I haven't heard of the Drake equation, but I'll certainly look it up.
Let me explain my argument a little more scientifically, and looking a the question entirely statistically without bringing God into it.
We have some probability that a planet supports intelligent life which is not zero since we have Earth. As our population (size of the universe) approaches infinity, so does the number of planets supporting intelligent life. But the universe isnot infinite. It has some finite number of planets in it.
So what can we deduce about the number of planets with intelligent life in the universe? Without some notion of the probability of a planet supporting intelligent we cannot deduce anything. However big the universe may be, that probability can still be insignificant. We have no idea what that probability is, because we don't have a significant sample size.
The argument "the universe is nearly infinite so..." is flawed because the universe is not nearly infinite. Nothing is nearly infinite if it is finite, and even if we say (incorrectly) that the universe is so big it might as well be infinite, then we must come to the conclusion that there is also an infinite number of planets supporting intelligent life which is as ridiculous as it sounds.
We're talking probabilities here, so nothing in this argument says that intelligent life elsewhere is impossible. I'm just refuting the argument: The universe is very big therefore the existence of other intelligent life is likely.
On what has become a side note, the original link is really interesting, thanks!
EDIT: I just re-read your post and noticed this: "(nearly, because although the space is infinite, the question of whether matter is likewise infinite is not certain, although very likely)".
Is that so? I didn't realise that infinite matter was very likely, I thought the opposite was true. Haven't estimates been made of the mass of the universe?
If matter is infinite the argument that there are an infinite number of intelligent life supporting planets is not ridiculous at all, but I thought it was ridiculous because I thought the universe was generally thought to be of finite mass.
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