Three chess geeks walk into a bar. Only one's nose is broken.

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You cannot prove or disprove any of these. The scientific method requires that you test your hypotheses. Until you actually find a supreme being, you cannot prove or disprove any of these. Therefore these questions are currently meaningless. M

Before I can prove anything I need a definition of supreme being.

Ok, haven't studied philosophy so I'll just do point one rather than go through them all as I could be totally off beam and get shot down in flames.

1) I have to assume, as you say it's easy to prove there can be only one supreme being, you can't mean "supreme being" as in a term to describe a god, as that is unprovable.
If you mean supreme as in the ultimate and being as a living thing, then yes I think there can be one supreme being.
For there to be a supreme being there needs to be some kind of measure put in place. Take athletics, it's easy to pick which athlete is supreme in their field as their speed or performance record can be easily measured.
A supreme being would be more difficult to assess. Take here on earth, if you tried to find one single supreme being from the many species that exist here, then how would that be judged? Intelligence, speed, longevity etc etc. Assuming some standard measure was accepted then yes, a supreme being exists right here on earth.
Then go into the as yet unknown, should life on other planets be discovered, they could be assessed by the same measure. So once the supreme species is measured and identified, within that species there will be one supreme individual according to this aforementioned hypothetical standard or measure; a supreme being.

Ok before I waffle on am I on the right track?

So then there could be infinitely many species in universe all having their own supreme species being. Now we have to assume that the different species supremes can be compared. But then does it converge?

Suppose there exist two different supreme beings A and B.

Since A is supreme in terms of supremity we have B is strictly less then A .

Since B is supreme in terms of supremity we have A is strictly less then B.

The two statements now imply tht in terms of supremity A is strictly less then A.

That clearly is a contradiction. Therefor there cannot be two different supreme beings.

This proves 1) I guess even without definition of supreme being.

2) is more difficult....

Ok the other points are quick assuming point one was on the right track.

2) once the obviously difficult standard measure is established then a supreme being can be identified whether it be here on earth or beyond. We can speculate what is likely to be out in the unknown, but we can only measure what we know, so can only say with certainty that by this measure a supreme being must exist here.

3) given the high probability of life beyond earth, it's likely this supreme being, as measured by our standard, exists beyond here, but whether here or beyond the existence depends on our hypothetical measure, and assuming it's established then the supreme being exists in actuality.

Hope this isn't for your homework? Lol

But if there is an infinite sequence of increasing beings this not necessarily converges to a supreme being.

Everytime you think you have found the supreme one there can be found a bigger being, like the natural numbers it continues endlessly increasing....

I don t understand why that wouldn t work.... maybe Daniel Dennet doesn t either....

Of course if everything is finite then you are done....

True, but that's why I was saying you can only measure the known....unknowns are speculative....

Nope, only locally supreme.If there exist absolute supreme beings there can be at most one.

Not sure what you meant there

Unknowns are speculative but that doesnot mean they can t exist.

Pythagoras theorem was not known before Pythagoras but nevertheless it was valid before Pythagoras and so existed in a higher sense.

Of course....though look at the question, he's asking ...1) prove that there can only be one supreme being.....so say we keep that simple and measure the supreme by simply the biggest. Therefore we can measure the biggest animal here on earth and therefore that's it simply proven. If in the future we discover something bigger then it's measured and proven.
We can speculate endlessly about what may or may not be out there but within the context of his question it comes down to there being a measure to prove which individual being is supreme. Lol hope that makes sense.

prove that there is a football floating on the Pacific Ocean.

You need to start another thread for that one

it was a post for the OP to think about how redundant his question is. man, people are so thick here.

Lol