### Potential Infinity?

Obviously, if, empirically speaking, actual infinities don't exist, then potential infinities are contradiction in terms as well. Something is either infinite or finite. If it is finite, it is not infinite. In empirical terms, potentiality towards infinity assumes infinity of potentiality which is a self-contradiction.

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July 11
1. In mathematics, a number can be added to another number, and so on; there is the potentiality for addition or subtraction. However, what this proves is only that we have a non-ending possibility of adding numbers, a rational category and not an empirical one -- obviously, no one imagines that a tree has the potentiality of adding infinitude of height and width; this is an empirically impossible concept.
2. In Zeno's paradoxes, the infinite divisibility is rational and abstract. Interestingly, reverse regressive infinitude should also challenge the notion of the two points from which the reverse divisions of space are infinitely made potentially.
3. Potential infinities, thus, are empirically impossible, though mathematically true against the givenness of the rational category of infinite quantity.
4. Zeno's paradoxes as such continue to challenge any attempt to rationalize reality.