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The Loop
Well, I see we got some space left on this tape and decided to usefully fill it and introduce you to a piece of information called the loop. Now the loop is a piece of information which gives the relationship between a postulate and what that postulate permits to be possible and what that postulate permits to be impossible. Now the first thing you should know about the loop is that it is not peculiar to this universe, it is a general principle that will be applicable to any universe. But it is certainly applicable to this universe, now what it amounts to is this; that if you have a postulate you can deduce from the postulate what is possible in the universe in terms of that postulate and knowing what is possible in terms of that postulate in the universe you can deduce what is impossible in the universe in terms of that postulate, and, knowing the next bit, knowing what is impossible in terms of that postulate in the universe you can deduce the postulate. So it is a loop, it is like having a , b and c and if you know a you can deduce b , and if you know b you can deduce c and if you know c you can deduce a , you got the loop. It is like a snake going round and being connected up
, the tail end of the snake is connected up to the mouth of the snake. The whole thing is connected up in a circle and that is why we call it a loop. Now it is very easy to prove logically that when we have a situation like that where b is a valid deduction from a and c is a valid deduction from b and a is a valid deduction from c that a and b and c are all identical to each other. In other words a equals b equals c (a=b=c=a) equals a, the whole lot are identical to one and another. It is very easy to prove this logically, I wont bother to prove it on this tape; you can find the proof in any logical text book. It is an easy proof, now I will give you a very simple example of this. Lets consider a particular loop, lets say that we entered a particular loop, we discover that all crows are birds, now that is the postulate, we got the postulate now, that is the relationship, thats the postulate; all crows are birds. Now from this we can quite validly deduce that it is impossible for the class of creatures that are crows and non-birds to exist, so that is our first deduction, we now deduced the impossible, what that postulate all crows are birds just what that postulate makes impossible in our universe, you see. Knowing that this class of creatures that are both crows and non-birds doesnt exist in the universe that the postulate has made impossible, we can now deduce what is possible in the universe in terms of this postulate. Well that turns out to be: we can either have birds in the universe or non-birds in the universe, or we can have both, that tells us what is possible in terms of our postulate. Now in that particular example we have not really learned an awful lot, but lets get very fundamental, lets take a very basic postulate in this particular universe that we all inhabit. We know in this universe that a thing cannot both exist and not exist simultaneously, we know that, we call that the law of the impossible in the universe, we know that, I have already mentioned that, this is on a earlier supplementary lecture, that this is a valid deduction from the basic law upon which this universe is constructed, this idea that a thing cannot both exist and not exist simultaneously, so here we have an element in a loop, you say ah we recognize this as an element of a loop, you say ok lets find the rest of the loop, there is 2 more elements in this loop, lets find the rest of the elements of the loop. Ok now we got the impossible, we should be possible now to easily deduce what is possible, yes, well, what is possible in this universe is that a thing either exists or it doesnt exist, that is possible, that exhausts the possibilities. So now we have the impossible, a thing cannot both exist and not exist simultaneously, that is the law of the impossible, now we have the law of the possible that a thing either exist or it doesnt exist. All right now that is 2 out of the 3 members of the loop, well what is the third member of the loop, the postulate here is that let x be the thing that exists, if the thing exists we call it x, well x equals x, if x equals x, that is the 3rd part of the loop. Now, these identifications, as I already said, each element of the loop, there are 3 elements in the loop, is identical to the other 2 elements, all parts of the loop are identical to the remainder of the loop. This identification is not a false identification, it is a true identification, so the postulate that x equals x, which obviously is true in this universe, all x-s are x-s, there is no doubt about that, all cats are cats and all kings are kinds and all coal heavers are coal heavers, all x-s are x-s is true. But what isnt immediately obvious is that to say that x equals x, that to say that x cannot both exist and not exist simultaneously is just another way of saying that x equals x, now that isnt obvious is it, but it is true, because of the loop. When we say that x equals x, another way of saying x equals x is to say that x cannot both exist and not exist simultaneously and another way to say that x equals x or to say that x cannot both exist and not exist simultaneously is to say that x either exists or it doesnt exist. So again you see, now we are into something useful, arent we, now we are really discovering something, it is not obvious that those 3 expressions are actually meaning the same thing, are simply different ways of saying the same thing, but it is so, I can assure you because of the identification in the loop, and the fact that the identification is a true identification. Now this loop will appear, I mentioned that at this stage we wont be using at this stage, I wont be discussing any further at this stage, but the loop will appear in a later supplementary lecture when we take up the subject of the anatomy of insanity, we will find this loop turning up again. So you see you discover that it does have some tremendous practical uses this does, but I am given it to you at this stage, maybe to fill up this tape, partly to fill up this little blank of this tape that we got here, and also to give you something to think about it, to get your mind wrapped around this idea of this connection between a postulate and the subject of the possible and the subject of the impossible, to see that there is very real connection between these 3 things, which is true in all universes, to prepare your mind for this idea. Ok that is all I want to say on the subject, I better get of the subject now before this tape runs of the end of the spool.
The Resolution of the Mind SHAPE \* MERGEFORMAT The Loop, 6th April 1994
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