean intersection
Take a universal set (U) of natural numbers: N
If E is the set of all the even numbers, then E c N but E ¬e N because "the set of even numbers" is not itself a number. (i.e. A is a subset of N, but not a member of N.)
Thus the process of "creating" a set seems to be an arbitrary "given" action performed by the thinker which is not present within the theory of sets. In other words, you cannot express the process of set creation within set theory, it is a mysterious process of "mind" that is required prior to set theory itself.
We can create a new universal set: the set of all natural numbers and sets of these numbers = N1
Now E c N1 and E e N1.
But if we create a new exotic set say all the even numbers and itself, E1
Then again E1 c N1 but E ¬e N1
Now we can continue this recursion one stage further, N2 = the set of all natural numbers, sets of these numbers and sets of these sets. There is an infinite recursion at each stage the new Nx not being a member of itself.
Is it possible to close this infinite recursion by being self referential? So that T was a set of sets of such sets to an infinitely level of recursion i.e. T e T
We would need to say something like: T = the set of all sets where each member x, if x ¬e N can be unpacked recursively until x e N.
However there is the obvious problem that this loop cannot be resolved because T = {T, ...} and at each stage it must start again to unpack itself.
However if we were to create a super set without complex conditions basically the set of everything. A set that truely can belong to itself. I have come to consider what the meaning of such a set is? Can it actually be formulated, is it meaningful?
Consider so far: there is the arbitrary process required by the human operator to construct a set. Even just using the empty set {} an infinite set can be created as is used to define the natural numbers (http://plato.stanford.edu/entries/set-theory/primer.html/l4). Quite how we construct sets tho is quite arbitrary and requires the "intelligence" of an operator to "decide" what to do. Logical systems can't solve themselves else the whole of maths and thought would be there on a plate. So while we can consider such a set, real set theory requires meaningful decisions by the operator to "create" sets and monitor the process of proof and deduction. The set T is composed from an indefinite number of meaningless and contradictory sets (like the set of all sets that do not contain themselves). It is a real chimera of no rigorous value.
Let us take such a transcendental set T which has one member namely itself.
T = {T}
This defines a recursive set so that unpacking any number of times gives us equalities of the form:
T = {..{{{{T}}}}..}
If we try to create a new set containing the transcendental set {T} we find that it is the same as T. The recursion works indefinitely in both directions (i.e. unpacking and repacking).
T has only one member itself, but defines an infinite "heirachy" of sets. Heirachy was the property that stopped us previously making {A} a member of A.
Now let us take an exotic transcendental set with a second non transcendental member.
T = {T, A}
This creates a recursion downwards when we try to "unpack" and a heirachy of the form
T = {.. { { { {T, A}, A} ,A} ,A} .. ,A}
However If we repack (recurse the other way) we can ask what is {T} ? i.e. what is the set containing T?
It clearly isn't T itself (which is {T, A} ) and it isn't a member of T either.
Again the process of heirachy stops us from including T within itself. It is no-longer a transcendental set.
If however we take the set A again (which is a subset of T) then we could repack the two together {T, A} and continue the recursion backwards.
...this is to be completed...
I was also thinking that the first exploration shows us that when a set is determined by reference to members it can't be a member of itself because there is the recursive problem of finding out what the members are.
However if a set is defined by reference to set properties that are clear regardless of the members then we can determine set membership without recursion, and then the possibility of self inclusion arises.
To investigate that I was considering the properties of a set. Let P be the set of all set properties
P = {definition, description, cardinality}
P should be self referential at least in that if it is a set it should fulfill those criteria.
P = {"a list of different entities separated by commas and enclosed in brackets", "the list of all set properties", 3}
Now using these we can construct sets without reference to their members, and so avoid the recursion problem.
1) A set containing a set: T = {T}
2) A set whose member is named T: T = {T}
3) A set containing 1 member T = {T}
But these are rather fake examples. A necessary example would be the set of all sets which MUST contain itself since it is a set. T = {T, ...}
I'll leave the investigation there for now till its clear where to go...
Using c to mean is a subset of, ¬c to mean not a subset of, e to mean is a member of, and ¬e mean not a member of, n to mean intersection
Take a universal set (U) of natural numbers: N
If E is the set of all the even numbers, then E c N but E ¬e N because "the set of even numbers" is not itself a number. (i.e. A is a subset of N, but not a member of N.)
Thus the process of "creating" a set seems to be an arbitrary "given" action performed by the thinker which is not present within the theory of sets. In other words, you cannot express the process of set creation within set theory, it is a mysterious process of "mind" that is required prior to set theory itself.
We can create a new universal set: the set of all natural numbers and sets of these numbers = N1
Now E c N1 and E e N1.
But if we create a new exotic set say all the even numbers and itself, E1
Then again E1 c N1 but E ¬e N1
Now we can continue this recursion one stage further, N2 = the set of all natural numbers, sets of these numbers and sets of these sets. There is an infinite recursion at each stage the new Nx not being a member of itself.
Is it possible to close this infinite recursion by being self referential? So that T was a set of sets of such sets to an infinitely level of recursion i.e. T e T
We would need to say something like: T = the set of all sets where each member x, if x ¬e N can be unpacked recursively until x e N.
However there is the obvious problem that this loop cannot be resolved because T = {T, ...} and at each stage it must start again to unpack itself.
However if we were to create a super set without complex conditions basically the set of everything. A set that truely can belong to itself. I have come to consider what the meaning of such a set is? Can it actually be formulated, is it meaningful?
Consider so far: there is the arbitrary process required by the human operator to construct a set. Even just using the empty set {} an infinite set can be created as is used to define the natural numbers (http://plato.stanford.edu/entries/set-theory/primer.html/l4). Quite how we construct sets tho is quite arbitrary and requires the "intelligence" of an operator to "decide" what to do. Logical systems can't solve themselves else the whole of maths and thought would be there on a plate. So while we can consider such a set, real set theory requires meaningful decisions by the operator to "create" sets and monitor the process of proof and deduction. The set T is composed from an indefinite number of meaningless and contradictory sets (like the set of all sets that do not contain themselves). It is a real chimera of no rigorous value.
Let us take such a transcendental set T which has one member namely itself.
T = {T}
This defines a recursive set so that unpacking any number of times gives us equalities of the form:
T = {..{{{{T}}}}..}
If we try to create a new set containing the transcendental set {T} we find that it is the same as T. The recursion works indefinitely in both directions (i.e. unpacking and repacking).
T has only one member itself, but defines an infinite "heirachy" of sets. Heirachy was the property that stopped us previously making {A} a member of A.
Now let us take an exotic transcendental set with a second non transcendental member.
T = {T, A}
This creates a recursion downwards when we try to "unpack" and a heirachy of the form
T = {.. { { { {T, A}, A} ,A} ,A} .. ,A}
However If we repack (recurse the other way) we can ask what is {T} ? i.e. what is the set containing T?
It clearly isn't T itself (which is {T, A} ) and it isn't a member of T either.
Again the process of heirachy stops us from including T within itself. It is no-longer a transcendental set.
If however we take the set A again (which is a subset of T) then we could repack the two together {T, A} and continue the recursion backwards.
...this is to be completed...
I was also thinking that the first exploration shows us that when a set is determined by reference to members it can't be a member of itself because there is the recursive problem of finding out what the members are.
However if a set is defined by reference to set properties that are clear regardless of the members then we can determine set membership without recursion, and then the possibility of self inclusion arises.
To investigate that I was considering the properties of a set. Let P be the set of all set properties
P = {definition, description, cardinality}
P should be self referential at least in that if it is a set it should fulfill those criteria.
P = {"a list of different entities separated by commas and enclosed in brackets", "the list of all set properties", 3}
Now using these we can construct sets without reference to their members, and so avoid the recursion problem.
1) A set containing a set: T = {T}
2) A set whose member is named T: T = {T}
3) A set containing 1 member T = {T}
But these are rather fake examples. A necessary example would be the set of all sets which MUST contain itself since it is a set. T = {T, ...}
I'll leave the investigation there for now till its clear where to go...
Thursday, 20 September 2007
The Ultimate
A brief foray into set theory last week came as an attempt to prove that the Ultimate must be a different type of thing to everything else. Hiding in the wings was the idea that the Mind must be a "given" in any thinking - not in Cartesian sense that there must be a thinker - but in the sense that thought can't hold together without something linking the thoughts etc. Whatever that is it can't be itself a thought. Its the general view that there must be a heirachy in any system where each level cannot access the higher level. Thus for example God cannot Himself a thing in the world He created, or that a Table can't be the same type of thing as its components etc
The form of the proof was that there cannot be a set containing the Universal set.
Let us refer to the ultimate Universal (E), the set of all things, and all sets of things. There is nothing which is not in this Ultimate set. The question is: is there a set containing E?
If there is a set containing E then it must be a member of E. However if there is not a set containing E then E is unlike all things in that it is not a member of any set.
Let us define a set T = {E}
and since T is a set it belongs to E. Now how do we define T'? On the one hand T' is everything else in the universal set E, on the other it is
...
to be completed there is a tricky bit here, creating a set seems to protect us from the problem!!!!
Anyway that has led to Alan Turing and the Universal Turing Machine. The question I seem to have posed myself since a child has been this question of the Ultimate and whether there is anything beyond it, or whether it even exists. Were it to be decided one way or another what the nature of the Ultimate was it seems to have a lot of ramifications. For one it would stop people fighting thinking that they have got the position of ultimate. It would also sort out the body/mind problem because the question there is one of ultimate: some say that matter is sufficient for everything and others mind, and the people in between have got oil and water. It sorts out AI and whether finite machines can experience a "World" it ties a lot that i've struggled for together so I'm interested. Whether it helps with that question of Life remains to be seen, a Life spent searching the answer seems a bad answer and a bad question!
i continue to explore this but realise with some humility that maybe my faculties are not up to it, and there have been some truley great people before me who have not to my knowledge devised any rigorous views of the ultimate. Infact the ultimate seems largely unexplored by most. Maths covers it with Cantor and his theory of infinities, religions cover it with God. The view seems to be that the ultimate is impossible and beyond finite minds.
Now with Turing machines at least we could show that any notion of "the ultimate" either was or was not computable?
The persisting idea for myself is that whatever is done it seems that we lie outside the system being devised. If we ever were to devise an ultimate answer we would lie outside. So I suspect any proofs come in the form that the Ultimate could never contain itself. Turing machines written on Turing machines? that was the plan tonight but its late I'm tired and pumping out "notes" onto this ticker tape for my "system state" to start again at some time in the future.
Stuff here from Daniel Dennett who've I argued against before but am taking more seriously now as a means of seeing if there are any immanent contradictions.
Searle, Strawson, Saussure note to self to consider them...
Its a huge question not least because whenever I try to frame the question the frame itself becomes a limit that needs to be reconsidered. There seems to be no foundation large enough to create a proof that covers everything? I'm looking for a limit of thought that might liberate a world beyond thought, yet even thought is a tricky thing which refuses exact definition.
The undecidability of it, non-computability of it might be the way forward. There is neither a proof of the infinite, nor the finite because it is even more abstract than that. Imagine living in a world which was proven to be infinite. Isn't that as frightening a prospect as one that was proven to be finite? Its an interesting thought. I certainly want to tidy all this up, as said before about narcisism i am tired of doing the same thing, the same tricks, the same questions. Its been the best part of a life now chasing after the Ultimate, the Big Question, the Gold country, but I am tired... and hungry
The form of the proof was that there cannot be a set containing the Universal set.
Let us refer to the ultimate Universal (E), the set of all things, and all sets of things. There is nothing which is not in this Ultimate set. The question is: is there a set containing E?
If there is a set containing E then it must be a member of E. However if there is not a set containing E then E is unlike all things in that it is not a member of any set.
Let us define a set T = {E}
and since T is a set it belongs to E. Now how do we define T'? On the one hand T' is everything else in the universal set E, on the other it is
...
to be completed there is a tricky bit here, creating a set seems to protect us from the problem!!!!
Anyway that has led to Alan Turing and the Universal Turing Machine. The question I seem to have posed myself since a child has been this question of the Ultimate and whether there is anything beyond it, or whether it even exists. Were it to be decided one way or another what the nature of the Ultimate was it seems to have a lot of ramifications. For one it would stop people fighting thinking that they have got the position of ultimate. It would also sort out the body/mind problem because the question there is one of ultimate: some say that matter is sufficient for everything and others mind, and the people in between have got oil and water. It sorts out AI and whether finite machines can experience a "World" it ties a lot that i've struggled for together so I'm interested. Whether it helps with that question of Life remains to be seen, a Life spent searching the answer seems a bad answer and a bad question!
i continue to explore this but realise with some humility that maybe my faculties are not up to it, and there have been some truley great people before me who have not to my knowledge devised any rigorous views of the ultimate. Infact the ultimate seems largely unexplored by most. Maths covers it with Cantor and his theory of infinities, religions cover it with God. The view seems to be that the ultimate is impossible and beyond finite minds.
Now with Turing machines at least we could show that any notion of "the ultimate" either was or was not computable?
The persisting idea for myself is that whatever is done it seems that we lie outside the system being devised. If we ever were to devise an ultimate answer we would lie outside. So I suspect any proofs come in the form that the Ultimate could never contain itself. Turing machines written on Turing machines? that was the plan tonight but its late I'm tired and pumping out "notes" onto this ticker tape for my "system state" to start again at some time in the future.
Stuff here from Daniel Dennett who've I argued against before but am taking more seriously now as a means of seeing if there are any immanent contradictions.
Searle, Strawson, Saussure note to self to consider them...
Its a huge question not least because whenever I try to frame the question the frame itself becomes a limit that needs to be reconsidered. There seems to be no foundation large enough to create a proof that covers everything? I'm looking for a limit of thought that might liberate a world beyond thought, yet even thought is a tricky thing which refuses exact definition.
The undecidability of it, non-computability of it might be the way forward. There is neither a proof of the infinite, nor the finite because it is even more abstract than that. Imagine living in a world which was proven to be infinite. Isn't that as frightening a prospect as one that was proven to be finite? Its an interesting thought. I certainly want to tidy all this up, as said before about narcisism i am tired of doing the same thing, the same tricks, the same questions. Its been the best part of a life now chasing after the Ultimate, the Big Question, the Gold country, but I am tired... and hungry
Argument for why I am a narcisist
I think I am better than other people
I have this problem with idealising girls, but then finding then worthless
I do not like being contradicted
I can fall into a world view where i seem to be the only one existing
I like being an object of adoration
I do not like order, and seek instability, arguing for in the form of an indefinable Ultimate which cannot be bettered.
So I was just reading about this on the web. It fits certain facts, in particular the issue I have grown tired of namely the struggle to prove my worth. It seems that unless I "am" somebody then my life is worthless. However becoming somebody in the sense of having a particular status is not enough because it draws me into a fixed status, a mediocrity, so i abandon any particular status in search of the Ultimate. The Ultimate being some state that cannot be bettered which is all encompassing and which avoids the problem of being bettered itself, of being incomplete, of being mediocre. So the chaos continues so that I do not become fixed into a mundane state.
My defense is that seeking to be better as a person is not a bad thing. That not associating with those who one deems lacking in such a lofty desire keeps one vigorous. To enjoy the company of one who sees one as special is no different from love. Being contadicted for the sake of it, or unjustly without apparent cause is annoying. There is something particularly unusual about being oneself which gives ones own perspective a automatic first place or first person. That without balance can lead toward self-obsession.
The main point is that I am tired of all these things already. I do not want have to be better than others. Can't life be a peaceful acceptance of oneself without struggle and likewise the acceptance of others without struggle. The problem there is that so often others seem to make crazy decisions which do effect oneself and you wish that you had been in the position to make that decision yourself: top of the list the decisions to do all this warring. Governments innocently say that it was a carefully taken decision yet to myself it was always absurd. That does lead me to want to separate myself from these "idiotic" people. "Idiotic people" is a phrase I am tired of hearing from myself.
Anyway to personal resolutions to correct any imbalance are thus: firstly to seek an even view of others. If people make "crazy" decisions I at least must realise that to them they made sense, even if I am too idiotic myself to understand why. Secondly it is impossible to seek a total world view so that you might be in a position to make "correct" decision for everyone. Thus an individual can never know what is best for others, and therefore never "help" in an absolute way others because the individual only ever has a partial picture. Thirdly (I have made suprising progress here) seeking a satisfactory existence without the attention of others, especially girls.
Fourthly gets its special line (blog entry) because it links directly into the general flow of the blog. The Ultimate? new post...
I have this problem with idealising girls, but then finding then worthless
I do not like being contradicted
I can fall into a world view where i seem to be the only one existing
I like being an object of adoration
I do not like order, and seek instability, arguing for in the form of an indefinable Ultimate which cannot be bettered.
So I was just reading about this on the web. It fits certain facts, in particular the issue I have grown tired of namely the struggle to prove my worth. It seems that unless I "am" somebody then my life is worthless. However becoming somebody in the sense of having a particular status is not enough because it draws me into a fixed status, a mediocrity, so i abandon any particular status in search of the Ultimate. The Ultimate being some state that cannot be bettered which is all encompassing and which avoids the problem of being bettered itself, of being incomplete, of being mediocre. So the chaos continues so that I do not become fixed into a mundane state.
My defense is that seeking to be better as a person is not a bad thing. That not associating with those who one deems lacking in such a lofty desire keeps one vigorous. To enjoy the company of one who sees one as special is no different from love. Being contadicted for the sake of it, or unjustly without apparent cause is annoying. There is something particularly unusual about being oneself which gives ones own perspective a automatic first place or first person. That without balance can lead toward self-obsession.
The main point is that I am tired of all these things already. I do not want have to be better than others. Can't life be a peaceful acceptance of oneself without struggle and likewise the acceptance of others without struggle. The problem there is that so often others seem to make crazy decisions which do effect oneself and you wish that you had been in the position to make that decision yourself: top of the list the decisions to do all this warring. Governments innocently say that it was a carefully taken decision yet to myself it was always absurd. That does lead me to want to separate myself from these "idiotic" people. "Idiotic people" is a phrase I am tired of hearing from myself.
Anyway to personal resolutions to correct any imbalance are thus: firstly to seek an even view of others. If people make "crazy" decisions I at least must realise that to them they made sense, even if I am too idiotic myself to understand why. Secondly it is impossible to seek a total world view so that you might be in a position to make "correct" decision for everyone. Thus an individual can never know what is best for others, and therefore never "help" in an absolute way others because the individual only ever has a partial picture. Thirdly (I have made suprising progress here) seeking a satisfactory existence without the attention of others, especially girls.
Fourthly gets its special line (blog entry) because it links directly into the general flow of the blog. The Ultimate? new post...
Tuesday, 11 September 2007
IMPORTANT: Reality refuses expression because it is a relationship
How ever you try to totally express reality you end up with a contradiction.
This is most famously used by Godel to prove that a logical system of maths will provide statements which cannot be proven. He does this by encoding the maths with integer symbols which are also the "data" of the system.
This is the same problem I've had with AI. A computer system that is designed to process itself to give it some sort of "self awareness" ends up in meaningless data crunching.
More generally the problem is that any theorum which claims to explain "everything" must end up explaining itself. Thus any "creative" feature of the theorum which defines distinctions between elements must itself be a product of those distinctions.
There can only be one such root theorum which is also meaningless because it self evident and defines nothing. At college I used to joke that it the fundamental thoerum should be called Q. It had no meaning because all other meanings were to be definied in terms of it. It is obviously meaningless and useless.
It also doesn't explain everything because the very creation of an discrete object "Q" distinct from any other objects "O" or "P" is unexplained.
The world begins in objects whether they be mathematical entities or perceptual or thought entities. An explanation of the process of object creation is obviously beyond the realm of objects themselves.
The reduction of "brains" or "sensory systems" to objects is a further theorum awaiting contradictions. A brain is a "thing", yet the process of identifying "things" we are trying to explain in terms of brains.
The materialists escape because they think that "thinghood" is a fundamental property of matter. So it then falls to the physicists to examine "thinghood". Yet every theorum and system of equations is itself a system of things and so like Godel will result in logic which patentally can be shown to be incomplete and contradictary.
In the intuitive realm our lives are problematised by such contradictions. Especially the belief that we ourselves are a "thing". If I am a "thing" how is it that I am related to the other expernal things which are not myself. The body/mind dualism and the soul, the Liberal Capitalist requirement for a fudged concept of "property" as a glue to stick individuals to things, even life/death have the hollow sound of this problem which struck.
In 1994 in the toilet of a supermarket where I was working as I washed my hands it suddenly struck me that the sense of "reality" that I experienced and seemed to real to myself but not to others was due to my own "existence" as a thing distinct from them. Logically I realised last week this is a very flawed piece of thinking. Its not a new observation! What is the justification in such thinking for my founding belief that "I" am a "thing"? This is the ghost of Descartes still haunting. If "things" are a product of what I might call Mind after the Buddhists, then how can I base the mind upon a thing? The sense of reality is not the product of a "thing which thinks" but rather the other way around.
And now after a million years in the wilderness it starts to come together. Every "thing" which exists especially every thought, equation, parameter, entity is the product of something which cannot be thought.
To try to express this higher reality in thoughts, in "things", leads to the endless contradictions and incompleteness of thought.
Thought is fractured and forever broken upon the back of "reality" which resists its expression in thought because thought can never think itself. Thought is not reality!
"Thingism" - the belief that the world is composed primarity of distinct entities each with a potential name - and that the interactions of these "things" is what creates the world is a "thing" itself. Good for many purposes but not good for understanding totality - which is another thing ... or so it would seem at first look... if totality can be recoded as Q see above for the problem!
The process of "thingification" occurs due to distinctions made by the Mind. "thingification" is the same as "creating distinctions". Mind is not a thing, a place holder identical to God in His most abstract formulation.
Distinctions are created and are not fundamental to some material reality. Afterall "material reality" would then be a thing itself so cannot be a founding principle or belief at all!!!!
Distinctions are thus in the realm of Mind (not a thing, not even Q).
Distinctions is logically synonymous with the idea of relationship. Its a dialectic.
In a relationship we only talk about the notion of "distinction" and "thinghood" because the relationship brings entities together in such a way that they gain their thinghood and at the same time gain their distinctness from one another.
No relationship = no "thinghood" and no "distinction".
Things do not have thinghood outside of a relationship because without being related to something else how can they be distinct?
Thus a very fine balance needs to be used to see the creative nature of "relationship". Its too easy to fall into believing that a relationship lies between already existing "in themselves" objective material relaities. See above or the logical problem with codefying things within a theorem which is itself postulating a thing.
Its also too easy to view a relationship as a "thing". Its a relationship between things which gain their thinghood from the relationship. Its a exact co-dependency.
In the ordinary realm thinghood is a great issue. Phobics and Philiacs alike create distinctions between things and labour these distinctions until they seem really important. We can almost identify people by their choices of what to labour. This person really doesn't like spiders, this person likes them so much they keep them as a pet, and most people don't really even see them. Neither the phobic or philiac sees the process of thingification, the distinctions they chose to make, and the relationships none of which are actually materially real. To undo a phobia or philia we need only see that it is not "real" and unchangeable and train ourselves to find other relationships and ways of thingifying the world. Such beliefs as wealth, status, and self are dominating philias under whose influence we spend much of our lives.
Beyond "thinghood" is impossible. That would be to imagine a realm of non- thinghood which would be a thing itself by virtue of the distinction and relationship we are making between the things and the non-things. In this world we've got the essential contradiction which lies within, the fracture which shows us that it has ended. Its is interesting to me that this ties together the endevours of science, maths, logic and philosophy (whose things are concepts!!).
Meditation is the main tool for gaining a liberation from thinghood. Its not a moving beyond - there is no beyond - its not a gaining of new distinct state that is just another thing. Its "liberation"... to be explored. I need to embark upon a disciplined process of meditation now to go on.
This is most famously used by Godel to prove that a logical system of maths will provide statements which cannot be proven. He does this by encoding the maths with integer symbols which are also the "data" of the system.
This is the same problem I've had with AI. A computer system that is designed to process itself to give it some sort of "self awareness" ends up in meaningless data crunching.
More generally the problem is that any theorum which claims to explain "everything" must end up explaining itself. Thus any "creative" feature of the theorum which defines distinctions between elements must itself be a product of those distinctions.
There can only be one such root theorum which is also meaningless because it self evident and defines nothing. At college I used to joke that it the fundamental thoerum should be called Q. It had no meaning because all other meanings were to be definied in terms of it. It is obviously meaningless and useless.
It also doesn't explain everything because the very creation of an discrete object "Q" distinct from any other objects "O" or "P" is unexplained.
The world begins in objects whether they be mathematical entities or perceptual or thought entities. An explanation of the process of object creation is obviously beyond the realm of objects themselves.
The reduction of "brains" or "sensory systems" to objects is a further theorum awaiting contradictions. A brain is a "thing", yet the process of identifying "things" we are trying to explain in terms of brains.
The materialists escape because they think that "thinghood" is a fundamental property of matter. So it then falls to the physicists to examine "thinghood". Yet every theorum and system of equations is itself a system of things and so like Godel will result in logic which patentally can be shown to be incomplete and contradictary.
In the intuitive realm our lives are problematised by such contradictions. Especially the belief that we ourselves are a "thing". If I am a "thing" how is it that I am related to the other expernal things which are not myself. The body/mind dualism and the soul, the Liberal Capitalist requirement for a fudged concept of "property" as a glue to stick individuals to things, even life/death have the hollow sound of this problem which struck.
In 1994 in the toilet of a supermarket where I was working as I washed my hands it suddenly struck me that the sense of "reality" that I experienced and seemed to real to myself but not to others was due to my own "existence" as a thing distinct from them. Logically I realised last week this is a very flawed piece of thinking. Its not a new observation! What is the justification in such thinking for my founding belief that "I" am a "thing"? This is the ghost of Descartes still haunting. If "things" are a product of what I might call Mind after the Buddhists, then how can I base the mind upon a thing? The sense of reality is not the product of a "thing which thinks" but rather the other way around.
And now after a million years in the wilderness it starts to come together. Every "thing" which exists especially every thought, equation, parameter, entity is the product of something which cannot be thought.
To try to express this higher reality in thoughts, in "things", leads to the endless contradictions and incompleteness of thought.
Thought is fractured and forever broken upon the back of "reality" which resists its expression in thought because thought can never think itself. Thought is not reality!
"Thingism" - the belief that the world is composed primarity of distinct entities each with a potential name - and that the interactions of these "things" is what creates the world is a "thing" itself. Good for many purposes but not good for understanding totality - which is another thing ... or so it would seem at first look... if totality can be recoded as Q see above for the problem!
The process of "thingification" occurs due to distinctions made by the Mind. "thingification" is the same as "creating distinctions". Mind is not a thing, a place holder identical to God in His most abstract formulation.
Distinctions are created and are not fundamental to some material reality. Afterall "material reality" would then be a thing itself so cannot be a founding principle or belief at all!!!!
Distinctions are thus in the realm of Mind (not a thing, not even Q).
Distinctions is logically synonymous with the idea of relationship. Its a dialectic.
In a relationship we only talk about the notion of "distinction" and "thinghood" because the relationship brings entities together in such a way that they gain their thinghood and at the same time gain their distinctness from one another.
No relationship = no "thinghood" and no "distinction".
Things do not have thinghood outside of a relationship because without being related to something else how can they be distinct?
Thus a very fine balance needs to be used to see the creative nature of "relationship". Its too easy to fall into believing that a relationship lies between already existing "in themselves" objective material relaities. See above or the logical problem with codefying things within a theorem which is itself postulating a thing.
Its also too easy to view a relationship as a "thing". Its a relationship between things which gain their thinghood from the relationship. Its a exact co-dependency.
In the ordinary realm thinghood is a great issue. Phobics and Philiacs alike create distinctions between things and labour these distinctions until they seem really important. We can almost identify people by their choices of what to labour. This person really doesn't like spiders, this person likes them so much they keep them as a pet, and most people don't really even see them. Neither the phobic or philiac sees the process of thingification, the distinctions they chose to make, and the relationships none of which are actually materially real. To undo a phobia or philia we need only see that it is not "real" and unchangeable and train ourselves to find other relationships and ways of thingifying the world. Such beliefs as wealth, status, and self are dominating philias under whose influence we spend much of our lives.
Beyond "thinghood" is impossible. That would be to imagine a realm of non- thinghood which would be a thing itself by virtue of the distinction and relationship we are making between the things and the non-things. In this world we've got the essential contradiction which lies within, the fracture which shows us that it has ended. Its is interesting to me that this ties together the endevours of science, maths, logic and philosophy (whose things are concepts!!).
Meditation is the main tool for gaining a liberation from thinghood. Its not a moving beyond - there is no beyond - its not a gaining of new distinct state that is just another thing. Its "liberation"... to be explored. I need to embark upon a disciplined process of meditation now to go on.
Subscribe to:
Posts (Atom)
-
The classic antimony is between : (1) action that is chosen freely and (2) action that comes about through physical causation. To date no ...
-
Well that was quite interesting ChatGPT can't really "think" of anything to detract from the argument that Jews have no clai...
-
There are few people in England I meet these days who do not think we are being ruled by an non-democratic elite. The question is just who t...
