Suppose there is an infinitely long ladder in front of me. I do not know that this ladder is infinitely long, only that it is either a very long (but finitely long) ladder, or an infinitely long ladder. What kind of evidence would I need to give me reasonable assurance (I don't need absolute certainty) that this ladder is indeed infinitely long?
I could walk a mile along the ladder and see that it still shows no signs of stopping soon. But the finitely long ladder would still be a better hypothesis in this case, because it explains the same data with a more conservative hypothesis. If I walk two miles, the finitely long hypothesis is still better for the same reasons. No matter what test I perform, the finitely long hypothesis will still better explain the results. Does this mean that, even if infinite objects exist, empirical evidence will never provide reasonable assurance that they exist?