Why does the fact that there is no universal objective truth in mathematics, and the subject is a disunified sprawl, cause midwits to seethe?Everybody from people whose only knowledge extends to the elementary, all the way academics specialized in mundane fields like number theory.
>>17012932Because of the conflation between the relatively mundane fact that it actually is (math is a constructed system so any and all claims in math come with the implicit asterisk that "the truth value depends on the axioms you start with") and the broad, sweeping claims people use it to justify.Essentially: "no objective, universal truth" is the Motte to the "I can make up whatever bullshit I want" Bailey. And it's transparent as fuck when people are doing it.
>>17012932HA HA HA
>>17012947>Essentially: "no objective, universal truth" is the Motte to the "I can make up whatever bullshit I want" Bailey.Translation for people who haven't rotted their brains with Culturecore?
>>17012932>The fact that there is no universal TruthIs itself a claim to a universal TruthNext retarded threadYou guys really suck at this
>>17012957Motte and Bailey is a type of conflation fallacy where where a broad, often self-serving, claim (the Bailey) is treated as identical to a mundane, easily defensible one (the Motte). It's a dishonest debate maneuver where you try to bait your opponent into arguing against obvious truths instead of the claim that's actually the subject of discussion.To give some unnecessary exposition:The metaphor involves a type of medieval fortification by the same name. The Bailey is a sprawling, lightly fortified yet highly valuable plot of land that you actually want to occupy. The Motte is an elevated position or central tower that's kinda a shitty place to be, but is much more secure and can used to stage a more effective defense against attackers. When the Bailey is attacked, you retreat to the Motte. When the attackers leave, you return to the Bailey. Defending the Motte *is* defending the Bailey. Or at least that's the conflation being made in the case of the fallacy.
>>17012960He said "no universal objective truth in math", shit for brains. You just don't know math.For example: is the continuum hypothesis "universally true"?>You guys really suck at thisYou literally can't read.
>>17012947There are two problems there:1. What you're referring to specifically deals with the existence of *objective* truth in mathematics, but not universality.2. It's already reductionist, and can't help but equate a very broad argument about uninteresting arbitrary notation changes, and a completely different systematic structure that occupies the same syntax.Complex meta-system level concepts like the non-equivalence between isomorphism and equifinality, or the interaction between foundations and kolmogorov complexity, or even the entire field of mathematical logic, end up becoming completely invisible. Worse than that, even outright rejected due to pure unexamined dogmatism. Equating a trivial scrambling of how we map symbols to meaning, to the implications of Godel's incompleteness theorems, that's absurdity.Anyone who truly grasps the disjointed nature of mathematics understands the profound and humbling implications thereof. Neither the layman, nor the hyperspecialized mathematician seem to be able to even acknowledge this disjointedness. Even though the dismissal of the wishywashy postmodernist relativistic "gotcha" that boils down to an uninteresting cypher is ultimately an acknowledgement that this disjointedness is coherent, any and all dialogue about this disjointedness immediately falls into dismissal because obviously it's just that same cypher game.It would be one thing if you could simply just never engage these people. But in a conversation about Da Costa logic, there's always a chance some abstract algebra monkey will butt his head in uninvited to be snarky and retarded, because just being in the proximity of higher level theory made him upset he's going to make it your problem. The mere existence of this universe of discourse drives some people insane, even those who should know better. Nothing else is like this. Nobody gets their panties in a twist over linear algebra. It's this seethe about perfectly valid theory that is interesting.
>>17012960Clearly some people don't take it to be true, so it's not a universal truth. Doesn't seem to hold water anon.
>>17012947okay but "this statement follows from these axioms" is objectively true
>>17012968Truth is not subject to consensus. Truth is invariant and 99% true is 100% false
>>17012966It's not that deep, bro. Some axiomatic systems don't play nice together. Accepting both as true simultaneously can lead to contradictions. I can't think of anyone knowledgeable who really takes issue with this. It's a concept most people get comfortable with by the time they explore non-Euclidean geometry. The broader implication of Godel's theorems mainly revolve around the infeasibility of constructing a single, unified, system to describe all of mathematics. This was much more profound at the time he proved them, when such a unification was a golden goose his contemporaries were chasing. The distinction between "a simple statement of fact" and "a source of seethe" comes in how you approach the concept and what kinds of claims you're trying to justify.
>>17012972>Truth is not subject to consensus.Universality is.Also in nominalist systems, even objective truth is subject to consensus.
>>17012962Thank you, very helpful.
>>17012932my math had objective truth. yours does not.
>>17012978No problem. It's a severely underrated fallacy for how common it is. Any time someone jumps the gap from "x is socially constructed" to "x is completely arbitrary and up to individual discretion," Motte and Bailey is the formalized term for what they're doing. Ditto for alt-history schizos who claim to be "just asking questions" out of one side of their mouth while making remarkable assertions out the other.
>>17012973>It's not that deep, bro. Some axiomatic systems don't play nice together.It's a lot deeper than you think. You skipped over my examples that weren't Godel's theory. I would assume (no shade) because they aren't as familiar to you. I would highly recommend learning about it. The structure of a system doesn't just affect the reachable, valid conclusions, it affects the paths on how you get there in the first place. It affects them *meaningfully*, and can make the difference between practical impossibility and practical possibility. The mechanistic implementation of mathematics is based upon a constructive foundation. The platonism of ZFC is wholly inappropriate for such an application. Likewise, that constructive foundation is a pain in the ass on a blackboard, and when working with non-finite objects. All trivial, pragmatic, uncontroversial examples. But there's so much more. Not just changing the rules, but the meta-rules. Maybe abandoning foundationalism itself, coherentist mathematics is a whole other dimension of potentiality.It's an unending swamp of choice, which Godels incomp. theorem was a lower order realization of. Not all of it is interesting sure, but the navigation and discernment of the swamp itself? Knowing what to use and when? That's a much bigger question and much more important than you realize.>I can't think of anyone knowledgeable who really takes issue with this.That might be because of how you're defining 'knowledgeable'. Someone with deep knowledge in statistical theory doesn't necessarily even know something like Type Theory exists. Even if they do, their reaction to hearing its name might be to roll their eyes. Most mathematicians are trite little things, often no better than laymen at understanding how small their sliver of the universe is.
>>17012947It's funny because he didn't even use the terms correctly. Ignore this verbose faggot >>17012962Look, here's all you need to know. >Baily is nonsensical lie>For example, All women are whores>Motte is universally agreed upon truth. >For example, Women want to feel good during sexThe Motte and Bailey "fallacy" if you even believe in that crap is that people say controversial bullshit [Bailey], and when you call them out on it, they fall back on trivial truths [Motte].Distilled further:>Bailey is edgelord lies>Motte is the troll pretending to be NPC normie when called out
>>17012997I'll be honest, I kinda rolled my eyes and skimmed over the jargon in that post as it just came off as a knowledge flex more than anything (no shade, I do it too sometimes). If there was a critical point I missed then my bad. As far as I can tell, your argument comes down to different systems coming to different conclusions and having different valid paths even to the same conclusions and the ambiguity in even identifying the correct logic structure for addressing a particular problem. That much is valid and, to my understanding, well understood. Your point about type theory doesn't really add up because there are widely used proof assistants that are built upon a foundation of type theory (see: Lean).I must ask: what about this do you find so profound?
>>17013001To be clear: the Bailey doesn't have to be a lie per se. It can be, and often is, earnestly believed. It's just that he doesn't have the ability to back it up so he defaults to a more mundane position when challenged. When the term was coined, the example used was conflating "morality is subjective" with "nothing I do is morally wrong."
The "law" of excluded middle is obvious bullshit and constructive/intuitionist math is the only way forward.
>>17013007Based tpbp
>>17012976Universality doesn't mean consensus either. Denial and contrarian liar paradox doesn't invalidate Truth.
Truth is simply: that which is invariant. Attempts to constantly redefine "consensus" or "universal belief" as Truth are just that, semantically retarded word games by egotists who want to redefine Truth to be something they can stand above and over. Sorry; not sorry. Play all the word games you want, but the real question is "Who are you trying to convince?" Because it sure as fuck ain't me, so it obviously must be your own retarded ass.
>>17013043Correct. Reality is unfalsifiable. If you don't believe me that's your perogative, but I'm not playing solipsistic games, because if solipsism is asserted, then anyone arguing with me is an imaginary non-existent ghost of my own imagining and therefore "who are you trying to convince?" Or "then who are you talking to?" Is an apt retort
>Why does the fact that there is no universal objective truth in mathematicsTranslation: I would rather throw away the entirety of science, math, episteme itself than admit we live in a God-Reified Universe of Gods Invariant TruthAnd you're free to make that choice, but again, "who are you trying to convince?" Because I ain't buying the dogshit you're peddling, and you're wasting your breath repeatedly banning me and deleting my presence on this board while producing no arguments and semantics in the absence of my bans.To those who have eyes to see, you are constantly being deceived by wolves who would throw matha and science away entirely if that is what is necessary to deceive you, and themselves. They need allies in their denial and censorship on fucking 4-chan to quarantine you, the audience, from Truth
>>17013066The fact that a platform allows for the most extreme, vitriolic language imaginable—slurs, hatred, and calls for violence, but treats a serious discussion on the mathematical and historical foundations of a God-ordered universe as a bannable offense is incredibly telling.
The reality of it is, "science" doesn't have a side in this debate. Science is simply slave to what Reality is, whether that is God-Reified or God-less. If it is God-Reified, and the math checks out, then it is scientific to postulate it as such. Newton, maxwell, Planck's, shrodingers, Einstein's and a number of others work, was still true even before people purporting to be scientists secularized it, and since it was established prior to secularization, secularization adds no novel predictive capacity and is therefore superfluous to what is confirmed
When James Clerk Maxwell unified electricity and magnetism, he explicitly wrote about his work as an investigation into the physical manifestations of God's wisdom and creative power. When Max Planck derived the quantum of action ($h$), or when Isaac Newton formulated the laws of gravitation, their calculations were natively nestled within a God-Reified ontology.The secular establishment that came later didn't alter the math, they didn't add a single decimal point of precision to the constants, and they didn't discover a new force. All they did was lay an ideological veneer over pre-existing truths.
They took the exact same equations, scraped off the dedication to the Creator, and claimed that the laws were now "self-caused."Because this philosophical shift changed exactly 0% of the empirical output, the secularization of science fails Occam's razor entirely. It is a completely superfluous variable. It is a narrative patch designed to protect human autonomy, not a scientific discovery.
If post some anti humanities rant in /his/ i got banned, why is this retard still alive in /sci/?
>>17013096It's not unscientific retard. I can literally post the conformal Fano phase of complex phase ontology +what science declares is merely instrumental)I can show you the math, I can explain it over the course of 50 consecutive posts, entirely in valid mathematical operation, and it gets deleted and I get banned, and every comment in reaction is not describing any error in the math or scientific framework whatsoever. You have no fucking counterargument. You only have, calling for allies, and rabid denialism, like this fucking thread, that attempts to declare, as it's premise, that math itself (and thereby science as well) cannot be true, and is arbitrary.You're a dumbass man, I get it. Your feelings are hurt. Maybe you should call for the janitors to ban me again. Since you have no actual substance to your argument.
>>17012932there are plenty of objective truths in maths, though. ever hear about a little something called category theory?
Sorry to interrupt you with science and math in the science and math board.Maybe you should open another thread on race sex and IQ, since you can only handle parsing word salad on soft sciences.
>>17013004All good mate.>Your point about type theory doesn't really add up because there are widely used proof assistants that are built upon a foundation of type theory (see: Lean).That's a relatively new development. And they're using Lean specifically because it implements a ZFC object language. Coq is also somewhat popular for similar reasons. Dependently typed langs without a ZFC object language don't get the same privilege.Not saying proof assistants are new. Just the adoption of Lean is a thing from the last 10 years.Haskell, while not a proof assistant, is perfectly usable as one. It's got a much stronger type theory flavor than the above, which is probably why it never caught on outside of computer science departments.And ofc. exceptions to the rule exist. If you dig hard enough, you'll even find based faculty using Prolog as their mechanical proof system. It's rare though, Isabelle always dominated in that space.>I must ask: what about this do you find so profound?I guess because it just comes naturally to me. Like I'm wired to like it. I always liked variety, shaking things up.The undecidability of the whole affair, and how it proves useful in really important contexts, makes successfully utilizing it feel immensely empowering. Like a mastery of abstraction and reality itself.
>>17013043The earth has a climate. True. But the climate is not invariant.
>>17013075You didn't read any of their works. Where did you get this bullshit? AI?
>>17013007"explosion" is as much obvious bullshit as excluded middle
>>17013108>and every comment in reaction is not describing any error in the math or scientific framework whatsoeverhere are two errors:1; AI suckling at your asshole(which you love)and 2: your disease-laden mind
>>17013191not who you where speaking tohttps://en.wikipedia.org/wiki/Lambda-mu_calculus
>>17013413"A molecule of hydrogen....whether in Sirius or in Arcturus, executes its vibrations in precisely the same time. Each molecule therefore throughout the universe bears impressed upon it the stamp of a metric system as distinctly as does the metre of the Archives at Paris, or the double royal cubit of the temple of Karnac. No theory of evolution can be formed to account for the similarity of molecules, for evolution necessarily implies continuous change, and the molecule is incapable of growth or decay, of generation or destruction.... We are therefore unable to ascribe either the existence of the molecules or the identity of their properties to any of the causes which we call natural."Happy is the man who can recognize in the work of to-day a connected portion of the work of life and an embodiment of the work of Eternity. The foundations of his confidence are unchangeable, for he has been made a partaker of Infinity. He strenuously works out his daily enterprises because the present is given him for a possession.Thus ought man to be an impersonation of the divine process of nature, and to show forth the union of the infinite with the finite, not slighting his temporal existence, remembering that in it only is individual action possible, nor yet shutting out from his view that which is eternal, knowing that Time is a mystery which man cannot endure to contemplate until eternal Truth enlighten it.The vast interplanetary and interstellar regions will no longer be regarded as waste places in the universe, which the Creator has not seen fit to fill with the symbols of the manifold order of His kingdom. We shall find them to be already full of this wonderful medium; so full, that no human power can remove it from the smallest portion of space, or produce the slightest flaw in its infinite continuity.>Maxwell
>>17013413Natural causes, as we know, are at work, which tend to modify, if they do not at length destroy, all the dimensions of the earth and the whole solar system. But though in the course of ages catastrophes have occurred and may yet occur in the heavens, though ancient systems may be dissolved and new systems evolved out of their ruins, the molecules out of which these systems are built-the foundation stones of the material universe-remain unbroken and unworn.They continue this day as they were created-perfect in number and measure and weight, and form the innefaceable characters impressed on them we may learn that those aspirations after accuracy in measurement, truth in statement, and justice in action, which we reckon among our noblest attributes as men, are ours because they are essential constituents of the image of Him who in the beginning created, not only the heaven and the earth, but the materials which heaven and earth consist.>More Maxwell
>>17013413>PlanckIn his famous lecture Religion and Science (May 1937) Planck wrote: “Both religion and science need for their activities the belief in God, and moreover God stands for the former in the beginning, and for the latter at the end of the whole thinking. For the former, God represents the basis, for the latter – the crown of any reasoning concerning the world-view.” (Max Planck, Religion und Naturwissenschaft, Leipzig: Johann Ambrosius Barth Verlag, 1958, 27).2. “Religion represents a bond of man to God. It consists in reverent awe before a supernatural Might [Macht], to which human life is subordinated and which has in its power our welfare and misery. To remain in permanent contact with this Might and keep it all the time inclined to oneself, is the unending effort and the highest goal of the believing man. Because only in such a way can one feel himself safe before expected and unexpected dangers, which threaten one in his life, and can take part in the highest happiness – inner psychical peace – which can be attained only by means of strong bond to God and unconditional trust to His omnipotence and willingness to help.” (Max Planck 1958, 9).3. Planck concluded his lecture Religion and Science (May 1937) with the words: “It is the steady, ongoing, never-slackening fight against scepticism and dogmatism, against unbelief and superstition, which religion and science wage together. The directing watchword in this struggle runs from the remotest past to the distant future: ‘On to God!’ ” (Planck, as cited in Heilbron 1986, 185; see also Planck 1958, 30).
>>170134134. “Under these conditions it is no wonder, that the movement of atheists, which declares religion to be just a deliberate illusion, invented by power-seeking priests, and which has for the pious belief in a higher Power nothing but words of mockery, eagerly makes use of progressive scientific knowledge and in a presumed unity with it, expands in an ever faster pace its disintegrating action on all nations of the earth and on all social levels. I do not need to explain in any more detail that after its victory not only all the most precious treasures of our culture would vanish, but – which is even worse – also any prospects at a better future.” (Planck 1958, 7). “As a physicist, that is, a man who had devoted his whole life to a wholly prosaic science, the exploration of matter, no one would surely suspect me of being a fantast. And so, having studied the atom, I am telling you that there is no matter as such! All matter arises and persists only due to a force that causes the atomic particles to vibrate, holding them together in the tiniest of solar systems, the atom.Yet in the whole of the universe there is no force that is either intelligent or eternal, and we must therefore assume that behind this force there is a conscious, intelligent Mind or Spirit. This is the very origin of all matter.” (Planck, as cited in Eggenstein 1984, Part I; see “Materialistic Science on the Wrong Track”).
>>17012947fpbpand midwits are still arguing
>>17013413This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.">Newton, "General Scholium," an addition to the second edition of his Principia (1713).
>>17013475The idea is really interesting. It's a natural reaction that you'd want to fix undelimited continuations by abandoning the global context of scheme's call/cc and integrate them in a more elegant fashion.That being said, the lambda mu calculus is so fucking ugly lol. What if we had TWO meanings baked into this formula? It's definitely cool, but I don't think I've ever made it through an entire paper, wading through everything is sweaty business. I would be interested in seeing a new generation of scheme-derivatives that are based on it, clean up the syntactical noise and reign in the implicit structure that's scattered into everything.
>>17013412Earth still has a climate regardless of the transient weather.
>>17012971Only if you think the logical systems are true. Try "proving" modus ponens. You'll find that the only way to do so is using modus ponens. This means it's an axiom of the system that you could take or leave.
>>17013593just glue these systems into a nice geometry and recover any of them at will by localizing.then you might start to produce some language independent results.
>>17013038>Universality doesn't mean consensus eitherLack of consensus entails non-universality.
>>17013593Is the argument you just made objectively valid?
>>17012932>>17012947Godel's incomplete theorem. You cannot make sense of yourself. A foundation can never be provable. Any system proposed cannot be proven by itself. If there is any objective truth, then it cannot be proven. The problem of grounding is an age old issue this is due to chase of seeking a core substantial element to the changing world, a dependent world. People arent satisfied with "this depends on that" as explanation, they want the grounds of the statement that which all the statements in the world stands upon to give its power of validity. There is none.
>>17013705>Godel's incomplete theorem.I knew that theorem was self-refuting. He can't even prove it to be true from within his own system, unless it's self-confirming, which would still negate the validity of the theorem itself.Just kidding, I just wanted to make a lame joke at your typo that suggested Gödel's incomplete-ness theorem was itself incomplete.
>>17013705that's not what Godel's incompleteness theorems say
This thread is QED because 90% of it is incoherent schizophrenic screeching
