(March 3, 2018 at 1:30 pm)polymath257 Wrote:(March 3, 2018 at 1:26 pm)RoadRunner79 Wrote: So as we progress from say 0 to 1, there is always another point Y between X and 1 where X<Y<1.
1. If you must pass through each of these points, you will never reach 1, because there is always another point Y which must be met.
Therefore Zeno concluded that if you can never end your journey or on the inverse (which isn't quite as intuitive) never begin your journey,
then motion is impossible. If you have to complete a endless number of points before you can get to the end (1) then you will never be at the end (1)
Do you agree? If not, where do you think that the error is?
1.) Please be more precise: exactly what process do we use to go from 0 to 1? Be specific.
2.) But yes, at any point there is another point to go through. And yes, we manage to go through all of them.
3.) The problem is that you are assuming we cannot compete an infinite process. Look at my comments on the definition of 'infinity' above.
1. ) In this case, we are cutting in half the distance between the current position and the end position. Which you agree, will never result in a number greater or equal to the end positions correct? In actuality, I believe that one would need to proceed through each point, between 0 and 1 sequentially. The dichotomy method of half marks allows us an abbreviated way to move forward, to systematically show an infinity and show that we that the end (1) will never be reached.
2.) If they are without end... how do you go through them all? That is the question. (And if you are going to say time again, then how does that help you to get to 1 if X<Y<1.... More or less time, does not help you complete this sequence, it's not a matter of completing it in a timely manner).
3. Using the same method, that you use to show an infinity, also shows that you cannot complete that infinity (hence the concept and the term). If you disagree with Zeno.... then where? You agreed to the premises including the math. Do you think that the conclusion doesn't follow that if X<Y<1 ad infinitum then an infinite number of halfway marks cannot be crossed, therefore the path can never be fully completed? If so why?
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. - Alexander Vilenkin
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther
If I am shown my error, I will be the first to throw my books into the fire. - Martin Luther