07-30-2021, 03:59 AM

A simple explanation I have discovered is that everything as the totality of all things can't contain itself. Because to put everything inside itself makes that contained part less than everything!

Then the next tricky question is, is everything as a totality infinite? When using proof by contradiction it starts with the opposite assumption:

Assume that everything (E) is finite. Then there exist relations between E and all its finite parts. And the relations themselves are also separate distinctions which means that there are additional relations going from the relations themselves. And those additional relations in turn have relations going from them and so on in an infinite regress. Hence E cannot be finite. Therefore by contradiction E is infinite. Q.E.D.

Can then E contain other infinities other than itself? No, because those smaller infinities would have to be separate parts. And there are no separate parts in E other than as a web of relations where each relation is connected to all other relations. As a metaphor, the smaller infinities would have to be like drops in an ocean without anything that can separate the drops from the ocean, and then the drops merge with the ocean.

Then the next tricky question is, is everything as a totality infinite? When using proof by contradiction it starts with the opposite assumption:

Assume that everything (E) is finite. Then there exist relations between E and all its finite parts. And the relations themselves are also separate distinctions which means that there are additional relations going from the relations themselves. And those additional relations in turn have relations going from them and so on in an infinite regress. Hence E cannot be finite. Therefore by contradiction E is infinite. Q.E.D.

Can then E contain other infinities other than itself? No, because those smaller infinities would have to be separate parts. And there are no separate parts in E other than as a web of relations where each relation is connected to all other relations. As a metaphor, the smaller infinities would have to be like drops in an ocean without anything that can separate the drops from the ocean, and then the drops merge with the ocean.