 The most famous paradox of all time has got to be the liar's paradox. Pretty much everybody's heard about it at some point in their lives. Philosophers have been writing about it for thousands of years. It's simple, it's profound, here it is. This sentence is false. Think about it for a second. Is that sentence true or is it false? If it's true that this sentence is false, it must be false because it claims to be false. But if it's false, it's got to be true because it claims to be false. So what's going on here? If it's true, it must be false. If it's false, it must be true. What's the resolution? And a lot of philosophers and thinkers have concluded there's a lot of profundity in the liar's paradox. It shows the inherent limitations of classical logic. It is something which is fundamentally a paradox, it's irreconcilable, it is true, and it is false at the same time, deal with it. I don't find those arguments particularly persuasive. In fact, I would say there's a fairly simple resolution of the liar's paradox, even though it's very tricky, but all you need to do is examine it very carefully. The way that you resolve the liar's paradox is as follows. Which sentence exactly is false? Here's what I mean. This sentence is false. What do the words this sentence reference? We have two possibilities. In the sentence, this sentence is false. This sentence could be referencing the entire sentence. This sentence could be referencing this sentence is false. Or this sentence could only be referencing this sentence. Those are the only two possibilities for what this sentence references. And what I would say is upon examination, both of those, when you really look at them, turn out to be nonsense. The liar's paradox is just nonsense. Okay, so let's take the easy example first. Let's say that this sentence references only this sentence. Well, then it's very easy to see that it's nonsense. If this sentence is false, it's referencing just this sentence. It can't be true or false. It's just an empty reference. It's like saying that shoe is false or that cloud is false or that this or that that. I mean, it's just pointing and saying is false. It's not a proposition to evaluate as true or false. It's just a reference. So that won't do. So in order for the liar's paradox to make any attempt at being sensible, this sentence has to reference the entire sentence. This sentence equals this sentence is false. But this runs into its own set of problems. If this sentence is, this sentence is false, then what the liar's paradox is really saying is this sentence is false is false. But this is a problem. Because if you substitute this sentence for itself, you're left with this sentence is false is false is false. And you substitute it for itself again. You're left with this sentence is false is false is false is false. Add infinitum. So you don't actually have a concrete answer to the question. What sentence exactly? This sentence is false is false is false is false is false. Add infinitum is not a proposition to evaluate as true or false. An easier way to see this is by substituting this sentence just for x. So we abstract one level. We say the liar's paradox is saying x is false. And what is x? x equals x is false. But if x equals x is false, that means the liar's paradox isn't x is false is x is false is false. And if you substitute x for itself, it's x is false is false is false. And you substitute x for itself again. It's x is false is false is false is false. Add infinitum. You will literally logically never end up with a concrete answer to the question. What is x when the definition of what x is requires a definition for itself, which is never defined. Okay, that's the reason the liar's paradox is nonsense. It's that this sentence or x is never defined. Any sentence which doesn't have concrete terms that it's evaluating as true or false or concrete propositions isn't a paradox. It's just nonsense. It's just a poorly constructed sentence. So next time that somebody comes up to you and says, ah, I have proof that there are real paradoxes out there. This sentence is false. You can the appropriate responses and say, well, that's nonsense. If you like this video, make sure to leave a comment and subscribe. If you'd like to see more videos like this, you can become a patron of my work over at patreon.com slash Steve Patterson.