Some animals will try to bury food scraps even when there isn't a lick of dirt in sight, but eventually, that instinct just starts to fade. I don't think it's a flaw or anything—it’s just the history of adaptation playing out.
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.
That actually makes sense. Maybe we can pull those facts out of the world of ideas, since they’re already implicitly tucked away inside our minds.
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. 🙂
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.
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.
Sam Martinez9 said:The merging of two clouds is an incredibly straightforward physical process. Its simplicity becomes obvious when you compare it to the sheer complexity of the physicochemical and biochemical processes occurring within a single cell of even a very rudimentary organism—take a common earthworm, for instance. There simply isn't a mathematical tool in existence capable of fully describing the functional mechanics of a cell in a worm.
Claiming that 1+1=1 is a distortion is only true if you view mathematics in total isolation from the rest of the world. I have nothing against that approach; one can certainly study mathematics as a self-contained discipline of the human mind.
However, once we start using mathematics as a tool to describe the physical world, we have to acknowledge that it only provides a partial map. It can never capture the entirety of our reality.
Of course, 1+1=2 and 2+2=4 remains perfectly accurate and precise when dealing strictly with numbers and pure math.
But when living organisms are involved, those rules only hold true in a very limited number of instances and over a restricted window of time.
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.
Sam Martinez9 said:Mathematics is essentially a description of nature. I've already mentioned how 1+1 can equal 1—take clouds, for instance.
In a biological sense, 2+2 could certainly result in 5 if one of those members is a pregnant woman.
Sure, you can claim 1+1=1 if you want to play pretend, but that’s just distorting mathematical facts to suit your own little worldview. Like I said in that other thread, if you're actually trying to describe two clouds merging, you'd use a complex mathematical model, not some basic addition with natural numbers.
I don't know what to tell you. Just some random noise. Nothing worth my time. kaže: You probably noticed that smiley at the end. The author didn't even bother to mention his base, so now we're just stuck in this state of uncertainty. What does 7 + 7 even equal in his math? Maybe he's working in hex or something. 🤷
Look, I don't get it. In the decimal system, you just write the numbers—you don't feel the need to state the base every single time. It’s the universal standard for communication. We aren't computers trying to chat in binary, and this isn't some programming seminar where we need to drop everything in hex just to share results.
Terry Martinez10 said:Now, if you decided to ask an economist instead, they might actually tell you it's true.
His take on mathematical truths? Irrelevant. Total waste of breath.
Terry Martinez10 said:Whether 2+2=5 is considered a truth or a lie really just depends on which angle you're approaching it from, or more importantly, who exactly you decide to ask.
Ask a mathematician and they’ll tell you straight up: 2+2=5 is just wrong. Math doesn't care about your "perspective." Numbers and addition don't change based on how you view the world. You look at one object, you abstract the number 1. Period. It stays the same regardless of your reality.
Jonathan Kelly8 said:It’s already there. Similar. The topic is already established—no need to keep repeating things we've already covered here.
This isn't working—if you actually want to get your hands on the truth or a verifiable fact, you really need to use... Constructive logic—if you can even call it that—is a bit of a headache. It’s all about proving things actually exist rather than just showing that their absence is impossible. I guess some people find that rigor refreshing, but to me, it feels like an endless loop of unnecessary hurdles. Maybe it’s just my cynicism talking, but it seems like a lot of extra work just to reach a conclusion that was probably obvious from the start. 🙂
That simply isn't true. 1 + 1 = 10In binary, I suppose. 🙂
We base our "facts" on uncertain observations—and I suppose we build our "truth" on nothing more than assumptions.
I don't know if that was your point, but 1+1=2 is true regardless of the system or the base you're using. You can't confuse the actual number with how you choose to write it down.
Mark Torres14 said:I disagree. Every math expression relies on facts. It can't just exist in a vacuum. Like, what's 2 of nothing plus 2 of nothing? It equals 4 of nothing. Mathematically sound, but totally pointless. 🙂
Look, I see things differently. Math is purely abstract until you actually apply it to something. You could call 2+2=4 an abstract fact, but something like "x+y=y+x"? That isn't even a fact—it's just what happens when you pick specific numbers for x and y.
Mark Torres14 said:If they intersected, they wouldn't be "parallel." Point blank. Stating that two parallel lines exist is both a truth and a fact at the same time.
Yeah, you got me there. Maybe a better example: 2+2=4 doesn't consist of "facts," even though that truth was definitely reached by observing facts. Or just "x+y=y+x".
Mark Torres14 said:If there’s actually a gap between truth and fact, does that mean you can have a truth that lacks facts? Or even worse, facts that aren't actually true?🤔
I'm thinking about axioms and theorems here. 🤔
"Parallel lines never intersect." That doesn't contain any "facts."
Amanda Jackson5 said:So, what you're getting at is that truth is basically just the end product of interpreting raw facts?
No. It’s about correct interpretation. Like in math—you follow strict deduction from axioms. It has to be formally structured, following actual rules of logic.
Amanda Jackson5 said:So, what you're getting at is that facts are specific instances while truths are universal? That would be a pretty clean distinction, except for the fact that there’s such a thing as universal facts and specific truths.
Look, just because a truth is general doesn't mean it applies to everything. Take complex numbers—they don't have prime factorizations. My point is simply that facts are more basic than truths. You can't have one without the interpretation process.
Amanda Jackson5 said:A logical judgment can be true or false, but that fact alone doesn't mean you can just equate a logical judgment with the concept of truth itself.
It’s necessarily true if it's formally sound and built on a correct interpretation of the facts. Facts themselves are true, just more basic. Like, take the statements "the road is wet" and "it's raining"—if those are the facts and you link them correctly, then the general truth becomes "If it rains, the road gets wet." Or look at math: you notice some numbers have prime factorizations, so if you use correct deduction from the axioms of natural numbers to prove it applies to every number, then you've got a universal truth.
Yeah, look, truth is just a broad logical conclusion you pull from a bunch of relevant facts. It's like saying it's a fact that every natural number can be broken down into prime factors, whereas the actual prime factorization of a specific number? That's just a single fact.
Those of us born with actual talent owe it to the community to step up. We live our lives surrounded by essentials that exist only because countless people put in the work, so we’ve got to pay it back—whether that’s through creating something new or just doing whatever else we’re good at.
It’s an exploration of how religious elements bleed into politics, culture, and aesthetics, tracing their evolution from the Enlightenment all the way through to postmodernism. One point that really stuck with me is his argument that religion ought to serve as a tool for criticizing politics. From what I gathered, Eagleton also takes aim at the postmodern tendency to treat belief merely as a tool—a mindset that basically creates a marketplace full of "instant" religions and "instant" philosophies. He spots religious undertones in both Karl Marx and Friedrich Nietzsche, arguing that postmodernism is essentially just a postscript to Nietzsche, once he stripped away metaphysical concepts like the Übermensch. He peppers the text with short quotes from various authors; you quickly see his view that postmodernism is basically “subjectivism without a subject,” obsessed with marginal phenomena and successful at merging art with commerce. He also tackles fundamentalism in the context of recent events and the war on terror, plus touches on nationalism and its striking resemblance to religion.
Peter F. Strawson, analysis and metaphysics although a book
Even though the subtitle claims it's an introduction to philosophy, this thing is pretty heavy. Strawson explains everything so thoroughly that the logic gets dense and demanding at times. His core argument is that by analyzing everyday language usage and conceptual structures, we can uncover underlying assumptions in logic, epistemology, and ontology. On the bright side, the goal of this program is to build a theory that acts as a sort of grammar for concepts. On the downside, there's a certain therapeutic effect when this kind of analysis forces concepts to align with the external world. The book moves through examples like freedom vs. necessity, causation and explanation, and the individual versus society. As the introduction notes, Strawson is best known for his contributions to the philosophy of language. He doesn't believe formal logic can fully capture everyday speech; rather, he argues that insights into formal logic should be sought within everyday language use, though he does show how certain sentences can be framed within formal logic. He identifies certain philosophical trends he calls internalism and externalism (even if those terms are used differently elsewhere); internalism deals with the elusiveness and indeterminacy of the external world, while externalism focuses on the elusiveness and indeterminacy of the subject.