[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?




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