Actual Infinity in Reality?

[SteveII]

THEREFORE, because infinite sets are a results of non-logical axioms (assumptions) that are not self-evidently true AND, the term 'exist' is not the same in mathematics, I stand by my claim that infinite sets in mathematics are not an indication that an actual infinite series or objects can exists in reality.

But the math shows that such assumptions lead to no internal contradictions: they are logical possibilities. And that is the whole point: that there is no *logical* obstacle to these being real.

The math is based on axioms (assumptions). It is question begging (circular reasoning) to say it is proof that they are logical possibilities. You have assumed an actual infinite in order to do further math with it. So, it gives no help to the argument that an actual infinity can exists. Therefore need we turn to something other than math:

1. You cannot get to infinity by successive addition.
2. You get absurdities when you propose an infinite number of actual objects (Hilbert's Hotel).
3. You get contradictions about how many squares and square roots there must be (Galileo's paradox)
4. Is the vase full or empty in the Ross–Littlewood paradox?
5. Is the lamp on or off in the Thomson's lamp paradox?
6. It seems we cannot traverse even a finite distance in Zeno's paradoxes

These coupled with the fact that we don't have anything in the real world that could be an actual infinite leads a rational person to the believe that an actual infinite of real objects is not possible.