the paradox of the souls restated

[Samkhya]

Dear cyber-hindus,

 

Here is the paradox of the souls: there is an infinite number of souls. But souls can be in two states: bondage and salvation. But suppose that at the beginning all souls are in a state of bondage. They make up a set called: "set A". And then suppose one soul is freed. So the remaining souls will form a new set called "set B". What I ask is whether the set B is infinite or finite? If it is infinite, it means that it is equal to the set A. Therefore, infinite = infinite - 1. It is a non-sense. If, however, the set is finite, it means that: infinite - 1 = finite, or, once we have changed the place of the terms, finite + 1 = infinite. It does not make sense either.

 

Perhaps you would object that additions and subtraction do not apply to infinite sets in the ordinary sense. But in the physical world, there is nothing, no rule, to prevent us from using additions and subtractions.

 

It has also been objected that there are many kinds of infinite. So, when we say: infinite = infinite - 1, we are speaking of two different infinites. The problem is that the identity of a number is made up of its units. Once we remove or add a unit, the identity of a number is destroyed. It is not merely a superficial change, such as one losing his hair. It's a substantial change. I thought that to say that there is a kind of infinite whose definition is: "infinite - 1" is self-contradictory. As soon as an infinite loses one of its units, its identity changes, I thought, and it loses the status of an infinite...

 

However, the problem can be settled by saying infinite is not the name of an individual but the name of a species of numbers. Thus, subtraction can change the identity of an infinite number, but its identity changes within the species it belongs to.

 

I conclude that there is no obvious contradiction in the statement that there exists an infinite number of souls.

 

What is your opinion?