On defeating a sociopath

There are people who really, genuinely, believe, as far as you can dig down, that winning is everything—that however many lies they told, allies they betrayed, innocent lives they harmed, etc. etc., it was all justified by the fact that they won and their enemies lost. Faced with such sociopaths, people like me typically feel an irresistible compulsion to counterargue: to make the sociopath realize that winning is not everything, that truth and honor are terminal values as well; to subject the sociopath to the standards by which the rest of us are judged; to find the conscience that the sociopath buried even from himself and drag it out into the light. Let me know if you can think of any case in human history where such efforts succeeded, because I’m having difficulty doing so.

Clearly, in the vast majority of cases if not in all, the only counterargument that a sociopath will ever understand is losing. And yet not just any kind of losing suffices. For victims, there’s an enormous temptation to turn the sociopath’s underhanded tools against him, to win with the same deceit and naked power that the sociopath so gleefully inflicted on others. And yet, if that’s what it takes to beat him, then you have to imagine the sociopath deriving a certain perverse satisfaction from it.

Think of the movie villain who, as the panting hero stands over him with his lightsaber, taunts “Yes … yes … destroy me! Do it now! Feel the hate and the rage flow through you!” What happens next, of course, is that the hero angrily decides to give the villain one more chance, the ungrateful villain lunges to stab the hero in the back or something, and only then does the villain die—either by a self-inflicted accident, or else killed by the hero in immediate self-defense. Either way, the hero walks away with victory and honor.

In practice, it’s a tall order to arrange all of that. This explains why sociopaths are so hard to defeat, and why I feel so bleak and depressed whenever I see one flaunting his power. But, you know, the great upside of pessimism is that it doesn’t take much to beat your expectations! Whenever a single sociopath is cleanly and honorably defeated, or even just rendered irrelevant—no matter that the sociopath’s friends and allies are still in power, no matter that they’ll be back to fight another day, etc. etc.—it’s a genuine occasion for rejoicing.

Anyway, that pretty much sums up my thoughts regarding Arthur Chu. In other news, hooray about the election!

90 Responses to “On defeating a sociopath”

  1. James Miller Says:

    We could exclude sociopaths from positions of influence if we could easily identify them. In 2011 I wrote this article saying that “future presidential contenders’ DNA will likely be scrutinized for signs of sociopathy.” https://hplusmagazine.com/2011/08/16/dna-politics-science-and-sociopathy/

  2. mattg Says:

    We have to blame society as well as the sociopath when considering the toxic fallout from political (or game show) competitions. There are numerous perverse rewards for the winner even when luck is the deciding factor. Not until the rewards are in line with our community goals will we have even adequate leadership.

  3. asdf Says:

    1) At least some of us out here think Biden is also a sociopath. At best he is perhaps a less colorfully incompetent sociopath than Trump.

    2) If we really think Trump is an existential threat to humanity who will stop at nothing to win, shouldn’t we ourselves be willing to steal the election to get rid of him? To do otherwise would be unilateral disarmament and plain stupid. If we postulate that the Deep State killed JFK for similar reasons, a little bit of election fraud seems like small potatoes by comparison. (I myself was resigned to a second Trump term pre-Covid, and figured we’d survive it like we survived the first one, survived GWB and Reagan, etc. Glenn Greenwald has a post up saying Trump was nowhere near as bad as GWB/Cheney.)

    3) James Miller, if we develop a way to identify sociopaths, then obviously the sociopaths will take control of it and use it to make sure that NON-sociopaths never get into power. Doesn’t sound great.

    4) This post by Zeynep Tufekci is worth reading for anyone thinking Trump is an outlier.

  4. Jon Awbrey Says:

    Reconciling with
    Despotism and Fascism and Racism
    is still just
    Despotism and Fascism and Racism

  5. 1Zer0 Says:

    Not sure if the US Constitution prevents something like this but let’s get creative about how to stay in power independent of election processes:
    Suppose Person A is president of the United States. Now A creates a new lifetime office “Emperor of the United States” which has higher authority than “President of the United States” and who can overwrite any decision of “President of the United States”. Than A crowns himself to be “Emperor of the United States”. So when Person B ( !=A) takes the office of President, he basically serves as a puppet under the Emperor of the US. Not sure if the US Constitution would permit the president to create a new power hierarchy though. But theoretically, one way how Trump or any of the president to succeed him can stay in office indefinitely. I generally disagree that there should be any way whatsoever of preventing a selected candidate from taking the office of president, now matter how many people consider him to be a sociopath. It’s the will of the people, that’s the only thing that really matters.

  6. Vadym Pozharskiy Says:

    1. Half of the nation doesn’t think the POTUS is a sociopath. This percentage gets even higher if you look outside the US (e.g., in Japan and Taiwan).

    2. There are still several months left. I urged the POTUS to move the U.S. Embassy in Israel back. Would be even better to disavow the peace deals in the middle east, for that’s what a sociopath would do.

  7. Scott Says:

    For those who don’t know who Arthur Chu is: he’s a former Jeopardy! champion, who notoriously won by ignoring decades-old conventions of Jeopardy! play and jumping around randomly to find the Daily Doubles. At the time, I found his approach delightful—since Jeopardy! is, after all, just a game.

    Unfortunately, Chu then parlayed his game-show career into becoming a social-justice activist who consciously, explicitly brought that exact same “winning-is-everything” philosophy to the task of trying to ruin the lives of anyone who disagreed with him—in the name of justice, you see. He even wrote about his regular practice of “mindkilling” himself—meaning, purging any thoughts about how his intellectual opponents might have valid points, if those thoughts made him even marginally less effective at destroying his opponents.

    If you think I exaggerate, spend a few hours scrolling through his Twitter account (but put on a hazmat suit first!).

    Five years ago, Chu (who at that point, I’d never done anything to or said anything about) published an article about me in Salon magazine entitled “the plight of the bitter nerd”; since then, he’s often used Twitter to slime me, typically using obscenities and once musing that he was “unhappy about my continued existence.”

    In general, I strongly believe we should bend over backwards to find redeeming moral qualities even in our enemies, even in those who despise us. But Donald Trump and Arthur Chu are two of the only people I’ve heard of who openly, explicitly espouse philosophies of “winning is everything / the ends justify the means.” It’s probably not by coincidence that they’re also two of the only people for whom my every attempt to look for redeeming moral qualities came up completely empty.

    One disanalogy is that unlike Trump, as far as I know Chu hasn’t suffered any dramatic public defeat, but only a gradual slide into angry irrelevance as his Jeopardy! days get further behind him.

    Incidentally, speaking of Jeopardy!, I was sad to hear about the passing of Alex Trebek.

  8. Jon Awbrey Says:

    Hitler was a sociopath.

    What do you say about people who actively supported the policies and “ideals” of Hitler? (Note: we are not talking exclusively about Germans here.) Are they sociopaths, too? Are they people who don’t know what a sociopath is? Are they people who simply don’t care whether a leader is a sociopath or not, so long as his politics serves their short-term interests?

    What do you call people who simply stand back (and stand by?) and let a sociopath run rampant over their country? Maybe their apathy makes them “apaths”.

  9. Scott Says:

    Jon Awbrey #8: I know for a fact that not all Trump supporters are “bad” in any conventional sense. Some are as sweet as could be and would show you every kindness if you met them in person. Yes, even if you were black or Mexican or an immigrant or a Democrat.

    Unfortunately, everything I’ve read about Hitler’s supporters is 100% consistent with that. Incredible though it sounds today, some of his supporters had nothing against Jews—or at least not any Jews who they personally knew. Or they felt a mild antipathy that stopped far short of “round them all up and murder them, including the kids.” In any case, they might have been pillars of their communities, wonderful to their children, just all-around mensches. Except for the Hitler part.

    I’m hardly the first person to have noticed this, or its many uncomfortable implications about human nature. We seem forced to say: yes, some people have intrinsic goodness, but they’re missing the part of their psyche that would notice the tension between that and the monstrous policies they support. Maybe it’s because they’re “apaths.” Or maybe it’s because they have moral values that are alien to liberal Enlightenment ones—placing, for example, the pride of the Volk or the plight of the unborn over every other moral consideration. Maybe it’s simply because renouncing their political views would feel to them like renouncing their own friends and loved ones and communities, everything that’s ever been good in their lives. Whatever the cause, though, it’s a genuine phenomenon that any student of humanity needs to wrestle with.

    (Also, for the billionth time, I am not drawing a moral equivalence between Hitler and Trump, or between their respective supporters. Trump is just a run-of-the-mill wannabe autocrat and gangster, notable mainly for his success corrupting the world’s oldest democracy, whereas Hitler was horrific even by the standards of autocrats.)

  10. matt Says:

    Any plans to get back to the continuum hypothesis? And I’ve got some dumb questions about that!

    1)Do I understand right that the theory ZFC+ “zfc is not consistent” has some things that it thinks are natural numbers, but which cannot be reached started from 0 by the successor operation? I’m using the term “thinks” loosely of course. And these things are what it believes encode some proof of a contradiction in ZFC? are these called “nonstandard natural numbers”?

    2)what about the theory ZFC + “zfc is consistent”? Does it have such similar nonstandard numbers?

    3)ok, finally, what about CH? You’ve explained that, contrary to your initial guess, forcing involves adding more real numbers to so that there are more reals than alpha_1. So, are those reals “nonstandard” in the same kind of sense? What I mean is, suppose I believe that the real interval [0,1] “really is” that thick black line containing “everything” between 0 and 1. Should I think that forcing was putting in stuff that really is in that line, or is it adding something totally different? Should my belief about that “thick black line” influence my belief on CH?

    I know these are totally heuristic questions, mostly, but since you started on heuristic grounds, why not?

  11. Doug S. Says:

    As far as I know you’re pretty much right about #1, except that they’re called “supernatural numbers”.

  12. Paul Topping Says:

    “We could exclude sociopaths from positions of influence if we could easily identify them.”

    Which is why there used to be a question about hobbies on job applications. 😉 But, only slightly more seriously, it wasn’t hard to tell that our 45th President was a sociopath. Certainly by the whole “birther” episode if not even earlier.

  13. raginrayguns Says:

    Matt #10: Any natural number N can be reached from 0 using the successor operation, by applying the successor operation N times. So, I don’t think it makes sense to say of any system that it thinks there are natural numbers and thinks they can’t be reached by the successor operation. Although of course a system might think there are natural numbers which I don’t think can be reached–which is just to say that I don’t think they are genuine numbers.

  14. asdf Says:

    1zero#5, creating an office like Emperor would require a constitutional amendment. The constitution was set up to protect the govt branches from each other (“checks and balances”) though reality has since tilted in the executive branch’s favor. But, transitioning from one president to another is a fancy process that only starts when the head of the General Services Administration signs a document saying who the new president is. The head of the GSA is, you guessed it, a Trump appointee, and she so far is refusing to sign the document. We’ll see how things go with that.

    Vadym #6, not saying you’re wrong but your conclusion doesn’t particularly follow from the election outcome. Plenty of Trump’s supporters know perfectly well that Trump is a sociopath, but support him anyway, in fact maybe because of it.

    Matt #10, 1) yes, any model of ZFC+not-CON(ZFC) contains a nonstandard number we can call x, that encodes a proof of a contradiction in ZFC. 2) ZFC+CON(ZFC) can also contain nonstandard numbers, since (like ZFC) it doesn’t prove its own consistency. So we could have a theory ZFC+CON(ZFC)+not-CON(ZFC+CON(ZFC)) and that would be nonstandard. And you can repeat that indefinitely. ZFC+CON(ZFC) is called “1-consistent”, ZFC+CON(ZFC)+CON(ZFC+CON(ZFC)) is called 2-consistent, and so on. If you make it “consistent all the way down”, that is called “arithmetically sound”. It would logical to call this “ω-consistent” but that is actually an old-fashioned term for 1-consistent, so it would get confusing. You might like this old article. 3) I wouldn’t say the reals added by forcing to the constructable reals are nonstandard. Rather it might be better to say that the constructable reals are missing a lot of standard reals that happen to be nonconstructable. But that is a matter of philosophy.

  15. gentzen Says:

    matt #10: Regarding 1: There are Turing machines which search for a contradiction in ZFC (and halt as soon as they found a contradiction). For some of them the theory ZFC+ “zfc is not consistent” will prove (i.e. “think”) that they do find a contradiction. Therefore, the number of steps such a Turing machine performs before halting is a natural number for your system. And if you apply the successor operation to 0 for each step of the machine, you will reach exactly this number. At least your system “thinks” so.

    But of course, it is possible that ZFC is inconsistent. So the number of steps performed by a suitable Turing machine searching for a contradiction in ZFC might indeed be a perfectly valid natural number. They only become non-standard in case ZFC is actually consistent.

    2) No, the axiom “ZFC is consistent” doesn’t allow to define concrete natural numbers in a similar way, because it just says that certain Turing machines don’t halt.

    3) As Scott explained, his initial model only contained an infinitesimal small fraction of all real numbers (i.e. only countable many). So it is quite possible that all newly added real numbers are perfect standard real numbers. And even if some of them would be non-standard, it would not really matter (as far as I can see).

  16. Gerard Says:

    I’ve long been aware that western societies contain a percentage of individuals who hold extreme right-wing authoritarian political views. However until recently I was under the impression that this population didn’t exceed the 10-20% range, which is a range that right wing parties in Europe have sometimes attained in elections in recent times. To realize that in the US today they now represent 40% or more of the population is disturbing. I believe that the Weimar Republic was effectively ended by an election where the Nazi Party only won 43% of the vote.

    It may turn out that the most lasting effect of Trump’s reign will have been to show the way for some future dictator to end our Republic.

  17. I Says:

    re CH: have you read about Woodin’s views on the CH? This paper claims that “some of the philosophical issues surrounding the Continuum Problem have been reduced to precise mathematical questions, questions that are, unlike Cantor’s hypothesis, solvable from our current theory of sets.” That’s pretty vague, but if you happen to know what that means already, could you say if you’re going to write about it?

  18. ike Says:

    for whatever reason, this hit hard.

  19. raginrayguns Says:

    Gerard #16: Many Christians don’t believe in Hell, although it seems to me that Jesus makes it pretty clear that sinners go there. Similarly, I suspect many Trump supporters have convinced themselves that what Trump really stands for is what they want him to stand for. Do you have any reason to think that >40% of the population hold extreme rightwing authoritarian views, other than that they are Trump fans?

  20. Gerard Says:

    raginrayguns #19

    No Trump is the evidence, that was my point.

    I don’t see how anyone who has listened to Trump’s diatribes over the past four years and still chose to vote for him could be anything other than a right wing authoritarian.

  21. Viliam Says:

    For victims, there’s an enormous temptation to turn the sociopath’s underhanded tools against him, to win with the same deceit and naked power that the sociopath so gleefully inflicted on others. And yet, if that’s what it takes to beat him, then you have to imagine the sociopath deriving a certain perverse satisfaction from it.

    I believe this is wrong. It is based on the assumption that the sociopath cares about you, albeit in the negative sense. They do not. They only care about themselves.

    Think of the movie villain who, as the panting hero stands over him with his lightsaber, taunts “Yes … yes … destroy me! Do it now! Feel the hate and the rage flow through you!” What happens next, of course, is that the hero angrily decides to give the villain one more chance

    Which is exactly what the villain wanted. Manipulating the hero is instrumental. The goal was never to corrupt the hero into feeling hate and killing the villain and thereby losing morally (the villain does not care about that). The goal was to make the hero confused (from sociopath’s perspective, any moral concerns are merely a confusion) in hope he would then do something stupid… which he did, but then got luckily saved by plot armor.

    asdf #3:

    if we develop a way to identify sociopaths, then obviously the sociopaths will take control of it and use it to make sure that NON-sociopaths never get into power.

    Luckily for the rest of us, sociopaths do not care about each other either. From a sociopath’s perspective, if pressing a button could kill all other sociopaths and also generate $1 of profit, it is worth pushing. (Less competition is good.)

    Counter-intuitively, we need to adopt a rule that the sociopath test can NOT be applied to politicians who are already in power; only to all future politicians. Then, the current politicians may vote in favor of the test, and we will get the desired results one generation later… which is better than never.

  22. Gerard Says:

    Then again it remains possible that we haven’t seen the last of Trump’s shenanigans. He just fired Secretary of Defense Mark Esper. What is the logic in firing a cabinet secretary two months before the end of his administration and what is Trump planning for those two months that he needs a compliant Secretary of Defense for ?

  23. mjgeddes Says:

    Trump hasn’t been vanquished yet Scott. It’s not over really until the electoral college votes are declared on Jan 6th. Betfair prediction market shows his price has come back in – implied chance of a Trump win remains small but still significant, with a price hovering around 14.00 (7% implied chance).


    Trump and Chu are indeed examples of ‘paper-clippers’ optimized for winning. Trump’s strategy is obviously to cast as much doubt as possible on results on the key states. He’ll be in with a chance if he can somehow stop states from sending their electors in time to vote on Dec 14th, or get a case through to the Supreme Court. Another possibility is that he can get some electors to switch and vote for him.

    To understand minds (both good, evil and neutral), we must understand Chu Space:

  24. raginrayguns Says:

    Gerard #20: Do you see how someone can read the bible, call themselves Christians, and not believe in hell? I think the analogy is pretty good–people who want to be a part of something “translate” what they hear into something acceptable. Do you think Trump fans are different from Jesus fans in this regard?

  25. Gerard Says:

    raginrayguns #24

    Let’s see, can someone read a book about a man that was written about 100 years after his death in a language he may or may not have spoken and have various views about a concept that didn’t really exist in the culture he lived in ? I would say yes.

    What I don’t understand is how people can call themselves Christians, have read the Sermon on the Mount, vote for Trump, believe in Hell and not believe they are going there.

  26. Bill Kaminsky Says:

    #1) I see what you did there, Scott. That’s a nice, comedic bait-and-switch with Arthur Chu and President He-Who-Shan’t-Be-Named. 😉

    #2) I hope your recovery from oral surgery is going well. Failing that, I hope your painkillers are giving you nice, warm relief rather than scary, hot delirium. I’ve had the latter. I wouldn’t wish it on my worst enemies, and that brings me to…

    #3) [My Main Point] I contend “What should we wish for our sociopathic enemies?” is a boring question. To me, the much more interesting question is: “what should we wish for our sociopathic (and sociopathic-adjacent) allies and, indeed, heroes?”

    To keep things as brief as my overly-verbose and OCPD-addled po’ po’ lil’ brain can, I’ll won’t really make an argument, but rather just offer the following hopefully thought-provoking question:

    What should we have done about Bertrand Russell [1] and others [2] who came to the conclusion the late 1940s and early 1950s that the best way to minimize the number of expected future murders in the 20th Century would be to exploit the USA’s inevitably-soon-to-end monopoly on deployable atomic bombs in order to wage a preemptive nuclear war on the USSR with the aim of establishing a benevolent world government [3] with a monopoly on nuclear weapons?! In other words, what should we do about undeniably smart and (at least publicly [4]) virtuous people who seriously and wholeheartedly concluded the definite murder of several million Soviets would’ve been the clear ethical course in comparison to what they wrongly-but-learnedly predicted was the inevitability of a WWIII that possibly could murder of hundreds of millions, if not billions, of people if years of a US/USSR nuclear arms race was allowed to happen?

    Footnotes [please feel extra free to stop reading… y’all needn’t indulge my overly-verbose, OCD-addled po’ po’ lil’ brain]:

    [1] In case you’ve never read Russell on the topic, here’s his argument in the pages of The Atlantic Monthly in 1951:


    I feel I should mention that preemptive nuclear war was not Russell’s stance on the problem of nuclear weapons for all that long. Once the USSR developed its own arsenal of deployable atomic bombs and once both the USA and USSR developed H-bombs, Russell went back to the pacifism that made him famous during WWI. For example, there’s the famous “Russell-Einstein Manifesto” of 1955:


    [2] The most famous among these “others” for this blog’s readership is John von Neumann. Wikiquote (https://en.wikiquote.org/wiki/John_von_Neumann) relates this mordant quip:

    If you say why not bomb them tomorrow, I say why not today? If you say today at five o’ clock, I say why not one o’ clock?

    Wikiquote lists the following magazine article as the source: “The Passing of a Great Mind” by Clay Blair, Jr., in LIFE (25 February 1957), page 96. I have yet to see an online copy of this article. If any of y’all know of one, I’d be grateful.

    [3] Ok, ok… not so much “benevolent world government” in terms of rainbows, ponies, and well-run social democracy, but “benevolent world government” in terms of as-good-as-can-be plausibly-expected given the task at hand is waging war to make an worldwide empire that’ll hold a monopoly on world-destroying nuclear weapons. Both Russell and von Neumann were voluminous readers of history from antiquity to their own times. They weren’t naive about the nasty things empires have always done. Indeed, they were both quite vocal about the fact that the USA and the UK were most assuredly empires that had done and were continuing to do many of the nasty things empires have always done. They just thought the USA and the UK were tremendously better than the USSR.

    [4] I say “at least publicly virtuous” since Russell in his private life was a callous womanizer and a bad father. And, if I recall Feynman’s memoirs correctly, von Neumann was some sort of gleeful peeping tom always trying to look up the skirts of the women working at Los Alamos on the Manhattan Project. Also, though it’s cartoonishly amusing “absent-minded professor” schtick, von Neumann really was infamous for reading while driving. I do believe he got multiple minor car accidents around Princeton as a result. That’s sociopathic unto itself. :O

  27. Scott Says:

    I #17:

      have you read about Woodin’s views on the CH? This paper claims that “some of the philosophical issues surrounding the Continuum Problem have been reduced to precise mathematical questions, questions that are, unlike Cantor’s hypothesis, solvable from our current theory of sets.” That’s pretty vague, but if you happen to know what that means already, could you say if you’re going to write about it?

    I’m aware that Woodin is arguably the world’s foremost CH expert for the past few decades, and that he’s repeatedly changed his mind about the cardinality of the continuum. And after a couple months studying the basics of the subject, I’m not even close to understanding any of Woodin’s arguments. In particular, I don’t know which “precise mathematical questions” he’s alluding to above. But if anyone else does, please fill us in!

  28. Scott Says:

    Gerard #22:

      Then again it remains possible that we haven’t seen the last of Trump’s shenanigans. He just fired Secretary of Defense Mark Esper. What is the logic in firing a cabinet secretary two months before the end of his administration and what is Trump planning for those two months that he needs a compliant Secretary of Defense for ?

    mjgeddes #23:

      Trump hasn’t been vanquished yet Scott. It’s not over really until the electoral college votes are declared on Jan 6th.

    On reflection, you’re both right. Today, I was absolutely terrified by McConnell’s (and most of the other Republicans’) refusal to accept the election outcome, together with the Trump campaign’s lawsuits asserting that if they can find a single irregularity anywhere, then the state in question needs to throw away its entire vote count and let the legislature appoint its own slate of electors. (Of course, they’ll only try this in states with Republican-friendly legislatures.) I don’t put it past the zealot-packed Supreme Court to swallow that “argument,” despite the farcical absurdity that it would invalidate almost every previous election. Which means: we’re now right at the beginning of the feared succession crisis—the one that I repeatedly banged the drum about on this blog. So, as Steven Pinker asked today, why aren’t we all more terrified?

    On the one hand, with even Fox News, George W. Bush, and (apparently) many in Trump’s campaign and family having acknowledged Biden’s victory, it seems hard to understand how a coup could possibly succeed. Certainly, at this point, there’s no coup that doesn’t paralyze the country and lead to widespread violence. On the other hand, given that we’re already on terra incognita and it hasn’t been a week, who can say how much further Trump’s minions are willing to go? (I don’t even ask about Trump himself; it’s a given that he’d take us to the deepest abyss and then keep digging.)

  29. lewikee Says:

    The behavior of the Trump minions and base is simple: they wait for someone high up to be bold enough to take Trump’s assertions seriously (McConnell and McCarthy) and once that has happened, they all jump on the Trump train, regardless of the truth or falsehood of his claims. To them, unison = legitimacy.

    His ridiculous assertions are snowballing into a unanimous Republican front right now. I expect Fox News to retract their call within 2 weeks. If they can identify the right path to the supreme court and they can bundle together five or so claims of voter fraud to put before the Supreme Court, there’s a decent chance they’ll invalidate battleground state votes.

    But have no fear, Susan Collins will be *very* disappointed.

  30. Timothy Chow Says:

    I #17: In a comment to one of Scott’s previous posts, I gave a very brief sketch of Woodin’s ideas, with some pointers to further reading.

    The technical details of Woodin’s work are formidable, and there’s no doubt that his best theorems are great mathematical achievements and his precise conjectures are mathematically important. But their philosophical importance is debatable. In the best case scenario, what will emerge is an axiom that appears to be consistent with ZFC and that yields an aesthetically pleasing picture of the set-theoretic universe. Said axiom is extremely technical and difficult to understand, and by no stretch of the imagination could be considered “self-evident.” If this axiom implies CH (or \(\neg\)CH), how much philosophical insight does that give us? Precious little, I would say. Sociologically, there’s no chance that the mathematical community as a whole will simply accept the new axiom as a new basic axiom for mathematics, so it’s not going to “settle” CH. (You might wonder, how can we be sure of that without understanding the axiom? Well, it’s precisely because the axiom is so difficult to understand that it won’t be readily accepted.) It certainly isn’t going to settle any debates about Platonism versus formalism or any of the other standard philosophical debates surrounding CH.

  31. Michal Says:

    I used to have a “winning is all that matters” attitude at one point in my life, but I changed my mind after reading these Slate Star Codex posts, plus thinking about the way a Tit For Tat strategy is more successful than an ‘always defect’ strategy in iterated prisoner’s dilemma, and realized that in many cases agreeing to cooperate with other people and limiting your actions accordingly is more effective than just doing whatever you think will help you win in whatever specific situation you’re in. Then again, I believed in winning at all costs mostly because I’d realized that none of the ethics I had been taught had any objective justification at around the same time I learned about the idea of economic rationality, and thus I concluded that it was irrational to follow moral rules. It’s said that you can’t argue someone out of something they didn’t argue themselves into, and I expect that for someone like Trump, whose focus on winning is a basic personality trait rather than a learned idea, this sort of approach wouldn’t work.

    Scott #9: I think you’re being uncharitable when you describe some Trump voters as having “moral values that are alien to liberal Enlightenment ones” because they place “the plight of the unborn over every other moral consideration.” Liberalism is a claim about how people should be governed (through constitutional democracy with rule of law and protection for individual rights), but it assumes that we already agree on what a person is. Pro-lifers consider fetuses people deserving of basic rights, so they see allowing abortion as equivalent to allowing murder; pro-choice people don’t consider fetuses people, so they see not allowing abortion as denying people the basic right of bodily autonomy. (I generally agree with the pro-choice side, but I can see why my opponents might make the choices they do.) The only way to resolve the debate (I think) is to get both sides to agree on whether fetuses should be considered people with rights, and without that, appeals to “liberal values” are not going to be helpful, since that’s not the point people disagree on.

  32. Sniffnoy Says:

    raginrayguns #19:

    I mean, I’d argue that a focus on the person rather than that person’s actual policies is itself a characteristic of authoritarianism…

  33. David R Says:

    Bill Kaminsky #26

    His official title is One-Term President He-Who-Shan’t-Be-Named.

  34. David R Says:


    I think that most of the ways people are saying that Trump could possibly pull off a coup are not actually possible. I am certainly not a legal expert so I am just basing this off of what I have read from legal experts. This guy’s twitter feed addresses a lot of people’s fears I think: https://twitter.com/greg_doucette

    He seems to say that basically there is no way any president other than Biden will be inaugurated on Jan 20, because even if state legislatures send Trump supporting electors, and the Senate approves them (which could definitely happen), the Democrat controlled house will just not approve them. Then apparently if there is an impasse up to the point of Jan 20, then we get Acting President Nancy Pelosi. Of course just because he is a lawyer doesn’t mean he is absolutely correct, but there seem to be other legal experts chiming in that they agree, and it is reassuring at least.

  35. Scott Says:

    David R #34: Greg Doucette’s Twitter thread is relevant and interesting, so thanks!

    But here’s my meta-worry: how could anyone *possibly* have so much confidence about how things will play out in a type of crisis that’s occurred precisely zero times before in US history and that depends entirely on human decisions and human interpretations of rules?

  36. Scott Says:

    Michal #31: It’s certainly possible to uphold liberal Enlightenment values while being anti-abortion. What I claim is impossible is to uphold liberal Enlightenment values while letting that issue (or indeed, almost any other object-level issue) override every other consideration. In other words, even the “vanilla of political ideologies” has actual content! 🙂

    Two of the central claims of liberalism are:

    (1) shades of gray are everywhere — on object-level issues, we constantly need to make difficult, non-obvious tradeoffs between competing value systems, and

    (2) getting the outcome you want, in some particular case, is essentially never worth trashing the democratic process that lets us produce such outcomes.

  37. David R Says:

    Scott #35

    Well I can’t really say anything other than you’d have to ask him, which may or may not get a response. But I think it makes sense to put more weight into what legal experts say and their confidence in it than to what seems to be pretty amateurish speculation by non-experts which I think is mostly based on fear. Though I doubt it is impossible to find legal experts that disagree with him. But from what I’ve read the law/rules seem pretty clear, so I don’t think that simply saying that people might interpret them wrongly is much of a counterargument.

    Of course you are right that his confidence is too high strictly speaking, since he says there is a 0% chance that Trump remains president. But he’s not a mathematician so maybe we can cut him some slack. Although actually he is an ex computer scientist according to his twitter profile.

  38. David R Says:

    Sorry for the double comment, but here is a place where he seems to lay things out pretty clearly: https://twitter.com/greg_doucette/status/1325988538064760833

  39. Tu Says:

    Timothy Chow #17:

    You are the man!

    Thank you for being so patient and generous with your time with respect to the commenters on this blog, even though you need to gingerly sidestep the culture war happening all around you to do so.

  40. Scott Says:

    Tu #39: Y’know, I had a whole thread specifically about CH, free from trivialities about an unfolding governance crisis that’s already the worst in US history including the Civil War. But CH discussion is like kudzu, growing everywhere! 🙂 Not that I’m complaining. I’ll treat it as a positive, hopeful sign, like the important physics that was done in the trenches of WWI.

  41. matt Says:

    So, since there are people who have looked into law a bit and can explain to dumb non-lawyers like me: if, like #34 suggests, the house can decline to approve Trump supporting electors, leaving President Pelosi, has this always been available as a loophole? I mean, even if there was a landslide victory for one candidate, agreed by everyone, so long as the House is in the opposite party, can they just decline to approve, making the speaker into the President? Is this one of those things that is present as a loophole, but just nobody exploited because it would be bad faith?

    Also, if we operate on the premise that Trump wants to somehow get things to the Supreme court so they can rule in his favor, why does he actually need to hire fancy and expensive lawyers? I mean, if the whole point is to win on partisan grounds, why bother filing a detailed brief, and instead just file a 1-sentence “I was robbed and I think I won”, and keep appealing until it gets to the court. Is it that the job of the fancy lawyers is to come up with a plausible reason, to give a partisan judge a fig leaf for a particular ruling?

  42. Tu Says:

    Scott #40:

    I guess I should clarify that I don’t mean to suggest that your posts on this subject are not worthwhile. I really enjoy reading your posts on politics, and fully support your approach of just calling this administration what it is. I think your writing on this subject is great, and in my mind focuses on the irreducible issues with Trump. This is of course in addition to your ability to produce novel, innovative insults that I can add to my arsenal!

    I was only trying to express amazement that T.C. is as willing to comb through the comment section as I am!

  43. David R Says:

    matt #41

    I was wondering the same thing actually, but it is not clear that this stalemate loophole is present under normal circumstances. If you read the tweets I linked to in #38, then you will see that he says that a “late” slate of electors appointed by a state legislature can only be counted if a majority of the House and a majority of the Senate agree to recognize them. The “late” refers to a state legislature appointing a new slate of electors after election day, which is normally when the electors must be chosen by (each party chooses their own set of electors). So maybe if the original set of electors for the winning candidate is sent to congress, then they have to count them. But again I don’t know because I am not a legal expert.

  44. fred Says:

    Scott #9

    “I know for a fact that not all Trump supporters are “bad” in any conventional sense. Some are as sweet as could be and would show you every kindness if you met them in person. Yes, even if you were black or Mexican or an immigrant or a Democrat.”

    Indeed, Scott, not all Trump voters are white racists – his support grew across all groups, including Latinos and African-Americans. Apparently the only group where he lost support is white voters…



  45. G Says:

    fred #44

    I don’t believe in reductionism of everything to “racism”, and I don’t believe even most white Trump voters are racist (beyond the extent to which everyone’s a little bit racist). That said, to say Trump “gained ground with” certain groups since 2016 is not an end-all be-all refutation of the claim. White non college educated voters still leaned Trump by a 20% margin (college educated was 50/50, I think), and Black voters still voiced 83% support for Biden vs 10% support for Trump (with that number as high as 20% for Trump for young Black voters). Thus, the effect is still in the “predicted” direction.

    The “gained ground with” metric, if you think about it, doesn’t really weigh on the question of racism in Trump’s base at all. It takes the difference (favored Trump over Biden) – (favored Trump over Clinton) and uses it to say something about the kind of person who likes Trump … but Trump is on both sides of the subtraction sign!

    I’d guess that the absolute margins are mostly due to religious beliefs — though, I admit I’m surprised that there are so many Black Christians who vote blue. And yes, the difference can tell us something about how people are reacting to what’s happened between 2016 and 2020, including the renewed rhetoric focusing on Black inequality… but there are many other factors at work as well, and it seems like it’d make more sense to look at a poll that asks about that issue directly (eg the polls that rank how much people care about different issues).

  46. Scott Says:

    matt #41:

      I mean, if the whole point is to win on partisan grounds, why bother filing a detailed brief, and instead just file a 1-sentence “I was robbed and I think I won”, and keep appealing until it gets to the court. Is it that the job of the fancy lawyers is to come up with a plausible reason, to give a partisan judge a fig leaf for a particular ruling?

    Indeed, my model is that Thomas, Kavanaugh, and Barrett would probably rule in Trump’s favor given a 1-sentence brief that simply said “Imagine how triggered the libs will be, imagine the suffering on their faces, if you just hand us the election!” But that for Gorsuch, Alito, and definitely Roberts, more of a fig leaf would be needed—like, maybe some actual small-scale fraud if they can find any, or even some guy who forgot and voted twice or whatever, with which to justify throwing out a whole state’s returns and replacing them with legislature-selected electors.

  47. anon85 Says:

    Scott #41: that’s at once too harsh on the Supreme Court, but at the same time, not nearly harsh enough on Alito. Except perhaps for Thomas, Alito is the single worst justice there!

    If Trump’s appeals get taken up by SCOTUS (something I would bet against — they would likely decline the case), then my guess is a 7-2 decision in which all justices except Alito and Thomas say that Biden gets to be president. Though if there’s a milder issue like “can Trump sabotage the incoming Biden administration a lot”, I expect a 5-4 or 6-3 decision in favor of Trump.

  48. Scott Says:

    anon85: Alas, you might be right. Alito probably belongs to the first group, the group that would write a concurring opinion in Biden v Trump that said in its entirety, “Stop punching yourselves, shitlibs!”

  49. fred Says:

    I wonder how long before it starts to sink in that Trump will never concede…
    not because he’s an isolated man refusing to accept the reality of his loss, but because the result of the election was never relevant.

    They never planned or even hoped to win.

    They planned a scheme to stay in power regardless of the results (and the massive 71 million votes on their side will make that plan easier to execute).

    What that scheme is, I don’t know, but, after watching today the very strange calm and confidence of Barr and Pompeo, and the continuing silence of republicans, it’s going to become rapidly clear to everyone else that we’re going through a coup… not some subtle lawsuit bullshit about recounts, but literally a bold “in your face” coup.

  50. fred Says:

    Just in:

    “Trump administration removes senior defense officials and installs loyalists”

  51. fred Says:

    The Trump administration has been telling us all along what was going to happen.
    Trump saying before the election that he can only win, and now Pompeo clearly saying “There will be a smooth transition to the second Trump administration” – no “if” in there…
    Not one word from Pence and from the vast majority of the GOP (they know what’s about to happen).

    Here’s how it’s gonna play out:

    Trump stalls the transition process to put all his loyalists in place in the military.
    Regardless of the results of ongoing legal proceedings about ballots, Trump keeps declaring himself the winner (at this point the actual result of the election is totally irrelevant), he uses the military to shield himself from any removal, overriding congress, the constitution, etc. Proclaiming that opposing him is treason.

    At this point protests/riots will happen in the cities (the likes of which we’ve never seen), Trump uses this as an excuse to deploy the military nation wide (Esper stood up to Trump when he wanted to do this during the summer protests), declaring martial law.

  52. Scott Says:

    fred #51: On the one hand, I have lots of smart friends patiently explaining to me why the sequence you describe could never happen, and indeed the military is completely irrelevant here.

    On the other hand, I have the knowledge that all over the world and all through the history of democratic governments, it has ultimately come down to the military, and whose orders it chooses to obey.

    What should a person believe??

  53. Gerard Says:

    Scott and fred:

    I don’t think there can be any doubt that the reality of power ultimately comes down to who chooses to follow whom. If a new leader is elected but all the government officials continue to follow the old leader then you have a successful coup. Of course the officials who matter most are those in the military, since they control by far the most force.

    There are two questions we should be asking: does Trump intend a coup and is there any chance he could successfully pull one off ?

    On the first point the DoD changes appear suspicious, though I’m still holding out hope that there is a more innocent explanation for them.

    On the second point, I think it’s very unlikely. US military officers swear an oath to uphold the constitution and I think most tend to take this oath quite seriously, so I think it’s highly unlikely that enough of them would support an unconstitutional president for a coup to be successful. There’s certainly no historical precedent for the US military becoming involved in political succession (which is definitely not true for many other countries).

  54. David Says:

    It’s worth replaying John McCain’s concession speech in 2008 to remind ourselves how it should be done.

  55. Bill Kaminsky Says:

    @Scott #52

    What should a person believe?? [in regard to Trump’s recent hirings and firings among the civilian leadership at the Department of Defense]

    Well, Scott, though Bayesianism allows us to claim the imprimateur of Capital-R-“Rationality” even when updating beliefs based initially on uninformed priors, I’m a big fan of following ye olde maxim of “go with what you know!” and thus focusing on areas where one has informed priors (or at least better than informed than, say, the 90th percentile of your fellow citizens).

    To be specific, though I see you removed

    When civilization’s collapsing, sometimes there’s nothing to do but math.

    I still think focusing on computer science rather than political science might be wise, both productivity-wise and mental-health-wise.

    With that attempt at a witty and urbane preface out of the way, let me pose my question to Scott and everyone else here who can offer at least a semi-informed opinion:

    What do y’all think about “end-to-end-verifiable secure voting” systems?

    I think this question is vital given our budding Constitutional crisis and given what I imagine is a large portion of Americans permanently and utterly losing faith in our current methods for running elections.

    Endnote: If you’re unfamiliar with the notion of “end-to-end-verifiable voting” (which, by the way, is usually abbreviated as either “E2EV secure voting” or, a tad sloppily, as “E2E secure voting”), then I recommend the following 2016 review article:


  56. Bill Kaminsky Says:

    Of course, my last comment maybe doesn’t speak to the widespread anxiety caused by Trump’s recent firings and hirings in the civilian leadership of the defense department. “Maybe” is probably an understatment. I can imagine a fully understandable retort, “Who do you think I am? A freakin’ Green Beret with long experience in that charmingly and euphemistically entitled mission of ‘foreign internal defense’?? How on Earth could I have a truly informed prior about what coups d’état look like??!”

    Well, I can’t point you to any advice from former Green Berets, but I can point you to the stellar defense policy writing of Fred Kaplan at Slate [see endnote for Kaplan’s stellar-if-nonetheless-admittedly-short-of-US-Army-Special-Forces credentials]:

    https://slate.com/news-and-politics/2020/11/trump-nsa-ellis-firings.html .

    In this article, Kaplan does admittedly express a general and profound unease. However, amidst that general and profound unease, he makes the point that Trump’s recent spate of hirings and firings are likely meant to give him *lobbying influence* in the future. To wit, when all’s said and done, Trump’s admittedly suspicious spate of hiring and firings are likely “just” Trump making a mad dash to replace the civilian political appointees in the Department of Defense with hack loyalists who shall in turn facilitate as many last-minute hirings as possible of civilian mid-level employees with civil service legal protections against “political” firings. In Trump’s uber-cynical mind (and maybe accurately too), these mid-level employees will be the kind of permanent, procurement-portfolio-possessing hack bureaucrats beloved by all the real-nitty-gritty-behind-the-scenes DC lobbyists in search of sweet, sweet federal goverment contracting $$$. Thus, they will belatedly secure for Trump power of the sort that’ll keep him attractive to the DC power elite business types (as opposed to the elite ideological types) who otherwise would be more-than-happy to see him exit the DC scene and so they can just get back to “business-as-usual” with establishment fixtures like Joe Biden and Mitch McConnell.

    ——- Endnote ———-
    While no Green Beret, I’ll note that Fred Kaplan isn’t some run-of-the-mill online-media-platform journalist. He has a Master’s (1978) and PhD (1983) from MIT’s Political Science Department and, in between those credentials, was a policy adviser for Wisconsin Congressman Les Aspin in 1978-80 as Aspin was climbing the greasy pole of the DC power structure on his way to being Chairman of the House Armed Service Committee (1985-93) and Bill Clinton’s first Secretary of Defense (1993-94). [Kaplan is also an excellent jazz pianist and jazz critic. I myself find Rennaissance Man versatility a general commendation, but YMMV (“your mileage may vary” as I’m wont to believe the cool kidz abbreviate)]

  57. fred Says:

    Scott #52

    Just the fact that we’re wondering which of the two will happen says a lot… WTF?!

    Some say that the replacements of Esper and top Pentagons could be about some upcoming action against Iran, which is scary in its own way – Trump knows Biden will probably re-enter the nuke agreement with them, so maybe Trump wants to preemptively blow up the Iranian nuclear processing plants? Maybe Netanyahu is also pushing for it?

  58. David Says:

    By the way, even NYT says Gore didn’t win Florida:


  59. John Baez Says:

    From the Washington Post today:

    Trump has been spending his days largely on the phone, calling advisers, allies and friends. The president has been “trying to find people who will give him good news,” one adviser said.

    Still, Trump has indicated in some of these conversations that he understands Biden will take over the presidency on Jan. 20, Inauguration Day. Rather than talking about a second term, Trump has been matter-of-factly discussing a possible 2024 campaign — an indication that he knows his time as president is coming to an end, at least for now.

    “I’m just going to run in 2024. I’m just going to run again,” Trump has been saying, according to a senior administration official who has spoken with him this week.

  60. Scott Says:

    John Baez #59: That’s the best news I’ve seen in days. Even if it’s true, though, by the article’s own admission he reverses himself from one hour to the next…

  61. Jon Awbrey Says:

    Re: Trump Continues to Bluster, But Hints He Will Run In 2024

    All the more reason to prosecute Individuell Eins for his crimes, starting with money-laundering, wire fraud, and working up to treason. If he can run a presidential campaign from Mar-a-Leavenworth, and if anyone could it would be him, then I guess we all deserve what happens to us.

  62. fred Says:

    John #59

    ““I’m just going to run in 2024. I’m just going to run again,” Trump has been saying”

    He’s gonna have to replace burgers with quinoa and hit the treadmill…

  63. I Says:

    Scott #28,
    Hah, fair enough.
    Timothy #27
    Hey, thanks for answering.
    Based off your comment in the other thread, it seems as if Woodin found an answer in the form of a precise mathematical statement, but one unrelated to was being discussed in “How Woodin changed his mind.” Is that accurate?
    Seeing as you’re an expert, could you say how one would go about understanding Woodin’s work on \(\Omega-\) logics? Would aquiring a working knowledge of infinitary logics as well as large cardinals be sufficient to start going through his papers?

  64. David R Says:

    matt #41

    Apparently what you described actually is possible: https://twitter.com/greg_doucette/status/1326946373581856768

  65. Ehud Schreiber Says:

    Hi Scott,

    in two out of the last three posts you’ve used the same literary device, which in itself is facile, not to say populist. You can and should do better.

  66. mjgeddes Says:

    Trump using his remaining time to cynically exploit his supporters – subjecting them to ‘debt collection’ tactics to milk as much cash from the gullible as possible.


    The world may have just managed to dodge a bullet, things were definitely at the start of a downward spiral in the US, and US democracy may not have survived 4 more years of that. The margin of 2-3% popular vote win to Biden is likely too much for Trump to overcome, but it was still alarmingly close!

  67. Scott Says:

    Ehud Schreiber #65: Start your own f-ing blog and show us how it’s done!

  68. Timothy Chow Says:

    I #63: I don’t fully understand your first question, but I think that the discussion in “How Woodin changed his mind” does cover the precise mathematical statements you asked about. Maybe what’s confusing is that not everyone agrees on the philosophical significance of these precise mathematical statements. Some think that major philosophical questions have been reduced to these precise mathematical statements, but others (including myself) do not.

    I am far from an expert in \(\Omega\)-logic. It’s a long row to hoe if you want to understand it in detail. I’d recommend starting with Woodin’s expository article The Continuum Hypothesis, Part II in the August 2001 issue of the Notices of the American Mathematical Society. If you survive that, you could try moving on to An \(\Omega\)-logic primer by Bagaria, Castells, and Larson.

  69. I Says:

    Timothy Chow #68:
    Sorry, that was a mess of a question reflecting a lack of understanding. Reading through “How Woodin Change His Mind” cleared up the misunderstanding. By the way, thanks for recommending it. It is quite shocking how readable it is for someone who isn’t a set-theorist. And they convey the broad strokes of what was going on! Do you know if the papers published in the Archive for History of Exact Sciences are usually that good?
    Would you mind answeing a couple of stupid questions on the paper. First, is the following statement roughly true? “If you assume certain sorts of large cardinals exist, you can’t use convert a small cardinal into a (sufficiently) large one”. Further, why can forcing can kill off infinitely many Woodin cardinals but not unboudedly many?
    Thank you for your patience, it is much appreciated.

  70. duck_master Says:

    My take on sociopaths is that it is impossible, by arguments, to induce a person (or more generally, an agent) to follow terminal values that they did not already have. This means that, when it is clear that a a person is a sociopath (i.e. they lack a terminal value for love, joy, compassion, etc.*), then, as a person with such a terminal value**, the best thing for you to do is to is to make that sociopath lose as hard as possible. (This also suggests that, for the AI alignment problem, one should not try to make misaligned AIs aligned, but instead try to build AIs so that they are aligned in the first place.)

    *I don’t know what this actually is in normal humans, but I think we can set this matter aside for now.

    **note: I also have this terminal value

  71. Timothy Chow Says:

    I #69: Unfortunately, I don’t have good answers to your questions. I don’t know anything about Arch. Hist. Exact Sci. I also don’t understand Woodin cardinals well enough to answer your question about the need for a proper class of Woodin cardinals, but here’s my guess. The way forcing works is that you take a suitable poset \(P\) in your ground model. One might naïvely think that the way to perform iterated forcing is to directly build an increasing chain of countable transitive models, but it turns out to be better to think in terms of a sequence \(P_1, P_2, P_3, \ldots\) of posets in your ground model. So eliminating infinitely many Woodin cardinals presumably means taking the limit of a (possibly transfinite) sequence of posets. My guess is that if there are “only” infinitely many Woodin cardinals then it’s straightforward to define this limiting poset, but if there’s a proper class of Woodin cardinals then there’s no way to make sense of such a limit.

    I don’t quite understand your question about converting small cardinals into large ones. Larger cardinals generally have higher consistency strength, and forcing doesn’t increase consistency strength, if that’s what you mean.

  72. I Says:

    Timothy #71
    Hmm, that account of killing off Woodin cardinals is quite intuitive. The question on forcing & large cardinals was mostly about seeing why Lévy-Solovay Theorem limits the kind of large cardinal embeddings that can exist in a small forcing extension. Thanks for pointing out the question doesn’t make sense.

  73. william e emba Says:

    The attempted coup wants to turn the usually automatic confirmations into battles. Pence and the Senate ultimately count the electoral college votes, and if it’s a question that the new Senate is not GOP enough, they could easily interfere with swearing in new non-GOP senators and then claim victory.

    And this is assuming they don’t do a Henry II vs Thomas Becket.

  74. william e emba Says:

    One reason a proper class of Woodin cardinals is so interesting is a deep theorem of Woodin, regarding the generic absoluteness of \(L(\mathbb R)\) under set-forcing in the presence of infinitely many Woodin cardinals. Since a set-forcing can only collapse a bounded many Woodin cardinals, such a generic extension continues to have infinitely many Woodin cardinals, and therefore \(L(\mathbb R)\) remains absolute.

    Roughly speaking, the theory of \(L(\mathbb R)\) is always the same once you have unbounded many Woodin cardinals. For example, determinacy for “real-definable” games must hold, and this can’t be lost using set-forcing.

    Forcing with a proper class is possible. (This isn’t done by taking “limits”.) Class forcing isn’t automatic, however, because if you try to force the collapse of all the ordinals to \(\omega\) or add a proper class of new subsets of \(\omega\), the resulting model obviously is not one of ZF. The basic method, due to Easton, is quite straightforward, and consists of a class forcing that factors into a set-forcing that does things at its level, and a proper class “remainder” that has no effect on the lower level sets. And since you can do this factoring at any cardinal, you can get a proper class of forcing results in one generic extension.

    A far more subtle version of class forcing was invented by Jensen, based on joint work with Solovay, which showed how to cleverly “code” a generic subset of \(\omega_1\) be a subset of \(\omega\). Jensen discovered how to iterate this up all the cardinals, which meant that a single new generic real coded up the entire proper class of new subsets added. It’s extremely difficult, to say the least.

    Sy-David Friedman has pushed this “coding the universe” method very far. Among other things, he has invented “hyperclass forcing” which consists of a limit, of sorts, of universes found by class forcing. (So TC’s intuition was mostly correct!) But attempts to get the method to work with Woodin cardinals has not yet been achieved.

  75. Timothy Chow Says:

    william e emba #74: Thanks for the additional information! But I’m a little confused by your last statement, which makes is sound like it’s an open problem whether some version of class forcing could someday be devised that kills unboundedly many Woodin cardinals. But isn’t it a theorem that if there are unboundedly many Woodin cardinals then there is no forcing extension that violates projective determinacy?

  76. william e emba Says:

    It’s a theorem (a la Levy-Solovay) that no set-forcing can kill off unboundedly many Woodin cardinals. But class-forcing can kill them all.

    An example of such a forcing was (if I remember correctly) used when violating GCH at every cardinal, due to Foreman-Woodin.

  77. I Says:

    william e emba #74

    Thanks for the explanation. If you wouldn’t mind, could you expand on why set forcing can’t kill off unboundedly many Woodin cardinals? What’s so special about them as compared to other large cardinals? Preferably explained in a way that doesn’t use much higher set theory, though perhaps that’s too much to hope for.

    As for the coding, are you saying that this generic real somehow encodes all the information regarding the differences betwee a forcing extension of some base model? Surely you can’t do this for all base models of set theory?

    Scott, if you’re reading this, sorry for derailing your recent threads. Who would have thought a one line question about second order logic could lead to such a kerfuffle.

  78. moscanarius Says:

    Hi Scott

    Since you mentioned Arthur Chu: did you see that that other guy who bashed you at the time, Dr Nerdlove, was kind of caught in a kind of… creepy… situation some time ago?


    Surprise, surprise!

    (Anyway, if you think this is too gossipy for the comments, feel free to delete it)

  79. Scott Says:

    moscanarius #78: Schadenfreude is not one of the nobler emotions. So, to whatever extent someone who shamed me on behalf of SJWs was himself shamed by other SJWs, there’s a strong onus on me to resist the urge to enjoy it.

  80. moscanarius Says:

    Scott #79

    I agree. But I’m weak and cannot avoid it, and anyways this was a few months ago and it’s clear he will not get much trouble for it. Still, it stands as an illustration that the guy with the pitchfork is not above being eaten too, perhaps even earlier than his targets will.

  81. Konohamaru Says:

    It requires divine grace to make a sociopath change.

    “Can an Ethiopian change his skin or a leopard its spots? Neither can you do good who are accustomed to doing evil.” (Jeremiah 13:23)

    Making a sociopath change is described by St. Ezekiel as a miracle equal to taking a pile of dry bones and bringing them to life again. (Ezekiel 37)

  82. william e emba Says:

    Roughly speaking, set-forcing can only affect cardinals up to the size of the poset (or Boolean algebra) used. What make a large cardinal “large” is, in essence, the fact that it can’t be built up from below. Not even its consistency can be proven from below. And set-forcing only introduces “truly” new sets at the level of the set used for forcing. (Larger new sets are simply the obvious ones built up from the set-sized generic set that was introduced.)

    So given a proper class of Woodin cardinals, only set-many of them can be “damaged” by a set-forcing.

  83. william e emba Says:


    “Coding” is used in several senses in logic and set theory, so I’m not sure what you are actually asking.

    One key idea of forcing is that given a base model \(M\) and a forcing poset \(P\in M\), there exists a “generic” set \(G\notin M\) such that there exists a “minimal universe” extending \(M\) and containing \(G\), denoted \(M[G]\). The meaning of “generic” is roughly that although no particular fact about members of \(G\) can be ascertained inside \(M\), many general facts about \(G\) itself can be worked out from inside \(M\), and they depend closely on the choice of \(P\).

    So it is possible to say that \(G\) codes this information.

    Easton generalized this to proper classes \({\bf P}\subset M\) with proper class generic \({\bf G}\subset M[{\bf G}]\).

    Which leads to another use of “coding”, which I mentioned before in response to TC, was that Jensen invented the remarkable technique of “coding the universe”, in which a proper class forcing is equivalent to adjoining a single real. Said real “codes” the proper class \(\bf G\). The techniques involved are extremely complicated, and only work over sufficiently \(L\)-like universes.

    PS: Sorry for the delay in responding, my computer is in the shop, so I only have 30-minute Monday-Friday public library usage at the moment. (Like most of my colleagues, I’m not allowed on my University campus for the time being.)

  84. haifa Says:

    “Let me know if you can think of any case in human history where such efforts succeeded”

    The obvious example is the United States’s decision to retreat from Vietnam. In this case, the counter-arguing was done by the public, in the form of protests and such. Otherwise the war in Vietnam could have conceivably continued up to this very day.

  85. haifa Says:


    Since you disapprove of “the end justifies the means” arguments, you will probably like the article “Sacrifice and Sacred Honor: Why the Constitution is a ‘Suicide Pact'”. by Professor Peter Brandon Bayer from the University of Nevada.

  86. Sandro Says:

    I know I’m late to this party, but just wanted to say that I don’t get the big deal over violating so-called “democratic norms”.Trump is certainly an asshole for violating them, but if these norms were critical to the operation of the Republic, then they would have been codified into the Constitution. And if Trump could stage a coup by violating a few norms, then what does that say about the stability of the Republic?

    Furthermore, the status quo established by these norms is not at all helping the majority of Americans. Why do you think they elected someone who literally doesn’t give a damn about such things? The election of Trump, and especially his near re-election, should be the start of a real conversation about what is lacking about representation in the US. It should have been a galvanising moment, just like George Floyd’s death started a movement and conversations about about race and police brutality.

    That’s not at all what we’ve seen. Instead of blaming the failures of the system and the parties that run it, we got 4 years of denial and digging this hole deeper, 4 years of sowing division among fellow citizens that have more in common with each other than the political elites of their tribe, to the point where Trump got even more votes this time around.

    I think you’re playing a little too much into this Scott. I understand your reasons, that you want to stop the hemorrhaging before dealing with the cancer, but reconsider whether you’ve correctly identified which is the real underlying condition, and which is more urgent to address. In my mind, defeating Trump should have been EASY both times, but the political elites that run the show simply aren’t responsive to their citizens, and Trump played on that.

  87. I Says:

    william e emba #83

    Thanks for taking the effort William. Though it is kind of funny that you’re in a similair situation. Anyway, it was Easton’s idea of “coding the universe” with a single real that was causing the confusion. It makes sense that the models must be restricted somehow, but it still feels suprising that this works at all. Is it too difficult for someone new to forcing theory to grasp?

  88. william e emba Says:


    Jensen did “coding the universe”. Easton invented ordinary class forcing. Solovay noticed that if you took a direct product of finitely many Cohen-style forcings for increasing the powers of different alephs, then if you analyzed the product forcing top-down, each factor successfully increased the relevant power sets. For example, you can starting from a model of GCH, make \(2^{\aleph_0}=\aleph_5\), \(2^{\aleph_3}=\aleph_9\), and \(2^{\aleph_{\omega+1}}=\aleph_{\omega_{\omega_2}+3}\). Easton figured out how to do this “top-down” analysis with infinitely many alephs, which on the surface does not make sense. And it was so simple, it worked with a proper class forcing.

    Yes, a beginner can learn Easton class forcing right away after mastering the basics.

    The basic idea of coding the universe is rather simple, once you’ve mastered the basics of forcing. The Jensen-Solovay “almost disjoint” forcing gives a model where the standard generic set adjoined by the forcing, of size \(\aleph_1\) is equivalent to a model obtained by adjoining a single real. A beginner can learn this rather easily.

    Jensen then iterated almost disjoint forcing, obtaining a real that codes a set of size \(\aleph_1\) which codes a set of size \(\aleph_2\), etc. up the entire class of cardinals.

    Jensen’s was an extremely complicated forcing construction. Not for beginners or even your average practitioner. Jensen’s original version was simplified by several people, but it is still complicated and needs “fine structure”. And the new “simplified” version was then a springboard for S-D Friedman to make it all very complicated again, with numerous applications.

    PS: While I got my machine back, the motherboard had to be replaced and the hard drive was unreadable, so they replaced things and installed Windows, and I’m having a very difficult time re-installing Ubuntu, even as a mere Windows app. I’ve been using Unix in some form or other for 40 years now, and I am very unhappy with this latest development. But I can take my time replying now!

  89. I Says:

    William #88
    Thanks for the catching the error in the question and answering both versions. Hmm, well maybe in a few years someone will write a dummy’s guide to Jensen’s coding.

    Good lord, what happened to your laptop that both your hard drive and motherboard had to be scrapped? Sorry to hear you’re having troubles with installing Ubuntu. Is there no support for your particular laptop?

  90. Sniffnoy Says:

    Sandro #86:

    I know I’m late to this party, but just wanted to say that I don’t get the big deal over violating so-called “democratic norms”.Trump is certainly an asshole for violating them, but if these norms were critical to the operation of the Republic, then they would have been codified into the Constitution.

    No? That doesn’t follow. Not everything critical is in the constitution; indeed, it’s impossible for it all to be. Your argument would only work if the US had always operated purely according to the constitution and never according to anything additional. But this is clearly false; even ignoring non-legal norms, if you just read the constitution, it doesn’t actually make any sense on its own, but rather assumes a background of common law! (E.g., what’s a writ of habeas corpus? Gonna have to look outside the constitution for that!) And as I said it’s impossible for everything critical to be in the constitution because y’know such basic ideas as “the laws do in fact matter” are required. I mean, notionally you could put that in the constitution, but that’s circular. Point is, it’s pretty critical that there’s no large-scale revolt, and the constitution can’t stop that!

    And if Trump could stage a coup by violating a few norms, then what does that say about the stability of the Republic?

    Pretty terrible things, undeniably! But the fact that a republic was less stable than we had realized, doesn’t excuse an attempt to destroy it!

    Of course the reality is that Trump couldn’t do this on his own just by violating a few norms; he needed the help of the Republican Party and the groundwork that they’ve laid for this over the past few decades. But once again, that doesn’t excuse Trump’s role in it.

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