There is no problem with equality, as long as you keep it where it belongs; conceptual. 1=1 is a statement of perfection, needing no other reference. The trouble starts when you want to apply this analytic truth to the world of experience, in which there is no ambiguous example of 1=1.Moyo wrote:Why not build the whole system of relations on the same basis that this "=" is. It seems that if we can do this we avoid arbitrariness and acheive consistency.
The whole system of cartesian products and orderd pairs are an unnecesary frameworkthen and we can build mathematics without the suspect (because it doesnt involve computation) theory of sets.
It seems though that when you say a thing is itself you use two refferes 1. thing and 2. itself and are implicitly implying a colloqial version of (a,a).
This may be a limitation inherent to consciousness such as the failure to define "objective reality", and just as we may never have a definition for objective reality we may never be able to define equality.
So whatever crazy conclusion you think you might have reached about the existence of "GOD" (whatever that is), we all know that god only exists as a concept in your own mind, and not the world of experience.