There are finite things we cannot measure.
Incorrect. We do not know any such thing. Why do you think this?
If the universe is spatially infinite then it because it started out spatially infinite, and it is presumed that it was hot and dense everywhere. When it talks of everything coming from some very small point, it is only referring to everything that we can see. Therefore the spatially infinite universe option would mean the content of the universe is also an infinite quantity.
To be sure most explanations of the big bang make it sound like a finite universe because that is more easily understood. It is easier to picture and describe. But it is not actually required by the theory.
We’ve been over this in other discussions – @heymike3 was involved. Maybe you missed it/them.
And it now sounds like you are advocating for absolute space which you formerly have decried.
I am not advocating anything. I am only telling you what we do not know.
No, you are telling me what you do not know.
We do know that this universe started with a bang, a bang that began producing things in time. You can never have more than what has been produced up to any given time, and that will be true always. You can never have more than has been produced up until now, no matter what now you pick and however far in the future you want to go. Capisci? We know that there can never be an infinite number of things in the universe.
Space began to exist and is expanding… with time. So neither is space infinite. Yeah, that’s a little hard to get your head around.
Okay, there is still discussion about that, but it is not necessarily infinite:
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I had said that in the sense of spatial infinity. If we cannot reach, not measure, the border or end of the universe, then we cannot know whether it is finite or infinite.
There is a good argument that it is finite because space had a beginning and grew with time, and time has only progressed as far as time has progressed. See above.
We do not know whether there was an earlier universe that had space that collapsed. Space therefore could be in a pulse. It need not have a primal beginning.
Correct! We don’t know whether it is finite or infinite. If I were to guess, I would frankly guess finite because I think that is the more simple option – not that I think Occam’s razor is valid (I don’t). …and perhaps my thinking that finite is the more simple is a subjective judgement anyway.
But science is not about subjective judgments or guesses. It is about evidence – and we don’t have any on that particular question.
And if the universe is spatially finite then the result will be a finite number of things in the universe. But if the universe is spatially infinite then the result will be an infinite number of things. …because even 1 thing produced in an infinite number of places is an infinite number of things.
Correct. I am limiting myself to what we know from science. I cannot preclude the possibility that somebody has had divine revelation on the topic. Kudos to you for catching that.
Wrong. Not at any time will there be an infinite number of physical things. It is a logical mirage that has duped you. (Do I need to find where you decried absolute time and space? Because that is what you are now pleading.) Your little irony is ironic.
What you really need is for an infinite number of things to have popped into existence at the same time for your imaginary scheme to work. When the production of things progressed sequentially from the beginning of the universe you will never arrive at your imagined infinite number of things, never as in no real, but only pretended, time.
Nah… the number of things may proceed to infinity, but an infinite space does not necessitate an infinite number of things.
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If space is not infinitely divisible, then it is composed of parts, and those parts necessarily have an objective relation in… meta-space??
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Exactly. It can only proceed towards infinity but there will never be an infinite number of things. Maybe the operative word is never. Like in never-never land, only in the imagination.
Incorrect. What you need is for an infinite number of things to come into existence during an interval of time. There is an infinite number of different points between zero and one even though none of them are in same place on the line. Your arguments are like those of Zeno’s paradoxes. Just goes to show that how poor a substitute philosophy can be for science.
Sorry, you are never going to actually have an infinite number of things. That’s not philosophy, that is just counting and sequential time.
That is only a mathematical concept of infinitesimally small points, not a reality of actual things. My sorrow continues. 
If space is infinite, then there are an infinite number of inches.
Right?
Especially if it turns out to be circular.