The "There is no truth" paradox...

Honestly, your post just proves my point about what happens when you stop looking at the actual meaning behind things—you know, the semantics—and just start thinking like some kind of machine. It’s easy to fall into that trap, I guess.

I think maybe you're also getting a bit mixed up about what semantics actually means.

I laid out my mathematical model for self-reference, and I’m sticking to it: it’s basically identical to yours. Functions don't really have an initial "value"—they just describe a specific logical structure. It's a program, much like your sentence. Only difference is one runs on a processor while the other runs on your brain.
Variables are part of the syntax here, so they aren't even relevant.

Besides, you can express recursive functions linearly. I just used Pi as an example for a more recognizable algorithm. And just because it "goes somewhere" doesn't mean it isn't looping. Complex loops are still loops.

Let me weigh in here too.

First off, let’s get one thing straight: I have zero training in philosophy. I haven't touched a textbook on logic, psychology, or any of that academic fluff. All I have is my own way of thinking through things logically...

Imagine one guy tells his friend that truth doesn't exist. Naturally, the friend won't buy it for several reasons. First, if what he said is true, then "truth doesn't exist" is itself a truth, which contradicts him. Second, he’s convinced truth exists simply because his mind isn't wired to accept a paradox like that.
Now, compare this paradox to that famous image of people climbing stairs in an endless loop.
Suppose we actually find ourselves on those stairs with no exit. Would we keep climbing? Or would we head down? Regardless, we act. We move. Even if we see the stairs just circle back upward forever, our only options are up or down. That’s the reality.
In any scenario, we are performing an action—climbing or descending, moving forward or backward. By doing so, the paradox evaporates, because a true paradox shouldn't allow for any kind of action.
Some might argue there's no real action since we aren't "getting anywhere," but I disagree. We are getting somewhere; we are reaching a higher elevation than where we started. No matter how futile the effort seems, we still choose whether to go up or down, to ascend or descend from our current spot. Because we can make that choice, the paradox ceases to be. A paradox, by definition, cannot permit action, change, or decision-making. Those are the core components that make a paradox a paradox. Or am I wrong?
Similarly, the idea that there is no truth can technically be true, because we decide whether or not to believe it. If we choose to believe it, we can't, because we already committed to the belief that truth doesn't exist. Once we stop believing that, we conclude that truth *does* exist, so we believe again, and we're right back where we started. It's a loop. But we are the ones choosing that initial leap of faith or skepticism. In doing so, we build a chain of facts and conclusions—repetitive as they may be—that lead us further toward an answer, closer and closer to Pi.
The bottom line is that we take action and we make decisions. Therefore, it isn't a paradox. I'm concluding that paradoxes don't truly exist, regardless of what any fancy theory claims.
It's the same deal with someone mentioning a black hole. We can decide if we want to scientifically uncover what lies on the other side or not. Until we act on it, it remains an object in the universe that we can't even call a paradox, because we haven't engaged with it yet.
So, don't come at me too hard, you educated philosophers. My primary philosophy is to follow my own reasoning. I don't think you can reach a quality conclusion by blindly following someone else's theories or monologues. I look at the very people who laid the groundwork for the topics discussed on this forum; they had no actual basis for their theses or conclusions to begin with...
Regards,

I'm with Nem on this one—and I'll try to explain it my way, even if I'm mostly just echoing what feralharbor2 already laid out.

feralharbor2 said:I think you’re equating these two things based solely on a surface-level analogy of "cycles."
With Pi, you get repetitive digits, but the function isn't actually looping back on itself; it's moving forward, providing more precision for the value. That repetition has zero connection to semantic self-reference—or the "emptiness"—of the sentence we're talking about. Repetition here just refines a specific ratio (Pi is just the quantitative relationship between a radius and a circumference). That ratio *is* the content. So, semantic content exists, unlike in that self-referential sentence.
Maybe your confusion stems from the semantic gaps and occasional ambiguity in the language used during math operations. For instance, a "function" can sometimes refer to the resulting number and other times to the operation itself. This linguistic fuzziness is annoying for semantic purists like me, but hey, you can't fight tradition when people use it as a shorthand.

Let's look at it this way. Let's temporarily ignore the self-reference that led Eric Bennett79 😁 to compare a logically contradictory judgment to a recursive function.
Take a judgment like "It is true that three is five." — that’s a semantically meaningless, contradictory statement, and a logical contradiction precisely because "truth is defined by how a description corresponds to something external to it." That statement fails right out of the gate because three obviously isn't five; it's inherently contradictory from the start.
The same goes for the self-referential judgment "this sentence is false." It's contradictory from the jump, so there's no point in overanalyzing it—any conclusion we reach will just loop right back to that initial flaw.
Any contradictory judgment should be tossed out immediately.

Eric Bennett79 says: Functions themselves don't have an inherent "starting value"; they just describe a specific logical construction.
And it's crucial that they truly lack an initial "value," unlike semantically contradictory judgments which *do* have an initial "value"—namely, the fact that they are contradictory because their terms are placed in impossible relationships with reality.
The starting value for any function is derived by plugging in or calculating variables based on their relationship, where "repetition just refines a specific ratio (Pi is just the quantitative relationship between a radius and a circumference)." Basically, those variables are related without contradiction from the get-go. A recursive function might cycle, but it's always moving forward, whereas in self-referential judgments, the terms are contradictory from the start, causing the logic to constantly snap back to its own failure.

Eric Bennett79 said:Look at the statement "The truth is that three is five" – that’s just semantically nonsense and totally contradictory. It's a logically flawed claim right from the jump because, well, the whole idea of "truth" relies on a description actually matching reality. Since three obviously isn't five, the sentence is broken before you even get started.
It's the same deal with an autoreferential claim like "this sentence is false." That one is paradoxical from the get-go, and there's honestly no point in overanalyzing it because any conclusion we reach is just gonna loop back to that same starting problem.
Any kind of contradictory claim should just be tossed out immediately.

Man, saying "The truth is that three is five" is just plain old wrong. There's zero paradox involved there.
But when you say "this sentence is false," *that's* where the paradox kicks in, strictly because the sentence is talking about itself.
Honestly, comparing those two things is a total stretch.

mistyfox812 said:The statement "the truth is three fives" is just plain false. There isn't some deep paradox hiding in there.
A paradox actually shows up when you say something like "this sentence is false," and that happens specifically because of self-reference.
Comparing those two statements doesn't really work.

I guess the analogy still holds, just maybe not on the level of the paradox itself, but rather regarding how flawed the initial premise is.
The whole idea of "this sentence is false" isn't broken because of the paradox—the paradox is just what happens later once you follow the logic of the initial nonsense. It’s already fundamentally flawed from the start because its self-reference makes it totally hollow.

mistyfox812 said:I laid out my mathematical model for self-reference for you, and I’m sticking to my guns—it’s totally analogous to yours. Functions don't really have an initial "value" either; they just describe a specific logical structure. It's a program, much like your sentence. Except one runs on a processor, and the other runs on your brain.
Variables are part of the syntax here, so they aren't even relevant.

Besides, recursive functions can be expressed linearly, and I only used Pi as an example for a more recognizable algorithm. Just because it "goes somewhere" doesn't mean it isn't looping. Complex loops are still loops.

It’s not analogous. Or rather, it is, but only on a surface level that doesn't matter here.
A recursive function only looks self-referential because of the mathematical syntax used to describe it, but that isn't a problem since everyone implicitly understands how it works.

It DOES NOT act ON ITSELF!!! It acts on the previous step, the preceding operation. So even if the symbols are identical, everyone knows it represents an action—an operation performed not on itself, but on the prior result.

The fact that a function doesn't have an initial value as such, but instead represents a quantitative relationship or an operation, is irrelevant because you always have to "inject" some value into a function for it to start processing anything.
Syntax only matters if its meaning, or semantic content, is clear. Mathematical syntax is sometimes, strictly speaking, ambiguous, but that’s not an issue because everyone knows what it means. With recursion, there is no "looping in circles," just the repetition of an operation on a previous result.

It might seem the same to you because the logical progression of the sentence "this sentence is false" always operates on the previous result, BUT you failed to notice that the self-reference of that sentence isn't in that repetition, but in the initial statement itself.
This probably seems similar to a recursive function to you because the syntax appears self-referential, but it isn't. It’s just an illusion created to save time, and everyone knows how it works even if the syntax is ambiguous.

A recursive function never processes itself. It’s a process; it processes a number, then takes that result and does it again, and again...
A function is a description of an operation, so the fact that it looks like it exists on both sides of the equals sign in mathematical notation isn't a sign of self-reference; it’s understood that this is just the previous phase of an iterative process.

With the sentence "this sentence is false," the initial statement is flawed because the "operation"—if we want to call it that—which is inherently a process of determining truth by matching the statement's content to something external to it, cannot function. The truth of the statement fails to connect to anything outside the statement right from the start.
So, the initial CONDITION for the "truth operation" to be possible 😉 isn't met and the "function" this sentence represents is just pure nonsense.

It’s probably like when you write a function in math that means nothing—no meaningful operation at all—just an error that makes a mathematical expression nonsensical.
I'm no mathematician, but I'm pretty sure mathematicians can come up with stuff like that.

But LOOK, the further logical development of that initial statement keeps going because it is an operation that isn't contained within the initial statement, which already contains a broken "truth-determining" operation. The process spins in circles because it uses a logical procedure that is "outside" the initial statement, trying over and over to manufacture some sense out of a sentence that was nonsensical to begin with. So it's no wonder it never succeeds.

A valid logical statement has to be nothing more than an accurate description of something existing outside the statement itself. That’s the CONDITION, the AXIOM, if you want to call it that—it’s something you have to respect right from the jump. If you don't start there, then any further iterations aren't actually the result of some properly functioning recursive function. It’s just nonsense. You end up with a logical process that keeps trying and trying to fix things, but it can't, because it's fundamentally broken...

You really have to realize that the iteration of a logical process isn't built into the initial statement, unlike a recursive function where it’s implied. In this case, it's just the consequence of spinning your wheels in circles. It's just what happens when you have an error or some absurdity, which leads to this infinite loop of trying to correct that mistake. But logically speaking, it's just impossible.

feralharbor2 said:The analogy holds up—not because of some paradox, but because the starting premise itself is just broken.
The statement "this sentence is false" isn't flawed because it creates a paradox; the paradox is just the byproduct of trying to unpack a logic that was already nonsense from the jump due to being self-referential and empty.

So, there’s my (lack of) logic expertise. But hey, sometimes you gotta talk without knowing your stuff just so someone who actually does can tear your argument apart—that's how you spot the error and learn how to not screw up next time. I know newbies aren't exactly the most popular crowd on this forum, but damn, everyone has to start somewhere. 😬
Just a heads up: you don't need to reply to this. (And I know you won't anyway, but saying it makes me feel better—I can just tell myself you ignored me specifically because I told you not to. Still... 🙂 ) 🙂

Eric Bennett79 said:So, there's my supposed lack of logic. Look, maybe you have to talk nonsense sometimes just so someone who actually knows what they're talking about can tear your argument apart. That's how you spot an error and learn how to avoid making it next time. I get it, newbies aren't exactly welcome on this forum, but whatever, everyone has to start somewhere, I guess. 😬
Just so we're clear, you don't need to reply to this post (and I know you won't even if I didn't say that, but I'll feel better knowing I told you, because then I can tell myself you ignored it specifically because I asked you to. But still... 🙂 ) 🙂

I didn't actually correct any mistake of yours. There was a tiny slip-up in how you used the word "contradiction," sure, but I didn't realize you were basing your whole analogy on a paradox rather than on the initial invalidity of the statement itself—which is the crucial part here (and it's right).
What I was actually doing was correcting mistyfox812, who was claiming your analogy was garbage. It works fine, provided you look at the core issue regarding the initial statement and its semantic validity.

feralharbor2 said:Look, I wasn't trying to fix any mistakes you made. There was just a tiny slip-up in how you used the word "contradiction"—I didn't realize you were basing your analogy on a paradox rather than the actual validity of the initial statement, which is the whole point here (and it's right).
I was actually correcting mistyfox812, who was claiming your analogy didn't work. It does—provided you look at the core issue of whether the starting premise is semantically sound.

Wait, there are still good people left in the world 🙂 Nah, I'm just messing with you. I realized I nailed the main point, but I also saw where I tripped up when defining the statement I compared to your self-referential one. My logic was heading in the right direction, but yeah, there was an error there—even if it was minor and basically irrelevant.
I guess I'm just way too hard on myself about everything. But hey, being self-critical is a virtue. Or so I tell myself. 👍

I've been thinking about this, and I guess I have to agree with you guys... classic recursion isn't the right model here. I did stumble onto another angle, though, but I need to flesh it out first. It’s about self-reference during the actual construction of the expression—where the thread's value doesn't even enter the function; instead, the paradox itself becomes the output. I'll start a new thread once I iron out the kinks, and I'm pretty sure it'll make sense then. Until then, we should probably wrap up this interesting discussion 😁

If you actually pull it off, shoot me a DM so I don't miss the thread.

Logic is basically just this formal discipline.
If Savannah is bigger than Washington, D.C., but smaller than a small town in rural America, then Washington, D.C. is definitely smaller than that small town in rural America.
That’s a true statement. It doesn't even matter what "Savannah," "Washington, D.C.," or "small town in rural America" actually mean or how big they really are. You could just swap them out for A, B, and C to make it look more official:
If A is greater than B and less than C, then B is less than C. And that works for any A, B, or C you throw at it.
So, basically, logic totally ditches the idea of truth being about "matching reality to words" and just focuses on whether the statements themselves are internally consistent.

Look, I’ll be the first one to admit that logic isn't the ultimate way to communicate. Sometimes poetry can convey or show the truth way better, even if it doesn't care about logic or grammar. Truth in speech—logos, if you want to get fancy—isn't always logical truth.

But when we're playing in the sandbox of logic, all that matters is the structure of the statement, regardless of what it's actually about.

The Liar's Paradox is huge because it's such a simple, historical example of a logical paradox caused by self-reference. That whole concept became a massive deal in the 20th century because it exposed the flaws in trying to ground mathematics through logic—specifically regarding Gödel's theorems. I won't try to explain those theorems myself; I read about them once and think I got it, but honestly, I've forgotten most of it. All I remember is they get super messy if you try to be precise, which you absolutely have to be when you're talking about the link between logic and math.
Anyway, just wanted to share that much to show the cool possibilities hidden in this paradox. If anyone's interested, go grab a copy of the book on Gödel's theorems.

Someone and nothing say:
Logic is a formal discipline.
If Savannah is larger than Washington, D.C., but smaller than Smalltown, USA, then Washington, D.C. is smaller than Smalltown, USA.
That is a true statement. It doesn't matter what the terms Savannah, Washington, D.C., and Smalltown, USA actually mean, or how big they really are. If we just swap those terms for A, B, and C, we get a more formal version:
If A is greater than B and less than C, then B is less than C. And that holds true for any A, B, and C.
So, basically, logic abandons the idea of truth—as in the "correspondence between words and reality"—and focuses solely on the formal consistency of statements.

hollowpilot9: What you’re writing there is just one pragmatic, limited definition of logic. Formal logic has long been nothing more than a playground for philosophy departments! Savannah, Washington, D.C., and Smalltown, USA are just our anthropocentric concepts used to say A is bigger than B, and B is bigger than C, simply because that’s how we perceive things? But from what vantage point are we looking? If we look from C toward B, C is always larger than B, regardless of how much we try to convince ourselves logically that A is larger than B. Why? Because there is a distance of space and time between A and B—by the time we look at B, all of A might have vanished. Or if we move from B toward A, both A and B might change in size during the journey. They can't remain identical! That applies to linear logic. As for non-linear logic, this whole ABC relationship you're citing doesn't even apply, because in a non-linear system, A, B, C, and D are always the SAME. If one is searching for philosophical truth, it won't be found through formal logic.
Later on, you claim to be the first to suggest that logic isn't the most important element of speech. Sure, but you have to specify which logic you mean? Your logic and your wife's logic (assuming you even have one) aren't the same, and the logic of one contradicts the logic of the other, as well as their own individual logics. That is the logical catch of logic! I've already written about where formal logic has led us. We teach our children and ourselves that 1 : 2 = 1/2, while the entire universe seems to be laughing at us.
For a philosopher to reach Truth via a logical path, they must structure logic to mirror the logic of reality, rather than philosophizing based on some imagined "philosophical" logic. What appears as a paradox in traditional philosophy is actually an inversion today. One entity, or one phenomenon, is paradoxical to another. But there is a massive difference between whether that paradox is "jagged" or if it is complementary. Just take the traditional concept of opposition, which today has almost no connection to common sense. The concept of opposition was something only the most ignorant philosophers could have dreamt up!
You mention "logically grounded mathematics"? Such mathematics doesn't exist, precisely because all mathematics is paradoxical—or rather, complementary. It isn't even logical that 1 : 2 = 1/2!! It would be logical if 1 : 2 = 1/2 + 1/2. However, that flies in the face of our "common sense," which I’ve already pointed out is actually a "sick sense." You also bring up Gödel's theorems. Those are the very theorems that show mathematical logic is fundamentally different from the logic we've grown accustomed to and believe to be correct. Look up Gödel's mathematical cipher and compare it to the cipher of a DNA molecule, and everything will become clear. In that context, multiplication isn't multiplying, but rather division is multiplying. It's the exact opposite of our traditional logical common sense. Truth lies in the inverse, not in what we perceive to be truth. This is why modern neuropsychiatrists say negative perception is the triumph of consciousness. A philosopher should know that the world is seen upside down, not the way they think they see it! It's a fact that philosophers avoid—I don't know why.
"But in this way, since we are ignorant, we will first want to examine our opinions in relation to one another: what they actually are and whether they agree with each other or disagree entirely... When that is the case, what else is there to do but calmly, like people who have plenty of time, reconsider again—without getting angry, but truly exploring ourselves—what these phenomena are within us? (Plato, Theaetetus)"

I'll sign off on that, with one small addition: we are perhaps a bit smarter and more knowledgeable than our predecessors, even those called Plato.