But your fact (1) talks about the mass of life, not its density over some area. Thus (4) is an unsupported subconclusion.

Hmmm. I would claim that (4) is actually logically valid. Its like this: Imagine you have an infite grid made up of unit squares (ie the side length of each square is 1). And you have a ball of putty of some sort of finite volume/mass. If you squished the putty evenly over a given number of squares, found the mass of the putty in just ONE of the squares, and then multiplied that mass by how many squares you squished over, you would have the original mass of the entire ball of putty. Right?

BUT if you squished the putty over all of the squares (of which there are infinite), the mass over any single square would be zero. This is really easy and intuitive to prove.

So, lets prove it, using my most favorite kind of proof ever, a proof by contradiction! (skip this if you don't really care about this aspect)

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Suppose that after you squished the putty evenly over the squares, the mass over a single square is greater than zero.

Then, because you squished the putty perfectly evenly, every square must contain the same amount of putty.

Then every square contains an amount of putty with mass greater than zero.

But there are infinite squares, so the mass of the putty over all the squares must be infinite as well.

But I initially stated that the putty had finite mass, so this is a contradiction. Therefore, the mass over a single square must be zero.

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I claim that the error in my proof is actually between

** steps 4 and 5.** BUT to keep this from getting too mathematical, I actually would rather talk about the implications of my proof. Above, I just demonstrated how a proof by contradiction works. Basically, if you arrive in a logical contradiction in your proof, one of your initial assumptions must be incorrect.

If I add the initial assumption to my original proof "I am alive", then clearly the conclusion of my proof (there is no life) is a contradiction. Which means at least one of my assumptions must be false.

So, Either:

1) There is infinite life in the universe*

2) The universe is not infinite

or

3) I am not alive

*This isn't what I directly assumed, but it is an equivalent assumption as the choice of Earth was arbitrary

But there is no reason why any of those assumptions should have to be false for there to be no life in the universe. Which means that I MUST have messed up the proof somehow- that is, my contradiction is not actually a contradiction.