I am reading Hume's A Treatise of Human Nature and was struck by his arguments against infinite divisibility.
In Part II - Of the ideas of space and time; Section I - Of the infinite divisibility of our ideas of space and time Hume expands on his earlier assertion that the mind has a finite capacity.
Tis universally allow’d, that the capacity of the mind is limited, and can never attain a full and adequate conception of infinity: And tho’ it were not allow’d, ’twou’d be sufficiently evident from the plainest observation and experience. ’Tis also obvious, that whatever is capable of being divided in infinitum, must consist of an infinite number of parts, and that ’tis impossible to set any bounds to the number of parts, without setting bounds at the same time to the division. It requires scarce any induction to conclude from hence, that the idea, which we form of any finite quality, is not infinitely divisible, but that by proper distinctions and separations we may run up this idea to inferior ones, which will be perfectly simple and indivisible. In rejecting the infinite capacity of the mind, we suppose it may arrive at an end in the division of its ideas; nor are there any possible means of evading the evidence of this conclusion.
But my understanding of Zeno of Elea is that he argued differently, that finite bounds, i.e. where I am standing now to 10 feet away, are infinitely divisible. If you take half of where I need to be (5 feet), and again, (2.5 feet), again and again, you just keep getting halves, to infinity.
Was not this Zeno's proof that motion or change itself was an illusion?
I am not a mathematician, so I was looking for clarity on this. Is Hume right, or Zeno, or am I misunderstanding something?