Fact vs. Truth: What's the real difference?

lonegardener said:But that math is really just a *metaphor* for the idea, not an actual mathematical equation.

At the end of the day, you determine the actual bottom line by digging through the company's books, don't you? We just lean on those numerical metaphors to make describing a positive or negative impact a bit more digestible for everyone involved. Even so, we're still fundamentally talking about value added.

Amanda Jackson5 said:Facts have an opposite, obviously. It’s basically anything that doesn't qualify as a fact. As for what a "half-fact" would even look like, I honestly couldn't tell you—I don't think I've ever actually used that term in my life. You hear people toss around "half-truths" all the time in casual conversation, sure, but if we were sitting in some high-level philosophy seminar or a logic lecture, that wouldn't really hold much water.

I can't say I've ever really understood why people get so worked up about Orah. It’s one of those things that seems to occupy way more headspace than it actually deserves, almost like watching someone try to explain the intricate nuances of a local deli sandwich when we all know it's just bread and meat. It feels like a lot of noise over something that doesn't fundamentally change the landscape, much like how some folks obsess over a minor policy tweak at a company like Starbucks while ignoring the fact that the coffee is still just coffee. You have to wonder if there's some deeper subtext I'm missing, or if it's just another case of people finding excitement in the mundane. kaže:
If you think the absence of a fact counts as its opposite, you’re missing the point entirely. It doesn't work like that. If you take "nothingness" and pair it with an actual "thing," you just end up back at the thing itself—it's like trying to subtract zero from a dozen apples; you aren't left with anything different. And if you try to pit a thing against its direct opposite, they don't just cancel each other out into a void; instead, you usually end up with some kind of messy synthesis made of whatever scraps are left over, which means they weren't truly opposites to begin with.

The negation of an object—or even just the concept of a non-thing—basically encompasses everything that fails to qualify as a tangible entity. It’s easy to get lost in the weeds here, but we have to acknowledge there's a massive landscape of entities out there that simply aren't "things." In its purest sense, a non-thing is nothingness. And if you want to play the philosophical game, the direct opposite of that void is existence itself.

That’s fair enough, but I’m really just trying to use it in its actual, intended sense—you know, from a more philosophical standpoint, like when you're diving into metaphysics or logic.

I’m with you there. Truth is really just an epistemological concept—it’s all about that complicated tug-of-war between the subject and the object, or more simply put, the friction between what we perceive in our heads and what actually exists in reality.

There isn't some grand sequence of events here. We’re just playing around with colloquialisms at this point. Truth doesn't come in layers or stages; there is only one version of it, which is simply when a person holds an accurate perception of the reality existing outside themselves.

I’m on the same page as you there, but what I’m really chewing on is the philosophical distinction between truth and a fact—you can't really untangle them until we pin down some solid definitions for both terms.

Look, I hate to be the one to double down here, but I’m sticking to my guns: 2+2 equals 4, period. It doesn't matter how you slice it or what angle you take; it's a baseline fact, and unless someone can walk in here and actually dismantle that logic with a coherent, rational argument—which, let's face it, isn't happening—it remains the truth. Sure, we could play around with the idea that 2+2 equals whatever we want it to for the sake of some poetic flair or creative license, but that's just playing with semantics; it doesn't change the reality of the math. I suspect the real friction in this conversation stems from people blurring the lines between concrete facts and abstract concepts. You can get away with mixing those two worlds in specific arenas, like when you're navigating the nuances of high finance or interpreting a piece of modern art, provided everyone implicitly agrees on the rules of engagement. But outside of those niche contexts, trying to blend them just results in a lot of noise without any actual substance.

🤔 Didn't you claim once upon a time that "nothingness" and "being" were actually the exact same thing?

So, I read somewhere that according to Harvard, being and nothingness are basically two sides of the same coin, which might mean they could actually be opposites. Then you’ve got Sartre splitting things up into being-in-itself (that total lack of distinction) and being-for-itself (nothingness, or consciousness). To stay on track with this discussion, I came across Smith arguing that these high-level abstractions are actually just plain false. Honestly, looking at theoretical math, the most abstract concepts—things like classes, collections, sets, or categories—aren't even true or false. They just exist.

Harold Doyle3 said:🤔 Didn't you claim once upon a time that "nothingness" and "being" were actually the exact same thing?

It’s a bit of both, really. They are, because they both represent a state of absolute, immediate indeterminacy. But they aren't, because their actual definitions sit on completely opposite sides of the spectrum. That’s why you can't really pull them apart; you have to view them as part of the same unified concept.

Facts are just whatever someone decides looks true, even if it isn't. Truth is something else entirely—it's the raw, naked reality itself.

Amanda Jackson5 said:It’s a bit of both, really. They are, because they both represent a state of absolute, immediate indeterminacy. But they aren't, because their actual definitions sit on completely opposite sides of the spectrum. That’s why you can't really pull them apart; you have to view them as part of the same unified concept.

Is that what metaphysics deals with? Colloquially speaking, I mean—half-truths?

Harold Doyle3 said:Is that what metaphysics deals with? Colloquially speaking, I mean—half-truths?

Not exactly; it's more about navigating contradictions.

Amanda Jackson5 said:Not exactly; it's more about navigating contradictions.

What's contradictory here... two different truths?

Nicholas Gonzalez87 said:I went ahead and assumed a mathematical model existed, but honestly, I don't know enough about mathematical physics or meteorology—or whatever field this actually falls under. I study pure math, not applied stuff. I'm only familiar with the simpler models, like using differential equations to describe a vibrating string.

Quincy:

Saying 1+1=1 is only a distortion if you view mathematics as totally isolated from the rest of reality. And look, I have nothing against that; math is a product of the human mind that we can study as its own independent entity.

Sure, math is formal. In my view, 1+1=2 because it's deduced from the axioms of natural numbers. That proof is completely convincing to me.

Quincy:

But, when we use math as one of the tools to describe our world, we have to realize that math only describes our world partially. It can't capture everything.

Yeah, there are other sciences too.

My point regarding mathematics was that it functions as one activity within a much larger framework, whereas you were discussing mathematics in isolation. It's a common misunderstanding on these forums—one person discusses a component while the other speaks to the whole. Mathematics is an elite discipline, and you've certainly chosen a profound field of study. However, I was specifically addressing its limitations when it attempts to describe the *actual* world. People have this tendency to reduce everything down to physics and math; various philosophical movements, like materialism or physicalism, push that same narrative... but I find that to be a distortion.

Nicholas Gonzalez87 said:I went ahead and assumed a mathematical model existed, but honestly, I don't know enough about mathematical physics or meteorology—or whatever field this actually falls under. I study pure math, not applied stuff. I'm only familiar with the simpler models, like using differential equations to describe a vibrating string.

Quincy:

Saying 1+1=1 is only a distortion if you view mathematics as totally isolated from the rest of reality. And look, I have nothing against that; math is a product of the human mind that we can study as its own independent entity.

Sure, math is formal. In my view, 1+1=2 because it's deduced from the axioms of natural numbers. That proof is completely convincing to me.

Quincy:

But, when we use math as one of the tools to describe our world, we have to realize that math only describes our world partially. It can't capture everything.

Yeah, there are other sciences too.

But they all rely on mathematics. Every science focuses on a specific niche rather than the entirety of existence, which means they inherently require reduction and simplification.

Nicholas Gonzalez87 said:So, I read somewhere that according to Harvard, being and nothingness are basically two sides of the same coin, which might mean they could actually be opposites. Then you’ve got Sartre splitting things up into being-in-itself (that total lack of distinction) and being-for-itself (nothingness, or consciousness). To stay on track with this discussion, I came across Smith arguing that these high-level abstractions are actually just plain false. Honestly, looking at theoretical math, the most abstract concepts—things like classes, collections, sets, or categories—aren't even true or false. They just exist.

I really appreciate you looking out for us here,

I'd honestly suggest everyone else keeps that same mindset in mind too.

Harold Doyle3 said:What's contradictory here... two different truths?

Truth is really just a massive contradiction in disguise. You can have two different truths that hold up perfectly fine when you look at them as isolated abstractions, but once you zoom out and see the broader context, they clash head-on. It’s like how we can think about being and non-being as separate concepts in a vacuum, yet in any actual reality, they can't truly exist apart from one another; they're always tied together within the framework of existence itself.

I’ve been following the debate regarding mathematics and mathematical truths with interest.
The whole argument over whether math is invented or discovered has been going on forever, and there are plenty of different philosophical takes on what math actually is.
To me, John Polkinghorne’s view makes sense—he suggests that the lived experience of those working within the field carries some unique weight. He also points out how G. H. Hardy spoke for many when he said:

I’ll state my position quite firmly... I believe mathematical reality exists independently of us. Our role is simply to discover or observe it; the theorems we prove and describe so eloquently as our own creations are, essentially, just notes on our observations.

Kurt Gödel demonstrated that any axiomatic system, provided it has enough structural depth, will contain statements that are possible but undecidable—things whose existence can't be formally established. In other words, there are mathematical truths that math itself cannot prove, which means they can't be fully "trapped" within a logical web.
He really shook the mathematical world, though as a committed Platonist, I guess he wasn't surprised himself. He always seemed convinced that everything we see or imagine is just a shadow of some objective ideal existing outside our "real" world, right?

Maybe the key here is looking at experience. There is an experience that holds mathematical truths, but it doesn't necessarily have to be separate from other mental experiences. Those are actually facts, so they're just parts of the very reality or truth we're searching for.

Anyway, that’s more or less how I’m trying to wrap my head around it with you all. 😁

Gödel's work absolutely floored me. I honestly thought I was diving into the most rock-solid, foolproof discipline out there, and then... boom. There's one silver lining, though, at least for my own peace of mind: math can't just be derived from pure logic—even if Amanda Jackson5 would argue otherwise. To me, that actually solidifies math as its own independent field with its own set of axioms and methods.

I’m still stuck wondering if mathematical facts and objects exist in some separate realm outside our minds, or if they're just constructs we've agreed upon. If aliens showed up tomorrow, would they use the same math we do, or something totally different? 😁

Mathematical objects themselves are pretty indifferent when it comes to truth or falsehood; it's only the actual statements within mathematical logic that carry those labels of true or false.

Nicholas Gonzalez87 said:Gödel's work absolutely floored me. I honestly thought I was diving into the most rock-solid, foolproof discipline out there, and then... boom. There's one silver lining, though, at least for my own peace of mind: math can't just be derived from pure logic—even if Amanda Jackson5 would argue otherwise. To me, that actually solidifies math as its own independent field with its own set of axioms and methods.

I’m still stuck wondering if mathematical facts and objects exist in some separate realm outside our minds, or if they're just constructs we've agreed upon. If aliens showed up tomorrow, would they use the same math we do, or something totally different? 😁

Mathematical objects themselves are pretty indifferent when it comes to truth or falsehood; it's only the actual statements within mathematical logic that carry those labels of true or false.

As I’ve mentioned before, mathematics is simply a tool. Mathematicians are constantly refining it so that various professionals in their respective fields can achieve better results, whether those outcomes align with their original goals or not.

Here is my daughter, a mathematician, playing bridge and seeing some great results.
🙂

🙂 🙂 🙂

Amanda Jackson5 said:Truth is really just a massive contradiction in disguise. You can have two different truths that hold up perfectly fine when you look at them as isolated abstractions, but once you zoom out and see the broader context, they clash head-on. It’s like how we can think about being and non-being as separate concepts in a vacuum, yet in any actual reality, they can't truly exist apart from one another; they're always tied together within the framework of existence itself.

That’s exactly my point, which is why I argued that truth can be relative—meaning it's dependent on context—or even conditional, but a fact? A fact is absolute.
For example, the fact is that the Sun moves across the sky, regardless of whether someone believes the truth or falsehood of whether the Sun orbits the Earth or the Earth rotates on its axis.

Nicholas Gonzalez87 said:Gödel's work absolutely floored me. I honestly thought I was diving into the most rock-solid, foolproof discipline out there, and then... boom. There's one silver lining, though, at least for my own peace of mind: math can't just be derived from pure logic—even if Amanda Jackson5 would argue otherwise. To me, that actually solidifies math as its own independent field with its own set of axioms and methods.

I’m still stuck wondering if mathematical facts and objects exist in some separate realm outside our minds, or if they're just constructs we've agreed upon. If aliens showed up tomorrow, would they use the same math we do, or something totally different? 😁

Mathematical objects themselves are pretty indifferent when it comes to truth or falsehood; it's only the actual statements within mathematical logic that carry those labels of true or false.

Honestly, this whole thing feels like nothing more than a recycled version of that ancient scholastic tug-of-war between nominalists and realists—a debate that’s been circling the drain forever under different names, usually led by people who wouldn't know a profound truth if it hit them in the face like a sudden burst of hot water. The reality is much simpler: mathematical facts and objects exist everywhere, period. Their truth isn't found in picking a side, but in the dialectical way they overcome that very opposition. Hegel actually wrapped this up quite elegantly by demonstrating that every single concept is essentially a unity of itself, its "other," and the union of those two parts—essentially acting as the synthesis of the universal, the particular, and the individual as its constituent moments.

Harold Doyle3 said:That’s exactly my point, which is why I argued that truth can be relative—meaning it's dependent on context—or even conditional, but a fact? A fact is absolute.
For example, the fact is that the Sun moves across the sky, regardless of whether someone believes the truth or falsehood of whether the Sun orbits the Earth or the Earth rotates on its axis.

Every truth is relative. Absolute truth is basically just the sum of all those individual relative truths—a concept that reminds me a bit of how Lenin used to frame things.

Nicholas Gonzalez87 said:Gödel's work absolutely floored me. I honestly thought I was diving into the most rock-solid, foolproof discipline out there, and then... boom. There's one silver lining, though, at least for my own peace of mind: math can't just be derived from pure logic—even if Amanda Jackson5 would argue otherwise. To me, that actually solidifies math as its own independent field with its own set of axioms and methods.

I’m still stuck wondering if mathematical facts and objects exist in some separate realm outside our minds, or if they're just constructs we've agreed upon. If aliens showed up tomorrow, would they use the same math we do, or something totally different? 😁

Mathematical objects themselves are pretty indifferent when it comes to truth or falsehood; it's only the actual statements within mathematical logic that carry those labels of true or false.

You aren't alone there; Gödel basically turned the mathematical world upside down.
I think I wrapped my head around Gödel's incompleteness theorems thanks to a simpler argument about a supposedly autonomous truth-telling machine.
Either way, I'd say math isn't quite as reductionist as it seems at first glance.

As for your question, I'll just quote Hardy, who apparently once told Bertrand Russell: "If I could prove by logic that you were going to die in five minutes, I would be sorry you were dying, but my grief would be greatly mitigated by the pleasure of the proof."
What can you say? Mathematicians, I guess. 🤣
Anyway, the debates just keep going. Speaking of which, have you ever heard of Srinivasa Ramanujan? His story really struck a chord with me. They say that without any formal mathematical training, he arrived at incredibly profound results through what seemed to be pure intuition—almost like it was direct.

Amanda Jackson5 said:Honestly, this whole thing feels like nothing more than a recycled version of that ancient scholastic tug-of-war between nominalists and realists—a debate that’s been circling the drain forever under different names, usually led by people who wouldn't know a profound truth if it hit them in the face like a sudden burst of hot water. The reality is much simpler: mathematical facts and objects exist everywhere, period. Their truth isn't found in picking a side, but in the dialectical way they overcome that very opposition. Hegel actually wrapped this up quite elegantly by demonstrating that every single concept is essentially a unity of itself, its "other," and the union of those two parts—essentially acting as the synthesis of the universal, the particular, and the individual as its constituent moments.

Every truth is relative. Absolute truth is basically just the sum of all those individual relative truths—a concept that reminds me a bit of how Lenin used to frame things.

If this old scholastic debate persists under new labels, it implies there is an inherent momentum behind it. It suggests something is driving the discussion forward, fueled by a genuine curiosity to see where these arguments eventually lead.
And then you step in with Hegel and claim it’s all a wash—that we're just spinning our wheels and that it's better to simply walk away from the argument altogether? 🕺
Is Hegel someone who merely places a period at the end of a sentence to close the loop, forcing us to fit everything within his predefined circle? Is that actually his intention?
That is certainly the impression I get from your responses, which seem steeped in defeatism.

Sandra Murphy33 said:If this old scholastic debate persists under new labels, it implies there is an inherent momentum behind it. It suggests something is driving the discussion forward, fueled by a genuine curiosity to see where these arguments eventually lead.
And then you step in with Hegel and claim it’s all a wash—that we're just spinning our wheels and that it's better to simply walk away from the argument altogether? 🕺
Is Hegel someone who merely places a period at the end of a sentence to close the loop, forcing us to fit everything within his predefined circle? Is that actually his intention?
That is certainly the impression I get from your responses, which seem steeped in defeatism.

It’s not about it being futile; it’s more that the answer lies in finally reconciling those opposing sides.

Thomas Thomas63 said:You aren't alone there; Gödel basically turned the mathematical world upside down.
I think I wrapped my head around Gödel's incompleteness theorems thanks to a simpler argument about a supposedly autonomous truth-telling machine.
Either way, I'd say math isn't quite as reductionist as it seems at first glance.

As for your question, I'll just quote Hardy, who apparently once told Bertrand Russell: "If I could prove by logic that you were going to die in five minutes, I would be sorry you were dying, but my grief would be greatly mitigated by the pleasure of the proof."
What can you say? Mathematicians, I guess. 🤣
Anyway, the debates just keep going. Speaking of which, have you ever heard of Srinivasa Ramanujan? His story really struck a chord with me. They say that without any formal mathematical training, he arrived at incredibly profound results through what seemed to be pure intuition—almost like it was direct.

History is full of stuff like this. You ever heard of the Russellian paradox? It actually freaked mathematicians out so much they stopped using the term "set" for sets of sets, opting for "class" instead. I’ve actually got some books sitting on my shelf at home where you can see the whole mess laid out.

Thomas Thomas63 said:You aren't alone there; Gödel basically turned the mathematical world upside down.
I think I wrapped my head around Gödel's incompleteness theorems thanks to a simpler argument about a supposedly autonomous truth-telling machine.
Either way, I'd say math isn't quite as reductionist as it seems at first glance.

As for your question, I'll just quote Hardy, who apparently once told Bertrand Russell: "If I could prove by logic that you were going to die in five minutes, I would be sorry you were dying, but my grief would be greatly mitigated by the pleasure of the proof."
What can you say? Mathematicians, I guess. 🤣
Anyway, the debates just keep going. Speaking of which, have you ever heard of Srinivasa Ramanujan? His story really struck a chord with me. They say that without any formal mathematical training, he arrived at incredibly profound results through what seemed to be pure intuition—almost like it was direct.

I tried tackling the original paper once. All I really got out of it was that Gödel managed to encode statements of mathematical logic into arithmetic; everything else just felt like total esoterica that flew way over my head.

Thomas Thomas63 said:You aren't alone there; Gödel basically turned the mathematical world upside down.
I think I wrapped my head around Gödel's incompleteness theorems thanks to a simpler argument about a supposedly autonomous truth-telling machine.
Either way, I'd say math isn't quite as reductionist as it seems at first glance.

As for your question, I'll just quote Hardy, who apparently once told Bertrand Russell: "If I could prove by logic that you were going to die in five minutes, I would be sorry you were dying, but my grief would be greatly mitigated by the pleasure of the proof."
What can you say? Mathematicians, I guess. 🤣
Anyway, the debates just keep going. Speaking of which, have you ever heard of Srinivasa Ramanujan? His story really struck a chord with me. They say that without any formal mathematical training, he arrived at incredibly profound results through what seemed to be pure intuition—almost like it was direct.

And it isn't. I read somewhere that you can only really call yourself a professional mathematician if you're a Platonist.

Thomas Thomas63 said:You aren't alone there; Gödel basically turned the mathematical world upside down.
I think I wrapped my head around Gödel's incompleteness theorems thanks to a simpler argument about a supposedly autonomous truth-telling machine.
Either way, I'd say math isn't quite as reductionist as it seems at first glance.

As for your question, I'll just quote Hardy, who apparently once told Bertrand Russell: "If I could prove by logic that you were going to die in five minutes, I would be sorry you were dying, but my grief would be greatly mitigated by the pleasure of the proof."
What can you say? Mathematicians, I guess. 🤣
Anyway, the debates just keep going. Speaking of which, have you ever heard of Srinivasa Ramanujan? His story really struck a chord with me. They say that without any formal mathematical training, he arrived at incredibly profound results through what seemed to be pure intuition—almost like it was direct.

Yeah, sure. Some theories are beautiful, some proofs are elegant, some claims are trivial, and some structures are just incredibly rich. 😁

Thomas Thomas63 said:You aren't alone there; Gödel basically turned the mathematical world upside down.
I think I wrapped my head around Gödel's incompleteness theorems thanks to a simpler argument about a supposedly autonomous truth-telling machine.
Either way, I'd say math isn't quite as reductionist as it seems at first glance.

As for your question, I'll just quote Hardy, who apparently once told Bertrand Russell: "If I could prove by logic that you were going to die in five minutes, I would be sorry you were dying, but my grief would be greatly mitigated by the pleasure of the proof."
What can you say? Mathematicians, I guess. 🤣
Anyway, the debates just keep going. Speaking of which, have you ever heard of Srinivasa Ramanujan? His story really struck a chord with me. They say that without any formal mathematical training, he arrived at incredibly profound results through what seemed to be pure intuition—almost like it was direct.

Yeah, pure natural talent. I’ve got basically zero talent myself; I have to grind way too hard just to wrap my head around anything. 🙂