[Forboon]

Start at the axiom 1 = 1. 1=1 is the principle that deters man from discovering the universal theory. Until this law is formally put into question we will never succeed in getting any nearer to the unified theory than to the end of the universe.

The theory itself clearly will defy logic, if we leave no space for this in our equations there simply is no hope of coming up with it. The ability to hold to opposing thoughts true is needed in our logic. Paradoxes such as killing your father in time travel to the past (before you were born) could then be explained with a different rational. Not that it would make much sense to the mind only that it is mathematical plausible with a different logic system.

The problem that arises in tampering with the 1 = 1 axiom (everything is equal to itself at a certain time) is that by all means of understanding it is illogical and can't be done "legally". All attempts to prove the validity of 1 = 1 are rewarded with success. However, all accepted understanding of our mathematics and physics systems are based on one being equal to one. Therefore, any attempt to show validity equates to: one equals one because one equals one.

The theory can be discussed and hypothesized over and over, but mankind will never come up with anything close to it until 1 = 1 is questioned.

Kurt Godel proved that in a formal system all question cannot be answered with out certain contradictions, some claim that this disproves a possibility of a TOE. However, in a system which includes contradications as possible this proof suggests that the theory does in fact exist.

NF
Forsy44@msn.com

[wisp]

Hi Forboon

I believe that the TOE has the ether as its fundamental property, and that everything can be explained in terms of it.

But I doubt we will ever know why it exists in the first place.

The axiom 1=1 must be on equal footing with why the ether exists. We just have to accept some things as they are, in order to develop new ideas.

Maybe we are just not able to think about things in different ways. Or maybe our mathematics tools are limited and perhaps we should explore things using different methods.

[Canute]

Farboon

What you are talking about is 'non-dual' philosophy or reasoning.

In a non-dual world-view 1=1 is trivially or relatively true, for the reasons you gave. It is a tautology. However it is seen as giving rise to some confusion.

Because we so often model the world using mathematics we are tempted to believe that 1=1 actually means something beyond mathematics.

We therefore cannot explain how something arises from nothing, since this implies that 0=1. This is one of a number of problems that prevent us from constructing a genuine ToE.

But in a non-dual view 'ultimate reality' cannot be represented by either a 0 or a 1. By any definition of existence it both exists and does not exist. (This is tough to grasp but not mystical).

Originally Posted by Forboon Start at the axiom 1 = 1. 1=1 is the principle that deters man from discovering the universal theory. Until this law is formally put into question we will never succeed in getting any nearer to the unified theory than to the end of the universe.

Quite agree but I wouldn't put it like that. 1=1 is provably true in all circumstances. So I would say we won't get a unified theory until we realise that mathematics based on two-valued logic can only be done on the inside of Plato's cave, and must be abandoned at the exit on the way out.

The theory itself clearly will defy logic, if we leave no space for this in our equations there simply is no hope of coming up with it.

Again I half agree. But the theory need not be illogical. In fact I'd argue that it must not be illogical. It must go as far with logic as logic will go, but must ultimately transcend it, and be 'meta-logical' rather than illogical.

The ability to hold to opposing thoughts true is needed in our logic. Paradoxes such as killing your father in time travel to the past (before you were born) could then be explained with a different rational. Not that it would make much sense to the mind only that it is mathematical plausible with a different logic system.

Yet again I feel you are knocking on the gates of Buddhism. If you read Buddhist writings you will quickly see how their writers use contradictions and endless provisos to avoid taking sides on the truth so as not to misrepresent it.

But this is not because 'opposing thoughts are true'. It's because all assertions about reality are true and false to an equal extent, since there are two ways of looking at reality. (Think of 'Galilean' relativity). Reality is the 'non-dual' essence, and as such has only misleadingly dual and contradictory aspects. (Thus the two Brahman's, emptiness/fullness, its existence/non-existence and so on).

The problem that arises in tampering with the 1 = 1 axiom (everything is equal to itself at a certain time) is that by all means of understanding it is illogical and can't be done "legally". All attempts to prove the validity of 1 = 1 are rewarded with success. However, all accepted understanding of our mathematics and physics systems are based on one being equal to one. Therefore, any attempt to show validity equates to: one equals one because one equals one.

Agreed.

The theory can be discussed and hypothesized over and over, but mankind will never come up with anything close to it until 1 = 1 is questioned.

I'd be interested to know how you figured this out. Everyone seems to get there by a different route.

Kurt Godel proved that in a formal system all question cannot be answered with out certain contradictions, some claim that this disproves a possibility of a TOE.

Dangerous territory this for a non-mathematician like me. I would agree that he did prove this, but it doesn't follow very obviously from his theorems and it takes a bit of proving. Still, I agree. (So does Stephen Hawkings - try a search for his article 'The End of Physics'. )

However, in a system which includes contradications as possible this proof suggests that the theory does in fact exist.

I believe that you're right, if if I'm reading that as you meant it. This is completely crucial issue that is very rarely discussed. In fact I've never seen it seriously discussed. Again I don't agree with how you've put it but that doesn't matter.

If all formal systems of reasoning within which theories can be constructed must contain an undecidable question then let's acknowledge that, take advantage of the opportunity and pick a sensible one as our fundamental axiom.

This is what Buddhism does. It wouldn't work for science for the theory could never be completed, proved or tested. But this is not a drawback if that axiom can be verified by direct experience, if the reason that it is beyond proof is explained by the theory, and if the theory is based on both truth-values of the axiom.

Thus the Buddhist TOE is not a complete theory. It cannot be. If it was it couldn't be right. The final proof, the truth of its fundamental axiom, (or central ontological assertion), cannot be made, and its truth must be known directly. This is necessary ex hypothesis for it is entailed by the axiom.

Et voila - a perfectly logical structure for a theory that really could be a theory of everything rather than just a theory of some arbitrary sub-set of relative phenomena, and it does claim to be a theory of everything.

And you're quite right. In this theory there is a sense in which 1=1 is not always true.

Have you ever explored non-dual explanations of existence?




NF
Forsy44@msn.com[/quote]

[Steve Hanson]

I'm not sure what you folks are trying to identify in this thread. Please allow me to make a simple statement and perhaps you can tell me how it fits in or outside of what you are talking about.

Facts exist outside of our perception of them. Whatever the nature of reality actually is, my perception of it is not a prerequisite to that nature. I am not in it's causal chain, in other words.

Truth is simply a measure of the accuracy of my beliefs. The closer my beliefs are to what actually is, the more truthful they are.

[Canute]

Originally Posted by Steve Hanson I'm not sure what you folks are trying to identify in this thread. Please allow me to make a simple statement and perhaps you can tell me how it fits in or outside of what you are talking about. Facts exist outside of our perception of them. Whatever the nature of reality actually is, my perception of it is not a prerequisite to that nature. I am not in it's causal chain, in other words. Truth is simply a measure of the accuracy of my beliefs. The closer my beliefs are to what actually is, the more truthful they are.

I'd agree that perceptions cannot bring certain truth. For the same reason neither can conceptions. However is there not more to 'knowing' and 'believing' than perceptions and conceptions?

[Steve Hanson]

Nice response.

Yes, there is. We have to test our internal 'model' against what is.

That's the root of the problem. Our internal 'worlds' are just that: internal worlds. No matter what activity takes place inside my head, absolutely nothing outside my physical being is affected by that activity. If I act on those thoughts, that's a different story. But thoughts themselves affect nothing.

Because we see something doesn't mean our conclusions or conceptions are correct. Our perceptions are correct within the framework of their occurance because they constitute what we have to work with. They are the given, but they are not infallible. A case in point is a new theory that the universe is expanding; that every atom or particle is expanding at the same universal rate. If this theory is correct, our perception of existence is relative to that expansion and consequently some of our conclusions or conceptions (and models) are not valid. We are not built to see everything directly or perhaps even correctly.

But the nature of existence and our relationship to it is still the same. We are perception machines, basically, as is every form of life. To my knowledge, we are the only form of life that can enhance its perceptive abilities.

Yes, there is more to knowing than just percepts and concepts. We have to validate our understanding because we are aware that we are not infallible.

[Canute]

Here is another way of saying it. This is from the Kuan Tzu—a text from around the 4th - 3rd century B.C.

"What all people desire to know is that (meaning the external world).

But our means of knowing that is by this" (our self, our mind).

How can we know that?" (the external world)?

Only by perfecting this."

[Steve Hanson]

Another nice response. I liked it.

"by perfecting this" means a 1:1 correspondence between what we think and what is.

Very interesting. A lovely way of looking at perfection.

On the one hand we perfect an internal model of the external world and on the other we create an instance in the external world of an internal vision. Two opposite applications of perfection. Both hard to achieve.

Having now reread the original thread in the context of what we've just talked about, perhaps the need to rethink 1:1 arises from a fundamental flaw in our perceptive ability which would distort the 1 on the left side of the correlation: our internal model. If our perceptions are blind to certain phenomena, then all models based upon that blindness are flawed.

But what, precisely, are we blind to? That seems to be the road to the TOE. Unless we identify that, our efforts are in vain.

Mark McCutcheon's expansion theory does provide an answer to what that might be. We are blind to the expansion of the universe because we are part of that expansion.

How do we validate or invalidate that? How do we perfect the model?

[Canute]

I think you're seeing it just from a scientific perspective. The lines from the Kuan Tzu do refer to perceptions, as you say, but they also refer to our reasoning and conceptualising.

A conception is something apart from ourselves, an internal object. Thus even conceptions are that rather than this.

The writer was pointing it that if we want certain truth then we can't trust our perceptions or conceptions, and therefore we cannot reason out way to certain truth. However good science and philosophy gets we won't know the truth about the world, for to understand the world requires first understanding this.

This is what Aristotle said (certain knowledge is identical with its object) and Popper (certain knowledge requires the knower to become one with the known). Logic makes this conclusion inescapable.

So it's not just a question of checking our internal model with reality. Even the model is that.

[Steve Hanson]

Another fascinating response. Thank you. You are a fountainhead of other viewpoints.

It is ironic that in order to discuss this we have to fall back on words, which are all models (hopefully valid) of something that exists outside of ourselves.

We constantly deal with structures made up of those little models which we create on the fly in the form of sentences and documents and books. In the final analysis they are derivatives of our perceptions. If the structures we build are based upon models (words) that don't have a 1:1 correspondence with something that exists, then it is probable that what we build is not valid.

This entire discussion then, is that. And therefore cannot be used to explain this.[/i] Perhaps that can explain what this is not.