Is this a translation issue?
There was the claim that we might be alone. I ramped up the pessimistic approach by claiming for the sake of argument a low chance of having 1 intelligent species per 100 galaxies. That is the 1%. And even with that, there are over 100 Billion galaxies (in the visible-to-us part of the universe...). That is 100 with 9 zeroes trailing. I could cut off 6 more zeroes and there would still be 1000 intelligent species with that pessimistic approach of 1 species per 100 000 000 galaxies. I am not talking about our Milky Way right now.
And given that we have 300 Million planets in our galaxy that could potentially have such life, it do be a overly pessimistic approach.
Is there anyhting in that that you do not understand or dispute? This has absolutely nothing to do with the fermi paradox. The universe is big.
And on a trivial level, yes, of course, we do not have proof. But if you were to gamble with a demon, that we are the only ones in the universe, would you bet a dollar or not. You might change your mind, if the bet was about the galaxy, or for a bubble with 1000 light years around earth. The chance for another intelligent species approaches 1, the bigger you make the bubble, and as I like to say, the universe is big. So big that any intuition fails.
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The fermi paradox is precisly about colonizing expanding life. Only if you assume that this would be "normal" (or at least a percentage of species would do that) and life is abundant you can go back in time and ask, what would have happend a billion years ago, when such a species would have emerged in our galaxy. They could have colonized the better part of the galaxy in that time till now.
While you can use this to "prove" that it has not happened (duh), you can not infer from it, why it has not. And that includes the explanation that we are alone in the universe. You can't prove from nothing. This would be the same faulty logic as UFO believers use. They do not know what that thing glowing in the sky was, so it must have been aliens. You can't infer from non-knowledge*. But you can speculate, of course.
My faforite speculation is, that in our bubble of reach we are simply the first. Someone has to be.
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* Technically, non-knowledge is not the same as having found nothing were you would be able to find something. Like, you searched all your pockets and did not find your phone, so you do can conlcude, that it is not in your pockets. But you can't conclude for another person that they do not have a phone, just because you could not search their pockets. We barely see the person, let alone, if they have pockets or how big they are or if a bulge in there would be a phone or something else. Or in other words, while we can as of now detect some exoplanets, there would have to be extreme scenarios to be able to tell, if there is life on those. From the other side of the telescopes, maybe someon sees our star and say, wow, nice sun, heavy elements and all, pity all we can detect are several gas giants, lets point our precious telescope to more promising candidates.