Monday, September 10, 2007

The Omnipotent God - B

This is a follow up to part A.

Recall that * version of Gods is the same as unstrarred one except it refers to knowledge as opposed to power. Also recall the definitions of more knowledgeable and more powerful, which unlike the colloquial sense are umambiguous. Nevertheless it is worth reiterating here. To be able to do some task (defined here) is a measure of Power of an entity and his ability to carry out a proof in a formal system is a measure of Knowledge of a k-entity, which as shown here is same as entity, which also shows that power and knowledge are equivalent concepts. Taking inspiration from the knowledge versions G2* and G3* here we define G2 and G3 Gods. After this we can equivalently talk about G2/G2* and G3/G3*. For the sake of completeness, we also reiterate the definition of G1 here.

  1. The *list of tasks which God (called as G1) can execute includes any conceivable task. i.e, if there exists any entity, then all the tasks from its *list are also present in the *list of G1. We have called this *list as L1. And we have shown that any entity with L1 as its *list cannot exist. The star-version of G1 is G1*, which is in possession of a formal system capable of telling him all the truth. This runs into same contradiction as G4. This point actually shows that *List concept itself is troublesome. Hence we change tack and work only with Lists.

  2. A G2 god is one whose list is union of lists of all the entities. This means that such a God has already executed all the conceivable tasks, maybe before the universe began.

  3. A G3 god by contrast has not performed all the tasks, but is in the process of finishing it and will do so eventually.

In the sequel it is sufficient if we talk only about either the starred or unstarred versions not both. So we use the terms interchangeably.

Also for the sake of completeness we mention that the corresponding notion of G4 in context of omnipotence is the *list L1. (Since G4 is a formal system not a k-entity so its omnipotence-counterpart must be a *list rather than an entity). We have already agreed that L1 is non-existent.

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