One of the arguments I came across in favour of God’s non-existence provided the tipping point for this post. “God cannot build a wall which he cannot climb.” On the face of it, this is a very plausible argument. Nothing original, though; because arguments like these have existed since antiquity. The sage Kapila (from the Sankhya school of philosophy), some aeons ago, postulated something to this effect: “God cannot create because, if he is forced to create, he is not completely free. And a God who cannot create is no longer God.” Thus, we see very sound arguments, apparently, towards disposing of a God. The arguments, when dug a little deeper, are similar to the omnipotence paradox- “There is nothing an omnipotent being cannot do; and this is a limitation on such a being.”
At their very root, the formulations are applying the complement operation twice. The operation referred to is the complement operation in Set theory, i.e. A’ = U-A, where U is the universal set. So, in the language of set theory, the above arguments are effectively saying (A’)’ = A. Extending the same idea, it is equally logical to say that the error in truth is that there is no error. Or the truth in an error is that there is nothing true. As counter-intuitive as these arguments appear, they can be reconciled on a quantum mechanical basis. Let us take the first argument “God cannot build a wall which he cannot climb”. When we formulate this statement, we are restricting by our observation, the entity of God to either one of the two states – Of either climbing an already existent wall or building a new one. When the act of climbing is observed, there is no further building process. Similarly, when we try and observe the building operation, there is no further climbing. This is a limitation in observation – any observation tends to restrict the ‘observed’ to one single state.
The underlying dynamics are a part of a bigger scheme. It is always difficult when the ‘observed’ is also the means for our observation. For example, the science of light has always been eluding us. Sure, all of us robotically repeat that light is both a wave and a particle, but not one can have a mental picture of the same. We are only repeating the words. To understand why light is always eluding our intellectual grasp, one needs to realize that light is itself the essence of observation. What is meant is that light itself aids us in making observations. There is no substitute for light which we can use to observe light. So to speak, the light which is helping us observe is being used to observe light (itself). The light allowing the observation is interfering with the light being observed and thus in the process creating some disturbance. (Heisenberg’s uncertainty principle)
An everyday example: Say a new employer of mine wants a recommendation letter as a supporting document. Common sense suggests that he wouldn’t approve of it if I were to write my own recommendation. Why? The ‘observed’ (myself) and the means of observation (again, me) cannot be the same. And in cases where they are the same, they inevitably introduce some disturbance. Similarly, building which is aiding our observation is polluted by the ‘observed’- God in this case, because he is the builder as well.