The Ancient Paradox We Still Can't Solve

The Liar Paradox is an ancient philosophical puzzle. Philosophers have tried to solve it, but it has proven difficult.

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00:00 - This sentence is false
01:00 - The problem
04:36 - Can the Liar be solved?
07:55 - This sentence is not true
09:44 This sentence is a contradiction

[shafeequllahsatari]

Since the issue remains unsolved, we will leave it at that as well. Thank you for the insightful content and the generous free guide.

[ryancain]

My sincerest thanks for providing a reading guide.

[modernoverman]

The first half of my undergrad was studying math/physics, while the second half was studying philosophy, so take my opinion with a grain of salt: I think this highlight the limits of our imperfect language, which is subjected to evolutionary pressures. We ought to take a pragmatic approach and maybe just keep paradoxes like this at our side. Like science, we can push anomalies to the edge as long as the rest of the world remains consistent until more anomalies reveal a pattern in our language.

[vishwastanwar]

Language is a social construct. It doesn't by itself adhere to the logic of reality, but our closest estimation of it. We can just as well say "This sentence is a paradox" or "This sentence is x" where x means neither true nor false. Bending a language doesn't imply bending the logic itself.

Further, logic itself is culturally informed, and thus a near estimation of reality at best. So if it's a little shabby here and there, it shouldn't raise any alarms.

There. Solved. What was needed was just a little bit of continental philosophy.

[SurenEnfiajyan]

The problem I think is a particular type of self referencing (or any other infinite cycle), the self referencing / infinite cycling on the truthiness. "This sentence is true" is that problematic case because it's not evaluable. But "This sentence contains 38 letters or numbers" is not problematic because we can evaluate its truthiness despite it's a self referencing sentence. In programming there is a thing called infinite recursion when a function calls another function(s) and it calls other function(s), etc, without termination. This is a similar situation.

[BlackthorneSoundandCinema]

My perspective is that a paradox like this one simply highlights the fact that language can be used to create an empty image that is devoid of meaning. There are many combinations of words that also have no value, this one is just easier to recognize. It may be wise to think about that rather than spending time thinking about this specific specimen. Its only meaning is a warning.

[HaecSublimisVeritas]

The second way is correct if you go full Aristotle. The liar's paradox cannot be true or false, because it is not a proposition. By reductio ad absurdem: Suppose that "This sentence is false." is a proposition. What is the predicate? "False". What is the subject? "This sentence". What does the subject supposit for? "This sentence is false". So now we have the subject "This sentence is false" and the same predicate "false". Now the subject supposits for a proposition, and we have to evaluate its truth by going back to step 1. This process repeats infinite times and is in principle impossible of terminating.

[seraphir]

this was so extremely interesting beyond what I expected

[grgarciaxiv]

Jared, I'm pausing this at 8:24 at I'm tearing up. Your work is so beautiful--I love the Liar's Paradox, and many things about it, including Turing's relation to it (Leavitt, 2006). Thank you for your excellent thoughts, and moreso, words
Cheers, Giovanni

[Corredephd]

This sentence comes up on the first course of logic we take in any Mathematics Bachelors. The goal in Mathematical context is to illustrate something that was proven by Gödel, which is that not all Theorems in math can be proven to be true, or false. We have lots of open problems in math and it is believed that some of them can’t be proven, some are worth 1 million dollar if you’re able to prove it. Anyways, the liars paradox is not the most accurate example of the incompleteness of math but it’s fun.

[BanAaron]

In Buddhism we have something called a Tetralemma which solves for cases like this IMO. Things can be affirmation, negation, both, or neither. A lying statement can be both true and false at the same time under this logic.

[whitb]

Love this. Please keep making the analytical side of philosophy videos. They're excellent.

[williamfrost]

It seems to me this paradox touches the boundaries of how language can be prescribed.

[yanuzz]

I just read about this in Fritz B. Simon's book "My Psychosis, My Bicycle, and I: The Self-Organization of Madness". There he proposes that nothing is really static but everything is constantly changing. However, our language conceives of many things as static. This is in a way a simplification we need in order to be able to process the world at all. But it is not the actual reality.
So if we take the sentence "This sentence is false." we can solve it (albeit maybe in an unsatisfactory way) by adding an imaginary element: time. This is a little bit like in mathematics where, in order to solve the square root of 4 we need imaginary numbers, and we get not one but two answers: 2 and -2.
But going back to our sentence, we add the imaginary element time and we see that the answer oscillates – one moment it's true, the next it is false. Just like you described your feeling about it in the beginning. It is also a little bit similar to those ambigious images (e.g. rabbit-duck illusion), where your perception oscillates between different conceptions.

[atavax]

I wish you went briefly over how Tarski's solution avoids the contradiction.

[padmeasmr]

I love paradoxes, thank you for this. I wrote my MA thesis on the paradox of the actor, connecting Diderot and Sartre (quite paradoxical itself lol). Next year I would like to create a channel mainly about philosophy. I wish English was my mothertongue though.

[atavax]

what about the argument that a statement implicitly states that it is true so "this statement is false" is basically saying "this statement is true and this statement is false"?

[TedMattos]

Thank you for the video, Dr. Henderson. I appreciate your approach.

The video had me thinking about something that has been around society for some time - "Truth is subjective."
We hear people say, "Celebrate YOUR truth!" and "Your truth may be different than my truth."

I'd love to hear others' thoughts on this.

[BrianBell]

I loved this video. You had me at explosion. But seriously, I really appreciate all of your videos and learn something new with each release. Thank you!

[GreatBooksProf]

Really enjoyed this, Jared. Thanks for making it!