Sometimes I like to watch philosophy videos on youtube before I got to bed and paradoxes really interest me. One of which is Zeno and his paradoxes, his most famous ones being Achilles and the tortoise and the Dichotomy Paradox as explained in this Numberphile video:
Achilles and the Tortoise
In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. – as recounted by Aristotle, Physics VI:9, 239b15 Source: wiki
Achilles and the tortoise have a race and Achilles lets the tortoise get a 100 meter start. Then Achilles catches up with where the turtle was. In the time Achilles caught up to where the tortoise was, the tortoise advanced 50 meters ect ect ad infinitum.
The Dichotomy Paradox
That which is in locomotion must arrive at the half-way stage before it arrives at the goal.– as recounted by Aristotle, Physics VI:9, 239b10 Source: wiki
The Dichotomy paradox can be thought of as a moving of the hands to clap except one hand stays still, while the other halves the distance and halves the distance and halves the distance until there’s contact however according to the paradox, this should be impossible.
Another paradox of movement is Zeno’s Arrow as explained in this video by carneades.org:
This is a strange one where it argues that if an arrow is in motion, every moment it holds a single space in time and to be in motion it would be moving through spaces in time but every single moment it is not any other space in time but a the single space it occupies at that second therefore movement is impossible. I like to use this one as an excuse to not get out of bed in the morning.
If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
– as recounted by Aristotle, Physics VI:9, 239b5 Source: wiki
Zeno starts to loose me in the second round with The Paradox of Place:
if everything that exists has a place, place too will have a place, and so on ad infinitum.
As in all places have places until you get to the point of “Everything” as in “Life, The Universe, and Everything” which I feel like I can pretty much wrap my brain idea around the idea of “Everything” being a bubble in a sea of no-things, though I guess in a philosophical extent I can’t really construct a proof around a feeling. Maybe someday.
The Millet Paradox in it’s original phrasing is dated so I’ll attempt to update it so it’s more relevant.
Original: The argument is that a single grain of millet makes no sound upon falling, but a thousand grains make a sound. Hence a thousand nothings become something, an absurd conclusion.
Updated: A single vote in an election will not make a difference. However 1,000 can make a difference. How can 1,000 non-difference making single votes make a difference? (I realise this kind of misses the point, but I have voting on the mind with all the political drama in the US and UK)
All these paradoxes hint at this idea that Zeno had that nothing ever changes and maybe even that nothing is actually real.
This Wisecrack video sums it up in a pretty interesting way with their 8-bit Philosophy series.
As we learn in the video, Zeno’s teacher Parmenides argues that existence is timeless and that all things that ever were and are and will be exist at the same time, implying there can be no change because things exists at once, which sounds strangely like Nietzsche’s theory of Eternal Return or the “time is a flat circle” stuff (insert true detective picture).
I have no answers today. These paradoxes have stood the test of time themselves without changing which might be a reflection of their importance. Or maybe this is just several accounts of reductio ad absurdum, which itself would not be a new claim but a good one to make since it draws the connection between Zeno’s paradoxes of change and the practice of reducing arguments down to the absurd.
Tune in tomorrow for my first philosophy comic: Zeno’s Pantry Paradox