Philosophically, I don't rule out unicorns but scientifically I don't place much weight on them because there is no evidence for their existence.
The only "evidence" for "infinity" is in math and that's usually a marker for something breaking down.
As I see it, for every property we can think of, and I would assume finiteness and infinity are both potential properties, we have the two logical options that either it exists or it doesn't exist. I would also assume that the rational attitude to have is to accept you don't know something until you believe you have evidence for it. So, as far as I am concerned, I don't think I or anybody has any evidence either for the existence of infinity or it's non-existence. That's the rational position to have in my opinion (and nothing to do with philosophy).
Then scientists could try to decide what science is all about. There, it's a matter of consensus although I'm pretty sure you'll always have people with original views. So, yes, the consensus in science could be that infinities are assumed as not existing until proven otherwise. As long as you understand that this can only be a pragmatic move that for all you know may well have to be jettisoned as some point, you'll be fine. In other word, don't get dogmatic on this.
One aspect of being pragmatic may be that assuming finiteness could be more productive. Possibly, this leads you to deduce potential observables and this may in turn gives you a chance to falsify your theory and therefore make progress. In other words, it may be pragmatically better to assume a limit to have a chance that it will be falsified by experience. But I'm not sure that would work in all circumstances.
Theory suggests a "singularity" just before the Big Bang and most scientists consider that to be a break down in the theory and are looking for a quantum theory of gravity to correct that break down.
It's the same with black holes, a quantum theory of gravity is being looked for to deal with singularities there.
Yet, with the size of the Universe there doesn't seem to be as much skepticism regarding involving infinity.
It's only natural for scientists to try to reach a consensus on various aspects of what they do, but it's also natural in my opinion that you will always have individuals who will disagree with the consensus opinion and do their own things. I would assume there's no problem with that. The consensus is what it is and should be proclaimed as such but individuals get to decide for themselves whether they agree with it or not. No need to get dogmatic about this.
Personally, I believe our attitude to the notion of infinity comes down to our biology. We're apparently very finite beings and we tend to resent wastefulness. We don't like to think of an infinity of things if we can't see the usefulness of them. Then again, we think of the future as open ended. Most likely, that will be because we're unable to decide on any actual end of time, not only for the universe but more importantly for ourselves, at least in normal circumstances. So, we do have one clear notion of the infinite. And we also seem to take space as infinitely divisible by default. This is likely due to the fact that we are unable to perceive with our own senses any granularity in space. So, I would say that if evolution decided that it was somehow better for our survival that we should have at least two clear notions of the infinite, relative to time and to space, I think we should pay attention.
Then again, perhaps scepticism has been historically the better option to further progress in the sciences. But I don't think anybody knows which way the chip falls as to regard infinities.
EB
