Identity is isomorphic with membership (SRH)

interesting point to highlight from last post: Identity is isomorphic with membership.

When we define something in maths we can do so simply by identifying it in a set to which it is a member. Thus we might say that there exists an x such that x is in the set of natural numbers and x > 4 and x < 6. This is true when x=5 so we are talking about x being 5.

But this is ironic also. Because to be a member of the natural numbers is to define some property (or predicate) of x which it shares with all other natural numbers – hardly making it unique and individual. So to find my identity in being “black skinned” is hardly making me an individual but really just making me a member of black skinned people in which I would lose my identity. We must have some other notion of identity which is separate from the predicate to ensure that we gain some identity when we become a member! I believe that this unconditional entity which we feel enables us to add a unique 1 to what is an homogenous membership is what Buddha considers an illusion.

In maths I can’t find a way to “add 1” to a predicatively defined set, since all members that fit the definition are automatically members and so there is no way that some entity can be added.

However “countability” is an interesting concept. If the set can be ordered – like numbers are usually ordered according to the property of their magnitude 3 being larger than 2 comes after 2 – then each number has a unique place in the set. Suddenly its uniqueness is assured within the membership.

So we humans feel that there is some analogy to countability within the human race or the black race or the Arsenal football stand that preserves our identity while allowing us to be a member.

Interesting that some memberships have their own countability like height or bank balance. People can order themselves in a room according to height and people order themselves according to how rich they are. But again there is some individual countability that places each person as an individual within the set of human beings, or friends or whatever. This property for now must be the property of being a self.

Now I sat today to get a step closer to the SRH but have been forestalled. Yet here have run into it again. The hypothesis is that self-reference is impossible. I have been forced to modify this as self-reference is quite easy. Impredicativity was a step further but draws in the idea of constructivism. Am I saying that you cannot construct a self-reference because you don’t know what to predicate before it is built.

Fractals repeat a form which must be completely built in order to build any part of them so this is not a problem. The assumption here is that the fractal exists and we merely have algorithms which find the points in the set. The set is defined then by conditions which allow a solution to exist which repeats itself.

So it does seem that self-reference may exist and we are only producing expressions to represent this. While the SRH is saying that nothing can exist which depends upon itself.

Looks like I need to clarify my notion of “existence”!