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.

A point in Omnipotence vs Omniscience

In Dawkins' The God Delusion there is an argument showing why omniscience and omnipotence are mutually incompatible. Roughly it goes like this :

If God is omniscient he must be knowing what he is going to do at some point of time (say one year later) in the future. Then he is powerless against changing it. Hence He cannot be omnipotent

As we understand, defining omnipotence and omniscience is a troublesome task at best. And to give it a concrete unambiguous meaning seems impossible. We have tried various tacks of trying to define both the things, none of which works. Ultimately these concepts are ill defined and logically contradictory. Hence they cannot be used to form unambiguously meaningful sentences. So the above proof stands invalid. We are not saying that omnipotence and omniscience are mutually compatible. Just that it doesn't make sense to ask this question. In this respect it is like many english questions which are grammatically correct but meaningless to answer. like - what is the shape of red color ? flaw : shape is not defined for color.

In fact as we have seen here, if at all omniscience and omnipotence should be expected to go hand in hand. But again it is meaningless to explore this thing further.

What is God : Omnipotence - A

To really understand the good/bad consequences of religion, we must first understand God on whose name all this is done. Almost every pious / theologian I have talked to evades this question. In fact they feel proud of the elusiveness of God. We as scientific rationalists would try to have a thorough understanding of God and decide His likely existence and influence on the material world. After thinking through it, I have several different possible definitions of God. In this article I will explore one possible approach. First let us have some preliminaries. The bold entries are definitions to be taken in a literal sense, quite often self-evident. I am not being mathematically precise (in spite of being a mathematician) here just to maintain the flow.

In order that God be able to influence something, he must be capable of executing some well defined actions. Let me define an Entity as 'something' which can execute a task to its end. A Task is a sequence of clearly well defined steps, which if stops gives us Result of the Execution. I don't want to call this an algorithm as I want to consider non-computational tasks too. Technically a Turing machine is synonymous with a algorithm. But we will differentiate between the two. In our scheme Turing machine is also an 'entity'. Our tasks / algorithms are not restricted to computations. One example each of the non-computational and computational type -

• To transfer all the apples kept on the table to a basket.
  
  1. If there are still apples left on the table pick one and transfer it to the basket.
  2. Check whether there are apples left on the table, if yes go to step 1, else go to step 3.
     
  3. Stop. The Result is basket full of apples.
     
  
  
• To find remainder and quotient of N when divided by M -
  
  1. Put Q = 0, R = N.
     
  2. If R less than M, go to step 4, else step 3
     
  3. Subtract M from R, put it as new value of R, increment Q by 1. Go to step 2.
  4. Stop. Result: Q is the quotient and R is the remainder.

Existence of an entity for us means it must be capable of executing at least one task and in fact must have actually executed at least one task, either Spontaneously (i.e without any external switches as all of us do) or Summoned (as we kick start a computer, or implore God to do something for us and he 'obliges'). I think this is a reasonable definition of existence of a being (which I am calling as entity). A drawback of this wide definition is that all computers are entities as well as several other machines, which is precisely why I shy from calling them beings. Some other entities according to our definition are -

• Cellular machinery for reproduction, protein production, etc. These presumably act spontaneously.
  
• Automated machines / robots employed in a industry for manufacturing. Summoned execution.
• Computers which automatically allot us airplane / train seats, etc.
• Don't forget that all human beings are also entities.
  

We need this wide definition of entity so as not to leave any possible entities out. An entity may be summoned at some time or spontaneous at others. It is clear that our God also must be an 'Entity', else He is inconsequential and thereby non-existent for all purposes. It is also clear that any entity has a corresponding List of tasks it has already executed. So according to our definition, empty list means non-existence. We also postulate that for any entity, its list must exist. Otherwise what possible meaning can the existence of an entity might mean? We will use this postulate as a test for existence. Two entities may have overlapping list or non intersecting ones. An entity X is said to be More Powerful than Y if X's corresponding list is strictly larger and subsumes that of Y. This I believe is a very reasonable definition of 'power'. We also consider a different type of list called *List which is just the collection of tasks the entity can execute. Let us take the colloquial meaning of 'can'. An entity's Action is the sum total of his executing any or all tasks from his *list.

The question that immediately comes to mind is : what is the corresponding list of God. We may have never seen Him, but consequences of his action must be evident in our world. Also a God worthy of His name must be more powerful than any other entity. Let us examine one possible list as worthy of God's, as well as analyze possible problems with it. First we try to ascribe one hypothetical *list to Him and see the consequences.

Consider all possible entities in the universe and sum total (logically, the union) of all possible corresponding *lists. God's *list is supposed to be strictly larger than this list. Let us call it the *list L1 and such a God as G1, which would be omnipotent. We want God's *list to be this collection as we want God to be able to do all such tasks that is why we have taken this definition of omnipotence. This very soon runs into logical contradictions. For example can God make a pile of stones heavy enough so that he cannot lift it up 1 meter from the ground ? It is straight forward to convert this crude instruction into algorithmic format (say the task T1) and it is also very clear that I am (you can put yourself too here) capable of executing this task, hence T1 is in my list. But if God can execute this task then he cannot lift that very pile. So we convert lifting of that pile into an task (say T2) and this task is clearly not in God's list. Otherwise if He cannot execute T1 then too He doesn't have at least one task (T1) in his list. Either way He is not omnipotent. We shall have more occasions to talk about Omnipotence in the future, where we will meet successively better Gods. And we shall also address objections to this reasoning.

We have actually demonstrated non-existence of the *list L1. Hence G1 also cannot exist, as we hypothesized. The above example also demonstrates that G1 cannot be strictly more powerful than all human beings. What a letdown God !!

PS : Here we see that talking about *lists leads to troublesome concepts. In the sequel we will only talk about Lists in the context of omnipotence. Also we had defined omnipotence using *lists, so we will redefine omnipotence using lists in the future and see the consequences.