Monday, August 20, 2007

What is God : Omniscience - C

This article is a follow-up to part B.

Before going further, we show that a K-entity and a entity is one and the same.
Since a K-entity is already an entity by definition, it suffices to show that an entity is also a K-entity. Any entity is supposed to be able to finish a task. i.e, after a finite number of steps the task is over and the result is obtained. So we define a formal system whose axioms are the steps of the task and rules of derivation are the transition from one step to next. Since the task finishes (in technical jargon, terminates) this must constitute a formal system. We also need to include the elementary logical rules too. This system may not be minimal, so we make in into a minimal system. Under this formal system, the performing of the task is same as a proof of the initial input leading to the result of execution of the task. Consequently the above mentioned entity has completed a proof in a system and hence is a legitimate K-entity.
The above argument shows that there is no difference between an entity and a K-entity. This is the reason we defined types of God as G1, G1* and so on. The star versions are the same concepts but related to knowledge. Therefore an omnipotent God is same as an omniscient God and subject to the same contradictions. But we will spell out everything in detail and leave no room for doubt. We have already seen that G1 and G1* Gods are contradictory. Later we will see that G2, G2*, G3, G3* are also contradictory but that needs more work and we will revisit this issue after learning some more things.

For now let us try a different tack for defining God. Instead of defining God to be an entity, we define him to be knowledge itself. It is not too far off course as this is one of the glib interpretations of omniscience. This is tantamount to defining God to be a Formal system rather than somebody who works with the system. Let us call such a God as G4. The question is which system is G4? Since we have many (far too many) systems, all of them cannot be God. Think about the elementary examples we considered in the earlier part. This is not what we intuitively understand by God. So we consider some stronger systems. Any God worthy of his name must be at least capable of doing arithmetic and be able to prove arithmetical statements (or at least understand the proofs if presented). This simple requirement actually poses the most formidable difficulty.

As proved by
Gödel, any system which includes ordinary arithmetic cannot be both consistent and complete. This is referred to as the Incompleteness theorem. Meaning, however many axioms we include in our system, there will necessarily be left out statements which will neither be false nor true in the system. So the system can always be enlarged by adding one more axiom and there is no canonical choice of any largest system. That makes the choice of G4 very difficult. On the one hand we want to include all the arithmetical theorems in our system and on the other hand we want G4 to be as large as possible (so that God comes closer and closer to 'omniscience'). But whatever system we choose as G4, there are competing systems which are as large and also many (far too many) which are strictly larger. This dilemma is akin to choosing the largest natural number. Whatever number you choose, there exist a (and infinitely many of them) larger number. Hence, G4 also becomes non-existent. In hindsight we can see that G1* was a defined to be a k-entity in possession of the formal system G4. Since G4 itself is problematic, G1* too cannot exist. So we see that all the grandoise talks of God being 'Pure Knowledge' is just vacuous.

Actually even if G4 existed, it makes little sense to worship a list of axioms. And in any case, this is not the popular understanding of God. As we have seen till now, the ontological status of God seems problematic and is getting mired into more and more contradictions. It leads us to suspect whether God is just a psychological construct. Or worse : an illusion constructed by the way our brain works. Not unlike the illusion we have of sun moving round the earth or the desert mirage. See this for a good example of an optical illusion :
If you move your head towards the screen while looking at the center black dot, the two outer circles seem to rotate.

If the above is true, then to be an atheist is to be free of precisely such illusions. In the future we will also discuss the emotional / psychological apologies for God / religion and examine whether religiosity is really needed for our life. Whatever we conclude, our motto is not to take any thing on faith, not even atheism. Whatever stands up to rigorous scrutiny will be our stand.

In the next article we will take a break from this grind of God and take a look at the real world.

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