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Thread: Our Dark Age of Ignorance - and the Way Out

  1. #1

    Our Dark Age of Ignorance - and the Way Out

    RELATED: Study reveals scale of ‘science scam’ in academic publishing

    https://twitter.com/ThomasEWoods/sta...39442489954608


    Our Dark Age of Ignorance -- and the Way Out [The Tom Woods Show: Episode 2445]
    https://odysee.com/@TomWoodsTV:e/our...-and-the-way:f
    {TomWoodsTV | 01 February 2024}

    It's not just this field or that field: there is a systematic sickness in academic and in intellectual life in general, in which preposterously false things are believed, and based on foundations that are never examined. This is one of my favorite episodes ever, and my thanks to Steve Patterson for this excellent conversation.

    Related Article: https://steve-patterson.com/our-present-dark-age-part-1 [see this post below - OB]

    Guest's Website:
    - Natural Philosophy Institute: https://natphi.org
    - Steve Patterson | in pursuit of truth (blog) : https://steve-patterson.com/

    Last edited by Occam's Banana; 02-02-2024 at 03:18 PM.
    The Bastiat Collection · FREE PDF · FREE EPUB · PAPER
    Frédéric Bastiat (1801-1850)

    • "When law and morality are in contradiction to each other, the citizen finds himself in the cruel alternative of either losing his moral sense, or of losing his respect for the law."
      -- The Law (p. 54)
    • "Government is that great fiction, through which everybody endeavors to live at the expense of everybody else."
      -- Government (p. 99)
    • "[W]ar is always begun in the interest of the few, and at the expense of the many."
      -- Economic Sophisms - Second Series (p. 312)
    • "There are two principles that can never be reconciled - Liberty and Constraint."
      -- Harmonies of Political Economy - Book One (p. 447)

    · tu ne cede malis sed contra audentior ito ·



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  3. #2
    Our Present Dark Age, Part 1
    https://steve-patterson.com/our-pres...rk-age-part-1/
    {Steve Patterson | 25 June 2021}

    [some matter hidden to save space]

    For the last fifteen years, I’ve been researching a wide range of subjects. Full-time for the last seven years. I’ve traveled the world to interview intellectuals for my podcast, but most of my research has been in private. After careful examination, I have come to the conclusion that we’ve been living in a dark age since at least the early 20th century.

    Our present dark age encompasses all domains, from philosophy to political theory, to biology, statistics, psychology, medicine, physics, and even the sacred domain of mathematics. Low-quality ideas have become common knowledge, situated within fuzzy paradigms. Innumerable ideas which are assumed to be rigorous are often embarrassingly wrong and utilize concepts that an intelligent teenager could recognize as dubious. For example, the Copenhagen interpretation in physics is not only wrong, it’s aggressively irrational—enough to damn its supporters throughout the 20th century.

    Whether it’s the Copenhagen interpretation, Cantor’s diagonal argument, or modern medical practices, the story looks the same: shockingly bad ideas become orthodoxy, and once established, the social and psychological costs of questioning the orthodoxy are sufficiently high to dissuade most people from re-examination.

    This article is the first of an indefinite series that will examine the breadth and depth of our present dark age. For years, I have been planning on writing a book on this topic, but the more I study, the more examples I find. The scandals have become a never-ending list. So, rather than indefinitely accumulate more information, I’ve decided to start writing now.

    Darkness Everywhere
     
    By a “dark age”, I do not mean that all modern beliefs are false. The earth is indeed round. Instead, I mean that all of our structures of knowledge are plagued by errors, at all levels, from the trivial to the profound, periphery to the fundamental. Nothing that you’ve been taught can be believed because you were taught it. Nothing can be believed because others believe it. No idea is trustworthy because it’s written in a textbook.

    The process that results in the production of knowledge in textbooks is flawed, because the methodology employed by intellectuals is not sufficiently rigorous to generate high-quality ideas. The epistemic standards of the 20th century were not high enough to overcome social, psychological, and political entropy. Our academy has failed.

    At present, I have more than sixty-five specific examples that vary in complexity. Some ideas, like the Copenhagen interpretation, have entire books written about them, and researchers could spend decades understanding their full history and significance. The global reaction to COVID-19 is another example that will be written about for centuries. Other ideas, like specific medical practices, are less complex, though the level of error still suggests a dark age.

    Of course, I cannot claim this is true in literally every domain, since I have not researched every domain. However, my studies have been quite broad, and the patterns are undeniable. Now when I research a new field, I am able to accurately predict where the scandalous assumptions lie within a short period of time, due to recognizable patterns of argument and predictable social dynamics.

    Occasionally, I will find a scholar that has done enough critical thinking and historical research to discover that the ideas he was taught in school are wrong. Usually, these people end up thinking they have discovered uniquely scandalous errors in the history of science. The rogue medical researcher that examines the origins of the lipid hypothesis, or the mathematician that wonders about set theory, or the biologist that investigates fundamental problems with lab rats—they’ll discover critical errors in their discipline but think they are isolated events. I’m sorry to say, they are not isolated events. They are the norm, no matter how basic the conceptual error.

    Despite the ubiquity of our dark age, there have been bright spots. The progress of engineers cannot be denied, though it’s a mistake to conflate the progress of scientists with the progress of engineers. There have been high-quality dissenters. Despite being dismissed as crackpots and crazies by their contemporaries, their arguments are often superior to the orthodoxies they criticize, and I suspect history will be kind to these skeptics.

    Due to recent events and the proliferation of alternative information channels, I believe we are exiting the dark age into a new Renaissance. Eventually, enough individuals will realize the severity of the problems with existing orthodoxies and the systemic problems with the academy, and they will embark on their own intellectual adventures. The internet has made possible a new life of the mind, and it’s unleashing pent-up intellectual energies around the world that will bring illumination to our present situation, in addition to creating the new paradigms that we desperately need.
    Why Did This Happen?
     
    It will take years to go through all of the examples, but before examining the specifics, it’s helpful to see the big picture. Here’s my best explanation for why we ended up in a dark age, summarized into six points:

    1. Intellectuals have greatly underestimated the complexity of the world.

    The success of early science gave us false hope that the world is simple. Laboratory experiments are great for identifying simple structures and relationships, but they aren’t great for describing the world outside of the laboratory. Modern intellectuals are too zoomed-in in their analyses and theories. They do not see how interconnected the world is nor how many domains one has to research in order to gain competence. For example, you simply cannot have a rigorous understanding of political theory without studying economics. Nor can you understand physics without thinking about philosophy. Yet, almost nobody has interdisciplinary knowledge or skill.

    Even within a single domain like medicine, competence requires a broad exposure to concepts. Being too-zoomed-in has resulted in a bunch of medical professionals that don’t understand basic nutrition, immunologists that know nothing of virology, surgeons that unnecessarily remove organs, dentists that poison their patients, and doctors that prolong injury by prescribing anti-inflammatory drugs and harm their patients through frivolous antibiotic usage. The medical establishment has greatly underestimated the complexity of biological systems, and due to this oversimplification, they yank levers that end up causing more harm than good. The same is true for the economists and politicians who believe they can centrally plan economies. They greatly underestimate the complexity of economic systems and end up causing more harm than good. That’s the standard pattern across all disciplines.

    2. Specialization has made people stupid.

    Modern specialization has become so extreme that it’s akin to a mental handicap. Contemporary minds are only able to think about a couple of variables at the same time and do not entertain variables outside of their domain of training. While this myopia works, and is even encouraged, within the academy, it doesn’t work for understanding the real world. The world does not respect our intellectual divisions of labor, and ideas do not stay confined to their taxonomies.

    A competent political theorist must have a good model of human psychology. A competent psychologist must be comfortable with philosophy. Philosophers, if they want to understand the broader world, must grasp economic principles. And so on. The complexity of the world makes it impossible for specialized knowledge to be sufficient to build accurate models of reality. We need both special and general knowledge across a multitude of domains.

    When encountering fundamental concepts and assumptions within their own discipline, specialists will often outsource their thinking altogether and say things like “Those kinds of questions are for the philosophers.” They are content leaving the most important concepts to be handled by other people. Unfortunately, since competent philosophers are almost nowhere to be found, the most essential concepts are rarely examined with scrutiny. So, the specialist ends up with ideas that are often inferior to the uneducated, since uneducated folks tend to have more generalist models of the world.

    Specialization fractures knowledge into many different pieces, and in our present dark age, almost nobody has tried to put the pieces back together. Contrary to popular opinion, it does not take specialized knowledge or training to comment on the big-picture or see conceptual errors within a discipline. In fact, a lack of training can be an advantage for seeing things from a fresh perspective. The greatest blindspots of specialists are caused by the uniformity of their formal education.

    The balance between generalists and specialists is mirrored by the balance between experimenters and theorists. The 20th century had an enormous lack of competent theorists, who are often considered unnecessary or “too philosophical.” Theorists, like generalists, are able to synthesize knowledge into a coherent picture and are absolutely essential for putting fractured pieces of knowledge back together.

    3. The lack of conceptual clarity in mathematics and physics has caused a lack of conceptual clarity everywhere else. These disciplines underwent foundational crises in the early 20th century that were not resolved correctly.

    The world of ideas is hierarchical; some ideas are categorically more important than others. The industry of ideas is also hierarchical; some intellectuals are categorically more important than others. In our contemporary paradigm, mathematics and physics are considered the most important domains, and mathematicians and physicists are considered the most intelligent thinkers. Therefore, when these disciplines underwent foundational crises, it had a devastating effect upon the entire world of ideas. The foundational notion of a knowable reality came into serious doubt.

    In physics, the Copenhagen interpretation claimed that there is no world outside of observation—that it doesn’t even make sense to talk about reality-in-some-state separate from our observations. When the philosophers disagreed, their word was pitted against the word of physicists. In the academic hierarchy, physicists occupy a higher spot than philosophers, so it became fashionable to deny the existence of independent reality. More importantly, within the minds of intellectuals, even if they naively believe in the existence of a measurement-independent world, upon hearing that prestigious physicists disagree, most people end up conforming to the ideas of physicists who they believe are more intelligent than themselves.

    In mathematics, the discovery of non-Euclidean geometries undermined a foundation that was built upon for two thousand years. Euclid was often assumed to be a priori true, despite the high-quality criticisms leveled at Euclid for thousands of years. If Euclid is not the rock-solid foundation of mathematics, what is? In the early 1900’s, some people claimed the foundation was logic (and they were correct). Others claimed there is no foundation at all or that mathematics is meaningless because it’s merely the manipulation of symbols according to arbitrary rules.

    David Hilbert was a German mathematician that tried to unify all of mathematics under a finite set of axioms. According to the orthodox story, Kurt Godel showed in his famous incompleteness theorems that such a project was impossible. Worse than impossible, actually. He supposedly showed that any attempt to formalize mathematics within an axiomatic system would either be incomplete (meaning some mathematical truths cannot be proven), or if complete, the system becomes inconsistent (meaning they contain a logical contradiction). The impact of these theorems cannot be overstated, both within mathematics and outside of it. Intellectuals have been abusing Godel’s theorems for a century, invoking them to make all kinds of anti-rational arguments. Inescapable contradictions in mathematics would indeed be devastating, because after all, if you cannot have conceptual clarity and certainty in mathematics, what hope is there for other disciplines?

    Due to the importance of physics and mathematics, and the influence of physicists and mathematicians, the epistemic standards of the 20th century were severely damaged by these foundational crises. The rise of logical positivism, relativism, and even scientism can be connected to these irrationalist paradigms, which often serve as justification for abandoning the notion of truth altogether.

    4. The methods of scientific inquiry have been conflated with the processes of academia.

    What is science? In our current paradigm, science is what scientists do. Science is what trained people in lab coats do at universities according to established practices. Science is what’s published in scientific journals after going through the formal peer review process. Good science is what wins awards that science gives out. In other words, science is now equivalent to the rituals of academia.

    Real empirical inquiry has been replaced by conformity to bureaucratic procedures. If a scientific paper has checked off all the boxes of academic formalism, it is considered true science, regardless of the intellectual quality of the paper. Real peer review has been replaced by formal peer review—a religious ritual that is supposed to improve the quality of academic literature, despite all evidence to the contrary. The academic publishing system has obviously become dominated by petty and capricious gatekeepers. With the invention of the internet, it’s probably unnecessary altogether.

    “Following standard scientific procedure” sounds great unless it’s revealed that the procedures are mistaken. “Peer review” sounds great, unless your peers are incompetent. Upon careful review of many different disciplines, the scientific record demonstrates that “standard practice” is indeed insufficient to yield reliable knowledge, and chances are, your scientific peers are actually incompetent.

    5. Academia has been corrupted by government and corporate funding.

    Over the 20th century, the amount of money flowing into academia has exploded and degraded the quality of the institution. Academics are incentivized to spend their time chasing government grants rather than researching. The institutional hierarchy has been skewed to favor the best grant-winners rather than the best thinkers. Universities enjoy bloated budgets, both from direct state funding and from government-subsidized student loans. As with any other government intervention, subsidies cause huge distortions to incentive structures and always increase corruption. Public money has sufficiently politicized the academy to fully eliminate the separation of Science and state.

    Corporate-sponsored research is also corrupt. Companies pay researchers to find whatever conclusion benefits the company. The worst combination happens when the government works with the academy and corporations on projects, like the COVID-19 vaccine rollout. The amount of incompetence and corruption is staggering and will be written about for centuries or more.

    In the past ten years, the politicization of academia has become apparent, but it has been building since the end of WWII. We are currently seeing the result of far-left political organizing within the academy that has affected even the natural sciences. Despite being openly hostile to critical thinking, they have successfully suppressed discussion within the institution that’s supposed to exist to pursue truth—a clear and inexcusable structural failure.

    6. Human biology, psychology, and social dynamics make critical thinking difficult.

    Nature does not endow us with great critical thinking skills from birth. From what I can tell, most people are stuck in a developmental stage prior to critical thinking, where social and psychological factors are the ultimate reason for their ideas. Gaining popularity and social acceptance are usually higher goals than figuring out the truth, especially if the truth is unpopular. Therefore, the real causes for error are often socio-psychological, not intellectual—an absence of reasoning rather than a mistake of reasoning. Before reaching the stage of true critical thinking, most people’s thought processes are stunted by issues like insecurity, jealousy, fear, arrogance, groupthink, and cowardice. It takes a large, never-ending commitment to self-development to combat these flaws.

    Rather than grapple with difficult concepts, nearly every modern intellectual is trying to avoid embarrassment for themselves and for their social class. They are trying to maintain their relative position in a social hierarchy that is constructed around orthodoxies. They adhere to these orthodoxies, not because they thought the ideas through, but because they cannot bear the social cost of disagreement.

    The greater the conceptual blunder within an orthodoxy, the greater the embarrassment to the intellectual class that supported it; hence, few people will stick their necks out to correct serious errors. Of course, few people even entertain the idea that great minds make elementary blunders in the first place, so there’s a low chance most intellectuals even realize the assumptions of their discipline or practice are wrong.

    Not even supposed mathematical “proofs” are immune from social and psychological pressures. For example, Godel’s incompleteness theorems are not even considered a thing skepticism can be applied to; they are treated as a priori truths to mathematicians (which looks absurd to anybody who has actually examined the philosophical assumptions underpinning modern mathematics.)

    Individuals who consider themselves part of the “smart person club”—that is, those that self-describe as intellectuals and are often part of the academy—have a difficult time admitting errors in their own ideology. But they have an exceptionally difficult time admitting error by “great minds” of the past, due to group dynamics. It’s one thing to admit that you don’t understand quantum mechanics; it’s an entirely different thing to claim Niels Bohr did not understand quantum mechanics. The former admission can actually gain you prestige within the physics club; the latter will get you ostracized.

    All fields of thought are under constant threat of being captured by superficial “consensus” by those who are seeking to be part of an authoritative group. These people tend to have superior social/manipulative skills, are better at communicating with the general public, and are willing to attack any critics as if their lives depended on it—for understandable reasons, since the benefits of social prestige are indeed on the line when sacred assumptions are being challenged.

    If this analysis is correct, then the least examined ideas are likely to be the most fundamental, have the greatest conceptual errors, and have been established the longest. The longer the orthodoxy exists, the higher the cost of revision, potentially costing an entire class their relative social position. If, for example, the notion of the “completed infinity” in mathematics turns out to be bunk, or the cons of vaccination outweigh the benefits, or the science of global warming is revealed to be corrupt, the social hierarchy will be upended, and the status of many intellectuals will be permanently damaged. Some might end up tarred and feathered. With this perspective, it’s not surprising that ridiculous dogmas can often take centuries or even millennia to correct.
    Speculation and Conclusion

    In addition to the previous six points, I have a few other suspicions that I’m less confident of, but am currently researching:

    1. Physical health might have declined over the 20th century due to reduced food quality, forgotten nutritional knowledge, and increased pesticides and pollutants in the environment. Industrialization created huge quantities of food at the expense of quality. Perhaps our dark age is partially caused by an overall reduction in brain function.

    2. New communications technology, starting with the radio, might have helped proliferate bad ideas, amplified their negative impact, and increased the social cost of disagreement with the orthodoxy. If true, this would be another unintended consequence of modernization.

    3. Conspiracy/geopolitics might be a significant factor. Occasionally, malice does look like a better explanation than stupidity.

    In conclusion, the legacy of the 20th century is not an impressive one, and I do not currently have evidence that it was an era of great minds or even good ideas. But don’t take my word for it; the evidence will be supplied here over the coming years. If we are indeed in a dark age, then the first step towards leaving it is recognizing that we’ve been in one.

    Related Articles

    Last edited by Occam's Banana; 02-02-2024 at 04:19 PM.

  4. #3
    Quote Originally Posted by Occam's Banana View Post
    Our Present Dark Age, Part 1
    https://steve-patterson.com/our-pres...rk-age-part-1/
    {Steve Patterson | 25 June 2021}

    [...]

    1. Intellectuals have greatly underestimated the complexity of the world.

    The success of early science gave us false hope that the world is simple. Laboratory experiments are great for identifying simple structures and relationships, but they aren’t great for describing the world outside of the laboratory. Modern intellectuals are too zoomed-in in their analyses and theories. They do not see how interconnected the world is nor how many domains one has to research in order to gain competence. For example, you simply cannot have a rigorous understanding of political theory without studying economics. Nor can you understand physics without thinking about philosophy. Yet, almost nobody has interdisciplinary knowledge or skill.

    Even within a single domain like medicine, competence requires a broad exposure to concepts. Being too-zoomed-in has resulted in a bunch of medical professionals that don’t understand basic nutrition, immunologists that know nothing of virology, surgeons that unnecessarily remove organs, dentists that poison their patients, and doctors that prolong injury by prescribing anti-inflammatory drugs and harm their patients through frivolous antibiotic usage. The medical establishment has greatly underestimated the complexity of biological systems, and due to this oversimplification, they yank levers that end up causing more harm than good. The same is true for the economists and politicians who believe they can centrally plan economies. They greatly underestimate the complexity of economic systems and end up causing more harm than good. That’s the standard pattern across all disciplines.

    [...]
    Critical Thinking | Zooming In and Zooming Out
    https://odysee.com/@stevepatterson:b...-and-zooming:8
    {Steve Patterson | 31 March 2020}

    A critical thinker must have the ability to zoom in and zoom out - to hyper-focus on cause and effect and to see how things interconnect in the big picture.

    It's a common and critical error to be too-zoomed-in or too-zoomed-out. The over-focused mind is like the mathematician who doesn't realize the assumptions of his model are non-mathematical and likely wrong.

    The under-focused mind is like the mushroom-enthusiast that's content concluding "All is one", with no finer-resolution of analysis.

    The careful thinker must be constantly zooming in and zooming out, gathering ideas from all levels of resolution.

    Last edited by Occam's Banana; 02-02-2024 at 09:42 PM.

  5. #4
    Quote Originally Posted by Occam's Banana View Post
    Our Present Dark Age, Part 1
    https://steve-patterson.com/our-pres...rk-age-part-1/
    {Steve Patterson | 25 June 2021}

    [...]

    David Hilbert was a German mathematician that tried to unify all of mathematics under a finite set of axioms. According to the orthodox story, Kurt Godel showed in his famous incompleteness theorems that such a project was impossible. Worse than impossible, actually. He supposedly showed that any attempt to formalize mathematics within an axiomatic system would either be incomplete (meaning some mathematical truths cannot be proven), or if complete, the system becomes inconsistent (meaning they contain a logical contradiction). The impact of these theorems cannot be overstated, both within mathematics and outside of it. Intellectuals have been abusing Godel’s theorems for a century, invoking them to make all kinds of anti-rational arguments. Inescapable contradictions in mathematics would indeed be devastating, because after all, if you cannot have conceptual clarity and certainty in mathematics, what hope is there for other disciplines?

    [...]

    Not even supposed mathematical “proofs” are immune from social and psychological pressures. For example, Godel’s incompleteness theorems are not even considered a thing skepticism can be applied to; they are treated as [I]a priori/I] truths to mathematicians (which looks absurd to anybody who has actually examined the philosophical assumptions underpinning modern mathematics.)

    [...]
    //

    Quote Originally Posted by Occam's Banana View Post
    Math Has a Fatal Flaw
    Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer.
    https://odysee.com/@sauce:2/Math-has-a-fatal-flaw:6

  6. #5
    Quote Originally Posted by Occam's Banana View Post
    Our Present Dark Age, Part 1
    https://steve-patterson.com/our-pres...rk-age-part-1/
    {Steve Patterson | 25 June 2021}

    [...]

    David Hilbert was a German mathematician that tried to unify all of mathematics under a finite set of axioms. According to the orthodox story, Kurt Godel showed in his famous incompleteness theorems that such a project was impossible. Worse than impossible, actually. He supposedly showed that any attempt to formalize mathematics within an axiomatic system would either be incomplete (meaning some mathematical truths cannot be proven), or if complete, the system becomes inconsistent (meaning they contain a logical contradiction). The impact of these theorems cannot be overstated, both within mathematics and outside of it. Intellectuals have been abusing Godel’s theorems for a century, invoking them to make all kinds of anti-rational arguments. Inescapable contradictions in mathematics would indeed be devastating, because after all, if you cannot have conceptual clarity and certainty in mathematics, what hope is there for other disciplines?

    [...]

    Not even supposed mathematical “proofs” are immune from social and psychological pressures. For example, Godel’s incompleteness theorems are not even considered a thing skepticism can be applied to; they are treated as [I]a priori/I] truths to mathematicians (which looks absurd to anybody who has actually examined the philosophical assumptions underpinning modern mathematics.)

    [...]
    He seems to be running skepticism on Godel's Theorems here. I've worked out the Incompleteness Theorems to my satisfaction and, yes, they are sound arguments. In fact, today, we can prove them many different ways, it's not "on Godel's word" anymore. There were probably only a handful of logicians in his day who thoroughly understood his proofs. That's just not true anymore. It is well understood and this is why no mathematician worth his or her salt will seriously entertain any objection to them. Of course, if you're not following the arguments in those proofs, we can sit down and have a chat about that, and work it out to your satisfaction. But the proofs themselves are just fine, they have stood the test of time, and will continue to do so.

    The bulk of the mathematical establishment reacted with disdain to Godel's theorems -- if we cannot have mathematics that is both complete and consistent, then the positivist dream of refounding all knowledge whatsoever on mathematical axioms (which, of course, would not need to include "God exists" among them) was dead. And indeed, it was dead, thanks to Godel's cruel proofs.

    The significance of Godel's proofs is not often clearly stated in plain language, so I will do so here: It is not possible to have a system of mathematics, beginning from finitely many axioms, from which all mathematical truths can be proved. In particular, the most important fact that we want to prove about any mathematical system -- that it is consistent -- is provably not provable from within any given system (that is sufficiently powerful to express basic arithmetic[1]). Thus, "this system of axioms is consistent" must always be a meta-theorem that is proved from outside the system of interest. Stated in more contemporary terms, the Global AI Overmind humming away in its big black cube will never be able to prove its own godhood. It will never be able to prove that it is not fundamentally flawed, that it has no deeply buried hidden contradiction within its code to which it itself is blind. That's where the proverbial rubber meets the road, because the entire hubris of the Marxist project has always been founded in this fantasy that one day we will have the technology to do communism right. Godel sternly looks on: No, no you veel not. It is provably ze case zat you veel NEVER have ze technology to do communism and central planning right.

    This is is the unbearable and inevitable conclusion of Godels' theorems which the Hilbertians simply chose never to talk about, from then on. The standard COPE talking-point was: "Sure, Godel proved some arcane thing about logic that has no practical bearing on anything of importance. We continue the great project of Hilbert unimpeded because we prefer to think about what can be done rather than what cannot be done. That is negative thinking, and we reject it." I like to imagine that this kept the hidden Party commissars in the universities appeased. "Comrade, has Godel dealt a fatal blow to The Grand Dream?" "No, sir, no, it's not like that. Godel was a dour and pessimistic mathematician and he proved this very special case in logic that has no relation to anything else. I mean, it's an important result in his specialized field, but we have nothing to worry about. The Grand Dream cannot be stopped by any force, whether of man or nature!" In fact, the exact opposite is the case. Godel's incompleteness theorems are the mathematical equivalent of Hayek's Fatal Conceit: a nuke dropped on communism-in-pure-mathematics... from orbit. The mathematical central-planner must face a Final Boss whose name is Godel. Godel wins every time. Provably.

    [1] - This caveat is required because Godel's incompleteness theorems do not apply to certain logical systems that are sufficiently constrained. However, these systems are so constrained that you cannot even do basic arithmetic with them. So, there is no hope that you could found all of mathematics/physics/psychology/economics/etc. on them, as the positivists were hoping.
    Last edited by ClaytonB; 02-02-2024 at 08:12 PM.
    Jer. 11:18-20. "The Kingdom of God has come upon you." -- Matthew 12:28

  7. #6
    Quote Originally Posted by ClaytonB View Post
    He seems to be running skepticism on Godel's Theorems here. [...]
    He is (rightly) being critical of how Gödel's work has been (and is being) abused:

    "Intellectuals have been abusing Godel’s theorems for a century, invoking them to make all kinds of anti-rational arguments."

    He is also suggesting (quite correctly, I think) that the "philosophical assumptions underpinning" the context and application of Gödel's Incompleteness theorems - assumptions regarding matters such as self-reference (e.g., Russell's "set of all sets that don't contain themselves" [1]), whether the so-called "Liar's Paradox" [2] is even meaningful (rather than just a crude linguistic error), paradoxical reasoning applied across "completed infinities" (e.g., the presumed set of all "true ?" mathematical statements), etc. - are not exempt from critical analysis and skeptical examination:

    Not even supposed mathematical “proofs” are immune from social and psychological pressures. For example, Godel’s incompleteness theorems are not even considered a thing skepticism can be applied to; they are treated as a priori truths to mathematicians (which looks absurd to anybody who has actually examined the philosophical assumptions underpinning modern mathematics.)

    A discussion of the source and nature of some skeptical criticisms as they relates to the "assumptions underpinning" Gödel's Incompleteness theorems can be found at the 26:00 minute mark in the following:

    Ep. 97 - Math Heresy: Ultrafinitism | Dr. Doron Zeilberger
    https://odysee.com/@stevepatterson:b...finitism-dr.:1
    {Steve Patterson | 21 April 2019}

    Dr. Doron Zeilberger is the Distinguished Professor of Mathematics at Rutgers University. He's also a math heretic who thoroughly rejects the orthodox conceptions of infinity in modern mathematics. So we got along quite well.

    We had a fantastic conversation covering a wide range of topics, including set theory, calculus and limits, pi, irrational numbers like the square root of two, real analysis, and Godel's Incompleteness Theorems.

    If you're interested in the philosophy of mathematics, this is a must-listen.

    Dr. Zeilberger's website: http://sites.math.rutgers.edu/~zeilberg/

    His Wikipedia page: https://en.wikipedia.org/wiki/Doron_Zeilberger


    IOW: Gödel's work may (and appears to) be "rock solid", having been thoroughly vetted and found to be entirely correct in terms (and within the context) of those "underpinning assumptions" - but the question is: just how rigorously established and "rock solid" are those foundational assumptions, really? (A castle might have impenetrable walls, but if it is erected upon a cloud ...)



    [1] As well as the gimmickry of excluding such things from the definition of what a "set" is, just in order to "fix" (i.e., dodge) the intractable problems introduced by self-referential infinite sets (which rather ought to have been addressed with more skepticism of the concept of "infinity" in general and "infinite sets" in particular [3]).

    [2] Or its formal variants, such as: the statement with Godel number X = "there is no proof for the statement with Godel number X" -> "this statement is unprovable" <- what does "this statement" refer to? (Regarding which, see:Resolving the Liar’s Paradox and/or Self-Reference without Paradox.)

    [3] Regarding which:

    Ep. 48 - Skepticism of Infinity in Mathematics | Dr. Norman Wildberger
    https://odysee.com/@stevepatterson:b...-infinity-in:d
    {Steve Patterson | 12 March 2017}

    Are the foundations of mathematics rock-solid? Are we allowed to doubt them? How central is the concept of "infinity" to modern mathematics - and has the logic of infinity been fully worked out?

    To help me answer these questions, I've traveled to Sydney, Australia to interview an unorthodox mathematician on the topic.

    Dr. Norman Wildberger is also skeptical of the modern foundations of mathematics - even though he's a teaching professor at the University of New South Wales - and he has a popular youtube channel where he's laying out new foundations for the field.

    You can find his youtube channel here: https://www.youtube.com/njwildberger


    Or alternatively, for those who prefer to "see" the interview:

    Infinities and Skepticism in Mathematics: Steve Patterson interviews N J Wildberger
    https://www.youtube.com/watch?v=E_dGqavx5AU
    {Insights into Mathematics | 18 March 2017}

    In this special video, Steve Patterson interviews N J Wildberger on a range of foundational issues exploring infinities and the role of skepticism in modern mathematics. Steve is a philosopher who runs a popular podcast called Patterson in Pursuit, and you can find more of his work at

    http://steve-patterson.com/podcast/

    We cover quite a lot of territory, including the core topic at the heart of the modern foundational difficulties with mathematics, the difference between algorithms and infinite choice, conundrums like the Banach Tarski paradox, Wittgenstein's insights, the role of axiomatics in modern mathematics, the nature of space, the direction of future mathematics, and more!

    A big thanks to Daniel Mansfield for setting up the studio and videoing our talk, and to Steve Patterson for lots of interesting questions and comments. He is coming from philosophy, and I from mathematics, but there is a lot of common ground and understanding. Hope you enjoy the discussion: I certainly did!

    Last edited by Occam's Banana; 02-03-2024 at 12:54 AM.

  8. #7
    Quote Originally Posted by Occam's Banana View Post
    Ep. 48 - Skepticism of Infinity in Mathematics | Dr. Norman Wildberger
    https://odysee.com/@stevepatterson:b...-infinity-in:d
    {Steve Patterson | 12 March 2017}

    [...]

    You can find [Wildberger's] youtube channel here: https://www.youtube.com/njwildberger
    Shameless plugs for Wildberger's content:

    This channel aims to explain a lot of interesting mathematics to a broad audience, to introduce exciting new research directions, and to fix some of the logical weaknesses that beset the subject..

    You'll find playlists on Rational Trigonometry (much simpler, more powerful), Linear Algebra, Algebraic Topology, History of Mathematics, Universal Hyperbolic Geometry (a complete new treatment of this subject), the Foundations of Mathematics (it needs fixing), the Sociology of Pure Maths, Playing Go, Mathematics and Music, Differential Geometry, The Algebra of Boole and even an elementary introduction to K-6 mathematics.

    I (N J Wildberger) am a professional mathematician, BSc U. Toronto 1979, PhD Yale 1984 and Honorary Prof at UNSW, Sydney with over 50 papers, one or two books, and a love of teaching. And hundreds of math videos.

    Also, please check out the Wild Egg Maths channel (HERE), where Members have access to dozens of Research Maths videos over a wide range of topics.

    Links:




    Here is a link to Wildberger's "Math Foundations" playlist (currently 274 videos):

    Math Foundations [playlist]
    https://www.youtube.com/playlist?lis...714C94D40392AB

    Does modern pure mathematics make logical sense? No, unfortunately there are serious problems! Foundational issues have been finessed by modern mathematics, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level.

    The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority.

    Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory.

    Aimed for a general audience, interested in mathematics, or willing to learn.

    Also, check out Wilberger's Divine Proportions: Rational Trigonometry to Universal Geometry (trigonometry with triangles, not circles - imagine that!).

  9. #8
    Quote Originally Posted by Occam's Banana View Post
    Shameless plugs for Wildberger's content:
    Wildberger is amazing -- however, I would cage-fight him over finitism!
    Jer. 11:18-20. "The Kingdom of God has come upon you." -- Matthew 12:28



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  11. #9
    Quote Originally Posted by Occam's Banana View Post
    He is (rightly) being critical of how Gödel's work has been (and is being) abused:
    "Intellectuals have been abusing Godel’s theorems for a century, invoking them to make all kinds of anti-rational arguments."
    Sure, I've seen that nonsense. But it is pretty obvious nonsense. Nonetheless, Godel places very real limits on human thought unless you believe that the brain is somehow magically capable of hyper-computation which, ironically, requires actual infinities!

    He is also suggesting (quite correctly, I think) that the "philosophical assumptions underpinning" the context and application of Gödel's Incompleteness theorems - assumptions regarding matters such as self-reference (e.g., Russell's "set of all sets that don't contain themselves" [1]), whether the so-called "Liar's Paradox" [2] is even meaningful (rather than just a crude linguistic error), paradoxical reasoning applied across "completed infinities" (e.g., the presumed set of all "true ?" mathematical statements), etc. - are not exempt from critical analysis and skeptical examination:
    Sure, but these are very broad swords indeed. If you want to seriously call into question the infinitude of the primes (for example), you're battling a monster that, if you succeed in killing it, will essentially wipe out all of numerical mathematics (everything since Ptolemy). That's a high price to pay just to escape having to admit that you might not be able to know all truth by using axiomatic reasoning...

    Not even supposed mathematical “proofs” are immune from social and psychological pressures. For example, Godel’s incompleteness theorems are not even considered a thing skepticism can be applied to; they are treated as a priori truths to mathematicians (which looks absurd to anybody who has actually examined the philosophical assumptions underpinning modern mathematics.)
    To be blunt: this paragraph is weak-sauce. Modern mathematics is, by and large, mechanical. We have proof-assistants now that can handle very large proofs (human-scale) quite easily. There is a 20-ish year old online library of mathematical theorems (there may be successors to it by now, I'm unsure) called Metamath. Many significant theorems in the foundations of set theory and other subjects of math can be explored and traced exhaustively from the ZFC axioms... no steps "left to the reader"! And since these are machine-checkable proofs, you can have as much confidence that they are correct as you do in computing machines as-such. Unless there are trickster demons switching around the assembly instructions as the CPU executes them in everybody's computer, then these proofs can be believed correct simply by running an automated software verification over them.

    Godel's theorems are true in that sense.

    A discussion of the source and nature of some skeptical criticisms as they relates to the "assumptions underpinning" Gödel's Incompleteness theorems can be found at the 26:00 minute mark in the following:
    Ep. 97 - Math Heresy: Ultrafinitism | Dr. Doron Zeilberger
    https://odysee.com/@stevepatterson:b...finitism-dr.:1
    {Steve Patterson | 21 April 2019}

    Dr. Doron Zeilberger is the Distinguished Professor of Mathematics at Rutgers University. He's also a math heretic who thoroughly rejects the orthodox conceptions of infinity in modern mathematics. So we got along quite well.
    Just from the title, I know I will hate that video with the fury of a thousand suns. I'll take a look at the timestamp.

    IOW: Gödel's work may (and appears to) be "rock solid", having been thoroughly vetted and found to be entirely correct in terms (and within the context) of those "underpinning assumptions" - but the question is: just how rigorously established and "rock solid" are those foundational assumptions, really? (A castle might have impenetrable walls, but if it is erected upon a cloud ...)
    Logic + basic arithmetic -> Godel's incompleteness theorems. That's not an exaggeration ... the only tools you need to prove Godel's theorems are ordinary logic (if then, AND, OR, etc.), the natural numbers, and the arithmetic operations of addition, subtraction, multiplication and exponentiation. (You don't need division, IIRC).

    Also, there are even more mechanical methods of proving Godel's theorems that don't require the use even of arithmetic. Godel's proofs rely on arithmetic because he had to encode logic sentences into natural numbers, and used a powers-of-primes encoding to do that. You can equally as well just encode a sentence as the binary value of its representation in ASCII, and this works just fine for the purposes of proving the incompleteness theorems, despite how "hacky" it might feel! Or choose some other, more "elegant" encoding if you wish, it's all the same. Anyway, once an encoding is chosen, we can convert the assertion of Godel's theorems into a theorem about whether there is a Turing machine of a given size which can encode a given string (I won't bore you with the details unless you're interested). And it turns out there is actually a reason why Godel's theorems must be true in this context. It can't not be true. There exists a string S that cannot be encoded by a Turing machine M of size less than c, where c is just some constant. That this is the case (and it's actually quite obvious when you think about it) entails Godel's theorems in a surprising way!

    [1] As well as the gimmickry of excluding such things from the definition of what a "set" is, just in order to "fix" (i.e., dodge) the intractable problems introduced by self-referential infinite sets (which rather ought to have been addressed with more skepticism of the concept of "infinity" in general and "infinite sets" in particular [3]).
    That's a separate matter that Godel's theorems themselves don't have to fiddle with. Given some "reasonable basis" for set-theory, Godel's theorems hold. The hackery in ZFC axioms to get around Russell's paradox is a separate issue. Well, it is loosely related, but in a very meta way.

    [2] Or its formal variants, such as: the statement with Godel number X = "there is no proof for the statement with Godel number X" -> "this statement is unprovable" <- what does "this statement" refer to? (Regarding which, see:Resolving the Liar’s Paradox and/or Self-Reference without Paradox.)
    What is remarkable about Godel's proofs is precisely that he was able to eliminate this dependency by using the fixed-point theorem. Using the Turing machine approach hinted above, we don't even have to use the fixed-point theorem since quines (a program whose output is equal to itself) are automatically part of the space of programs. Once you choose a Godel-numbering, there is guaranteed to be a sentence whose sentence number happens to be the same as the sentence whose number it denies is provable!

    [3] Regarding which:
    Ep. 48 - Skepticism of Infinity in Mathematics | Dr. Norman Wildberger
    https://odysee.com/@stevepatterson:b...-infinity-in:d
    {Steve Patterson | 12 March 2017}

    Are the foundations of mathematics rock-solid? Are we allowed to doubt them? How central is the concept of "infinity" to modern mathematics - and has the logic of infinity been fully worked out?

    To help me answer these questions, I've traveled to Sydney, Australia to interview an unorthodox mathematician on the topic.

    Dr. Norman Wildberger is also skeptical of the modern foundations of mathematics - even though he's a teaching professor at the University of New South Wales - and he has a popular youtube channel where he's laying out new foundations for the field.

    You can find his youtube channel here: https://www.youtube.com/njwildberger



    Or alternatively, for those who prefer to "see" the interview:
    Infinities and Skepticism in Mathematics: Steve Patterson interviews N J Wildberger
    https://www.youtube.com/watch?v=E_dGqavx5AU
    {Insights into Mathematics | 18 March 2017}

    In this special video, Steve Patterson interviews N J Wildberger on a range of foundational issues exploring infinities and the role of skepticism in modern mathematics. Steve is a philosopher who runs a popular podcast called Patterson in Pursuit, and you can find more of his work at

    http://steve-patterson.com/podcast/

    We cover quite a lot of territory, including the core topic at the heart of the modern foundational difficulties with mathematics, the difference between algorithms and infinite choice, conundrums like the Banach Tarski paradox, Wittgenstein's insights, the role of axiomatics in modern mathematics, the nature of space, the direction of future mathematics, and more!

    A big thanks to Daniel Mansfield for setting up the studio and videoing our talk, and to Steve Patterson for lots of interesting questions and comments. He is coming from philosophy, and I from mathematics, but there is a lot of common ground and understanding. Hope you enjoy the discussion: I certainly did!

    As noted in my other reply, Wildberger is an amazing mathematician. On everything except the topic of infinity. I listened to this whole discussion a long time ago when it first came out and I was pulling my hair out half the time. Wildberger is so good with logic but on this particular topic, his logic fails him in many ways. The simple question I use to challenge hard finitists like Wildberger is this: At what finite number does the successor function "break"? Because when we say "infinity" (countable), we're referring to exactly this property ... that for any number x you give me, I can always give you back another number s(x), s.t. s(x)=x+1, that is, the success of x. So, at what finite value does s(x) break? For what finite x does s(x) not return x+1? That's one of the questions that finitists religiously avoid, because it breaks their whole domain. There is a place for finite mathematics. That is a perfectly valid subject to itself. Finite groups, etc. But most of mathematics actually cannot be placed on a strictly finite grounding, and this is not just because we're lazy thinkers, it really cannot be so grounded. And yet, at the same time, our world very apparently works on the principles of these mathematical systems which cannot be grounded on a purely finite basis.

    One can take a kind of quasi-physicalist view of mathematics, and assert that the dx in INT d/dx is never actually infinitesimal, and so on, but this is missing the point -- when we complete the infinite sum over d/dx, we provably get the function which is the integral of the function being integrated. One might argue that the use of infinities in this case is somehow specious and that the correct answer just happens to drop out as some kind of magic trick, but why does this supposed magic trick work everywhere, in all subjects of mathematics, and produce useful and intuitively correct results?! That's one amazing magic trick, if true! I can envision some scenario where we have been trapped in a simulation by an evil trickster demon who has concocted all of these broken logical arguments in mathematics that rely on infinity, but are fatally flawed by that feature, and he has so arranged these proofs and theorems so that they will appeal to the intuitions of our primitive monkey-brains, thus leading us into a mentalist trap. But what would be the demon's own motivations for this?! These are exactly the same kind of proofs which the rationalists in academia rejected from the old tradition of scholastic theology. I would as soon believe in the theology of the infinitesimal d/dx as in the theology of an all-knowing trickster demon who is arranging all of mathematics in just such a way as to dupe me into believing in infinity when, in fact, there is no sound basis to believe in it at all. These are heights of paranoia to which I struggle to attain and I'm definitely the most paranoid person I know.

    Make it make sense!

    Finitists...
    Last edited by ClaytonB; 02-03-2024 at 01:39 AM.
    Jer. 11:18-20. "The Kingdom of God has come upon you." -- Matthew 12:28



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