I also always loved Xeno’s paradox … specifically the Dichotomy Paradox (Halving): To travel from point A to point B, you must first reach the halfway point, but before you reach that halfway point, you reach the halfway point of those two points and on and on and on into infinity … which suggests that in order to get from any point A to any point B, you have to cross infinity … but it’s impossible to travel to infinity so the suggestion of the paradox is that you should never be able to reach any point B
I don’t think I get it, the conclusion doesn’t make any sense to me at all
Because yes, there is an infinite amount of infinities when you think of decimals. We have two when it comes to integers - negative infinity and positive infinity, and there is an infinite amount of infinities between any two integers. 0 - 1, but also between 0.1-0.2, etc
That doesn’t mean you can’t add or multiply any two numbers just because there is an infinity inbetween.
Imagine a distance of any length. How long does it take to cross an infinite number of that length? It takes an infinite amount of time.
Divide the length between A and B an infinite number of times. We now have an infinite number of lengths, which means it will take an infinite amount of time to cross them.
Which means nothing ever actually moves and movement itself is an illusion.
I think the issue is purely semantical and if we had a way to discriminate between the ultimate infinity from the subinfinities, the whole paradox would become completely irrelevant
It’s an interesting exploit of not having that distinction though
I also always loved Xeno’s paradox … specifically the Dichotomy Paradox (Halving): To travel from point A to point B, you must first reach the halfway point, but before you reach that halfway point, you reach the halfway point of those two points and on and on and on into infinity … which suggests that in order to get from any point A to any point B, you have to cross infinity … but it’s impossible to travel to infinity so the suggestion of the paradox is that you should never be able to reach any point B
Zeno
I don’t think I get it, the conclusion doesn’t make any sense to me at all
Because yes, there is an infinite amount of infinities when you think of decimals. We have two when it comes to integers - negative infinity and positive infinity, and there is an infinite amount of infinities between any two integers. 0 - 1, but also between 0.1-0.2, etc
That doesn’t mean you can’t add or multiply any two numbers just because there is an infinity inbetween.
Imagine a distance of any length. How long does it take to cross an infinite number of that length? It takes an infinite amount of time.
Divide the length between A and B an infinite number of times. We now have an infinite number of lengths, which means it will take an infinite amount of time to cross them.
Which means nothing ever actually moves and movement itself is an illusion.
I think the issue is purely semantical and if we had a way to discriminate between the ultimate infinity from the subinfinities, the whole paradox would become completely irrelevant
It’s an interesting exploit of not having that distinction though
I was told by a philosophy professor that to understand the paradox, I should read Wittgenstein. I couldn’t figure out Wittgenstein.
That’s the paradox and that’s why I love this thought experiment.
There is infinity in everything and everywhere … yet we are told that we can’t cross infinity … yet we do it all the time.
We cross infinity all the time. Git gud
… to infinity … and beyond
and you don’t fly there either … you’re just falling with style