The Impossibilities of Reality

Hi, my name is Liam Helie, and because I have always been interested in paradoxes, I’m here to show you how to debunk, or solve, some of the most famous paradoxes, specifically, math paradoxes.

The first paradox we will be looking at is known as the lottery paradox.This can be best explained by imaging a situation. Imagine that you have one of 10 million lottery tickets. Based on that, it is completely rational to think that yours is not the winning ticket. If you see a second ticket, you would also be justified in saying that is also not the winner. It is not a matter of which specific ticket, even though one is the winner, you will be completely justified in saying “that ticket is not the winner” about any ticket. That leaves you with the justification that none will win, but the knowledge that one will definitely win.

So how do we explain this?

The key to solving this paradox is to group. It is completely justified that one ticket will lose, but if you two tickets, you are less justified to think that they are both losers, even though the difference is very small. With this we can think of grouping enough tickets together so that it can be rationally accepted that the winning ticket is in that bunch.

The second paradox that I will be covering is a series of statements that combine to create Zeno’s paradox.

In the 5th century BCE, Zeno of Elea gave a few statements that are also paradoxes to show why reality is singular, meaning that there is only one thing or entity, rather than plurality, the existence of more that one thing, and that reality is motionless. While I am not an expert on pluralism, there is a TEDx that goes much more in depth on the topic to understand it more clearly. The paradoxes are arguments in which plurality leads to contradictions of complete absurdity.

His three statements against motion were:

1. Suppose that reality is plural. Then the number of things there are is only as many as the number of things there are (the number of things there are is neither more nor less than the number of things there are). If the number of things there are is only as many as the number of things there are, then the number of things there are is finite.
2. Suppose that reality is plural. Then there are at least two distinct things. Two things can be distinct only if there is a third thing between them (even if it is only air). It follows that there is a third thing that is distinct from the other two. But if the third thing is distinct, then there must be a fourth thing between it and the second (or first) thing. And so on to infinity.
3. Therefore, if reality is plural, it is finite and not finite, infinite and not infinite, a contradiction.

His statement against motion can be described with the story of Achilles and the Tortoise.

This story says that Achilles and a tortoise were having a race. Achilles, to make the race more fair, gave the tortoise a 500 meter headstart. Achilles, trying to catch up to the tortoise, but once he gets to the 500 meter mark, the tortoise has moved 50 more meters, but once Achilles reaches 550 meters, the tortoise will have moved 5 more meters, resulting in Achilles never reaching the tortoise, which is completely absurd.

The reason that this is not completely true is because of the fact there are multiple infinities and not all of them are the same. If the tortoise started at 500 meters, then moved another 100, putting him at 600, then another 200, putting him at 800, Achilles never would have caught up to him. This series of 1+2+3+4 etc is a divergent series, meaning that the numbers go on forever and this sequence will never have an answer. In the case of the story, the tortoice is going slower and slower each time as Achilles is catching up, meaning that it is moving in a convergent series, meaning that there is a finite answer, allowing Achilles to reach the tortoise.

The third and final paradox is called the potato paradox.

While the previous two paradoxes were the more common falsidical paradoxes, which is actually false, the potato paradox is a veridical paradox, meaning that it is actually true.

This paradox can also best be described with a situation:

Imagine that a farmer has a sack containing 100 lbs of potatoes. The potatoes, he discovers, are comprised of 99% water and 1% solids, so he leaves them in the heat of the sun for a day to let the amount of water in them reduce to 98%. But when he returns to them the day after, he finds his 100 lb sack now weighs just 50 lbs. How can this be true? Well, if 99% of 100 lbs of potatoes is water then the water must weigh 99 lbs. The 1% of solids must ultimately weigh just 1 lb, giving a ratio of solids to liquids of 1:99. But if the potatoes are allowed to dehydrate to 98% water, the solids must now account for 2% of the weight—a ratio of 2:98, or 1:49—even though the solids must still only weigh 1lb. The water, ultimately, must now weigh 49lb, giving a total weight of 50lbs despite just a 1% reduction in water content.

This is actually true, with the math backing it up

While there are many, many more paradoxes, I feel like I have solved and explained some. I also overall enjoyed researching these and searching for which paradoxes to use because it has always been interesting to me.