# What are possible resolutions of the length unit paradox stemming from Zeno's Paradoxes?

The paradox in question: If every unit of length is made up of smaller units of length, it seems that you need to have units of length before a unit of length can come into existence. But this is clearly contradictory.

This paradox would seem to imply the following. Say you have two lines lying exactly on top of one another "|", and you want to slide one off the other to create space between the two, so that it now looks like this "||". If we need units of length before a unit of length can exist, then it seems we cannot create a length of distance between these two lines when we started with none, as we would need to have some length of distance already between them before we could have any length of distance between them.

Where does this reasoning go wrong?

• I do not see why smaller units of length need to "precede in existence" (whatever that means) bigger ones, why can't they all exist eternally, or "come into existence" simultaneously, or bigger ones first? Also, you "existence" is ambiguous between length unit (as a physical aspect) and the notion of length unit. Why can't sliding of the lines happen physically even if there were no notions of length units, or of length and lines for that matter? Or if those came to be distinguished only later after the whole process happened multiple times, which is how it historically was? Sep 12, 2017 at 17:51
• I have the same question as Conifold: "Why can't sliding of the lines happen physically even if there were no notions of length units, or of length and lines for that matter?" Sep 12, 2017 at 19:18
• The statement "every unit of length is made up of smaller units of length" seems to contradict the way we work with units. To work with units, one fixes one value (one meter, one kilogram are canonical examples), and then one subdivides as desired. Why would a contradiction arise from that? Sep 12, 2017 at 21:34
• @Conifold, the same argument can be applied to the concept of distance. If every distance is made up of shorter distances, we need to have distance before we can have distance. While they could come into existence at the same time, the fact that you first need the shorter distances before you can have / comprehend the full distance implies, to me at least, that one must come before the other. Sep 13, 2017 at 0:22
• This is not Zeno's argument at all, his argument is that we need to cover half the distance before we cover the whole distance. As for what we need to comprehend, I do not see why we can not comprehend all possible distances at once, they are all of a kind, and even if not why are shorter ones "easier" to comprehend and come first? This seems to conflate order of size with the order of understanding. Sep 13, 2017 at 0:33