• 0.999... = 1
    I agree. But I would like a better mutual understanding before we move on. I don't know for sure about you, but my comments were intended to provoke a reply, but only in the interests of a discussion. I thought you were doing the same. I didn't realize that you thought I was baiting you, which is a different kettle of fish. So I apologize.Ludwig V

    Not necessary, I willingly took the bait.

    Quite so. I'm afraid I was guilty of irony, which is always dangerous. His inability to recognize when the game is up is not particularly unusual. I can think of other examples.Ludwig V

    Over on the political forums in the Lounge, someone actually suggested to me with a straight face that Biden willingly stepped down. I confess I don't understand that degree uncritically parroting propaganda.

    I agree with you that the hysteria around everything is very damaging. But I think both sides are to blame. Each side thinks that it can win by escalating the emotional temperature; the media feeds on that and joins in. The question who started it is a good one - unless the answer is to be used as a weapon of further escalation.
    But neither side is really to blame. There can be little doubt that a large part of the problem is systemic - the whole set-up encourages escalation and the desire to win, rather than compromise. Again, it's not unique to the US. It's not difficult to think of other examples.
    Ludwig V

    The Dems refused to accept the result of the 2016 election and have been causing mischief since then, with Russiagate, two fake impeachments, lawfare, and then weakening Trump's Secret Service protection to the degree that he almost got killed. I doubt they're done yet.


    I see from the reports that the soup did actually damage the paint of the frame, so I was wrong about that.Ludwig V

    I hope these court cases will deter some of the vandalism.


    Responding to those protests with outrage and attempts to suppress is exactly what they want - to attract attention and controversy. Difficult as it may be, the only thing that would persuade them to stop is ignoring them. But it is also important to reward them when they do the right thing, there should be a reasonable response to civilized and legal protests.
    Failure to recognize when one is being baited is very common and failure to deal with it rationally - by not rising to the bait - frequently underlies escalation.
    Ludwig V

    You can't ignore people blocking major highways. Glad those leaders are going to prison.


    I'm not sure what you expect me to say.Ludwig V

    LOL I'm baiting you!

    It's definitely a bad thing. Needs to be checked out and any problems resolved - and any parties who haven't been doing their job properly held to account.Ludwig V

    Point being, EV's are a disaster. Green energy is a disaster. If the eco measures actually worked, I'd support them. They don't. They're a scam, and their negative impact falls mostly on the poor of the world, so that the upscale can feel better about themselves.

    But does it show that wind farms should be abolished?Ludwig V

    Many of those projects should be abolished, for good and sound reasons.

    I don't think so. The fact that so many people dislike them is much more relevant and it's right to be cautious about setting them up. Off-shore farms seem to be more acceptable, so it's better to be content with them. (There's the question of bird strikes as well, though I've heard that they may have found a solution to that.)Ludwig V

    Bird stew?

    I think it's unlikely that that on-shore farms can be a major contributor to the project of finding renewable sources of energy. For on-shore generation, solar farms may be more appropriate.Ludwig V

    You're halfway to my point of view. And now that Germany, for one, is starting to see the economic downsides of their green energy programs, the tide is turning.
  • US Election 2024 (All general discussion)
    He wasn’t removed at all. He decided not to run.Wayfarer

    LOL. Like Caesar decided not to be head of the Roman empire.

    Where do you get such nonsense? Seriously, you actually believe what you wrote? That Biden, the great statesman, woke up and decided not to run of his own volition? At the end of the USSR, the people stopped believing Pravda. You still believe.

    Famed investigative reporter Seymour Hersh has reported that Obama called Biden and told him that Kamala was on board using the 25th Amendment to remove him from office.

    Hersh's Substack is behind a paywall, but his information has been widely repeated.

    https://www.zerohedge.com/political/obama-instigated-anti-biden-coup-25th-amendment-threat-sy-hersh-reports

    https://thepostmillennial.com/seymour-hersh-obama-and-kamala-threatened-to-invoke-the-25th-amendment-on-biden-before-he-dropped-out#google_vignette

    https://x.com/RandyEBarnett/status/1818033920845431113

    Hersh's original paywalled article is here.

    https://seymourhersh.substack.com/p/leaving-las-vegas
  • 0.999... = 1
    Yes, Meaning is as ill-defined as metaphysics. It's usually easier not to mention it.Ludwig V

    Sorry I mentioned it.

    It is ironical that his most Presidential act has been not to stand for his second term. He'll be a lame duck until January, but that's normal. I expect the system will survive.Ludwig V

    Oh please. He left as gracefully as Caesar did.


    There's a paradox about democracy which "of the people, for the people, by the people" misses. It is crucial that the people who lose the election accept the result. That means that the process has to be very carefully organized so that there's as little excuse for contesting it as possible. So the events in January 2021 are a concern. I've also heard that some Trump supporters have said that they will refuse to accept the result if they lose; (I assume they will accept it if they win!). That's absurd. It puts Trump in the same territory as Putin and Xi Jinping. Bluntly, hypocrites.Ludwig V

    The Dem hysteria that started on election night of 2016 has been extremely damaging to the country.

    The people who were jailed were convicted under existing laws. The new law is an opportunistic grab by those who want to ensure that free speech is allowed, so long as it cannot be heard. It's a difficult balance to strike. My complaint about those protests is that they were too effective because they produced more opposition without taking their campaign forward. Protest needs to attract attention - especially media attention, of course - without creating more opposition for the cause.Ludwig V

    Well toss a can of soup on a painting then. You lost me here.

    Probably not. There's also solar panels, hydro-electric, tidal, wave, and volcanic. Still, it's pretty clear that lots of batteries will be needed. China has quietly cornered the market in the rare earths that are needed for them. Now, that's a sensible way to approach the issues. The rest of us will have to pay their prices or find alternatives.Ludwig V

    And the third world can suck eggs so that upscale liberal virtue signalers can feel good about themselves.

    There are two distinct problems. One is enabling as many people as possible to find decent jobs. That's a problem anyway. The other is enabling people whose jobs are phasing out to find alternative employment. That's more difficult. There have been many cases in the past (like phasing out coal) which have not been well managed. But it doesn't seem impossible. At least we could try harder.
    It quite likely that third world countries will suffer more. There's a lot of talk about providing additional help to them. That seems like a no-brainer, since unless they join in it will be hard to restore stability. But, curiously, it seems to be very difficult to make progress. Why? Who could possibly be opposing that?
    Does your link compare the damage to third world countries with the damage that will be caused by climate change? Or perhaps with the damage caused by existing free trade treaties?
    Ludwig V

    Let's agree to disagree. Sorry I brought it up. No wait, you brought it up and I let you bait me for a while.

    Clean air means less carbon dioxide and methane. Clean water means less plastic. Amongst other things.
    Sensible balance is good. But big corporations always end up defending their shareholders' interests and fail in the end. They just waste time and money.
    At least they threw tomato soup, which is easier to clean than pain. Paint has been used in the past for similar escapades. It can be cleaned off, but it is much more difficult to do so.
    Ludwig V
    her

    Ok. Well I'm all talked out here. I think we've long forgotten the topic.

    Did you hear about that windmill that fell apart, closing a beach during the height of tourist season? Fiberglass shards everywhere.

    https://www.cbsnews.com/boston/news/broken-wind-turbine-blade-atlantic-ocean-nantucket-massachusetts/

    ps -- This just came in. Couple of soup throwers were convicted, they're going to jail. So never mind on the soup. Looks like England has had enough of the eco-loons.

    https://www.thetimes.com/article/67d7c8f4-fbed-4ea1-94f3-252caa171723?shareToken=0b96051817d3dc87ee7ba226d3a18e34
  • US Election 2024 (All general discussion)
    I think we just don't agree on what a coup is. To me, not every power struggle that the incumbent loses is a coup.Echarmion

    Even ultra-lib Joy Reid called it a coup.

    Biden was not removed by lawful means.

    I don't really understand the show of indignation here. I'm sure you didn't just realise that the USA have a huge bureaucratic apparatus and that the president isn't actually required to make day to day decisions?Echarmion

    If there were a crisis, there's nobody making executive decisions. That's very dangerous for all of us.

    That is a much better question. It's impossible to know without having information from within the "war room". But even being in a situation where you're no longer sure whether the president is still capable of making emergency decisions is bad.Echarmion

    Glad you take my point.

    I agree it's unseemly. I'm not as worried though. At the end of the day there have always been weaker and stronger presidents. Under a weak president, power will tend to devolve to the VP, department heads and advisors. The fact that Biden's weakness is age related doesn't in and of itself make it more dangerous.Echarmion

    I'm glad you're not worried.

    I remember that everyone agreed that GW Bush was a fucking idiot. But noone called it treason.Echarmion

    Cheney and the neocons arguably committed treason. Many said so at the time. And if they didn't, they should have.
  • US Election 2024 (All general discussion)
    No surprise here: our economy and politics are run by overlapping elites.BC

    Never so obvious before. Propping up Biden for four years then swapping him out in a humiliating operation, if someone doesn't want to call it a coup. There will be repercussions from all this that are hard to see at the moment, but they won't be good.
  • Mathematical truth is not orderly but highly chaotic
    Anytime you want jazz album recommendations, just ring.TonesInDeepFreeze

    Ok!

    Jazz is one thing I know a lot about, unlike logic.TonesInDeepFreeze

    Haha very humble of you.
  • US Election 2024 (All general discussion)
    I wager that this little story is not over. The 25th amendment is invoked by the vice president and the cabinet. The vice president is Kamala Harris. Now she is the candidate for president. That’s a real, third-world coup, and that’s how desperate they are.NOS4A2

    They won't 25A him. They've just humiliated him, forced him to make a hostage video, and left a huge power vacuum at the top of the government. This could blow up very badly in the next six months.
  • US Election 2024 (All general discussion)
    A public pressure campaign? Why insist on a loaded word like "coup" when this is about who the candidate for the next election will be.Echarmion

    As I said, if you saw this play out in a corrupt foreign country, you'd call it a coup.

    They stabbed him in the chest, not the back. It was very visible and very public. Nothing hidden or conspiratorial about it.Echarmion

    Not conspiratorial? Perhaps you should look up the word. They stabbed Caesar in public too. That wasn't a coup?

    Even before the debate the common refrain was that Biden must demonstrate that he's not senile. He didn't. Biden had a lot of support at the time but he was not unassailable as the candidate. And in fact he failed to weather the storm. Nothing about this resembles a "coup", no organised group seized power in an orchestrated operation. One man lost his backing and the best placed person moved into the resulting vacuum.Echarmion

    They rigged their primary to get him nominated. They've been running a scam for three years. It blew up. But he is the legitimately nominated candidate. The insiders threatened him with God knows what, and he gave in. That's a coup.

    I mean probably the same people who run it most of the time? It's not like the president is required for day to day decisions.Echarmion

    So we don't actually have a president, just a figurehead run by an invisible cabal? We all knew that was true, but isn't it significant that this has now been demonstrated in public?

    And in a crisis, is there or isn't there an executive decision maker? And who, exactly, is that right now?

    It's half a coup. There's no president. This is very unseemly and there are great risks to this country right now. The Dems have arguably committed treason. They didn't lawfully 25A him. They did something unlawful. You want to defend that, knock yourself out.
  • US Election 2024 (All general discussion)
    I had to go and look that up, but that's absolutely crazy. Mob level shit.Tzeentch

    And then they call Biden a great patriot for gracefully stepping aside for the good of his country. Just like Caesar did.
  • US Election 2024 (All general discussion)
    I watched the Biden speech tonight. I've seen more believable hostage videos.

    As I understand it, he is not quitting the race for any particular reason; only "for the good of democracy." Meaning ignoring the will of fourteen million Democratic primary voters and replacing it with the decision of some Hollywood actors and big party donors.

    With respect only to his speech; that is, if you woke up from a year long coma and just saw his speech on tv tonight; why is Biden quitting the race? Can a president really get away with competing in primaries rigged for his nomination; keep insisting to the end that he is running; and then drop out while giving no reason at all?

    Are people going to buy this Soviet-level plot? Have we at last come to this?
  • US Election 2024 (All general discussion)
    If anything we can now test the theory of whether replacing one of the two unpopular candidates would ensure their victory. I mean Kamala is far from a generic Democrat, but it seems like voters don't really know much about her apart from her being VP and both sides are scrambling to define her right now so it'll be interesting to see how that plays out.Mr Bee

    Mr Bee, I saw your post last night. As I processed my news stream today it was "top of mind," as KJP once said. I found six items to help people process the Kamala phenomenon. This did come out a bit long, my apologies in advance.

    For the record I lived in the San Francisco bay area since the mid 1970s (no longer there) and have followed her career since before she became DA. I'm a seasoned observer of all things Kamala.

    So, six recent stories to put Kam in perspective.

    1) Brett Stephens questions the rush to coronation.

    In yesterday's New York Times, columnist Bret Stephens wrote an essay titled, Democrats Deserved a Contest, Not a Coronation.

    I've heard that some people can't read past the Times paywall, but it always comes up for me. I'll supply some quotes.

    Stephens is described by Wikipedia as a conservative, which perhaps mitigates my point a bit. Still, what he has to say is interesting. It gives people permission to think about putting the brakes on the runaway Kamala train.

    The last two times Democrats attempted to stage a coronation instead of a contest in choosing a presidential nominee, it did not go well. Not for Hillary Clinton in 2016. Not for Joe Biden this year.

    So why would anyone think it’s a good idea when it comes to Kamala Harris — the all but anointed nominee after barely a day?

    Maybe the answer is that a competitive process, either before or during the Democratic convention, would have been divisive and bruising. Or that Harris’s fund-raising advantages over any potential rival were already insuperable. Or that Democratic Party big shots (though not Barack Obama, at least not publicly yet) genuinely think the vice president is the best candidate to beat the former president.

    But the one thing the Democratic Party is not supposed to be is anti-democratic — a party in which insiders select the nominee from the top down, not the bottom up, and which expects the rank and file to fall in line and clap enthusiastically. That’s the playbook of ruling parties in autocratic states.

    It’s also a recipe for failure. The whole point of a competitive process, even a truncated one, is to discover unsuspected strengths, which is how Obama was able to best Clinton in 2008, and to test for hidden weakness, which is how Harris flamed out as a candidate the last time, before even reaching the Iowa caucus. If there’s evidence that she’s a better candidate now than she was then, she should be given the chance to prove it.
    — BrettStephens

    A point he makes is that she is a bad manager. Later in the piece he notes:

    The Washington Post reported in December 2021, following a series of high-level staff exits. “Staffers who worked for Harris before she was vice president said one consistent problem was that Harris would refuse to wade into briefing materials prepared by staff members, then berate employees when she appeared unprepared." — Stephens

    She doesn't put in the work. This point will be echoed in my next link.


    2) Kam missed an opportunity today to be seen as the next US president by everyone in the world.

    Not ready for prime time: Kamala Harris chooses to give a sorority speech over meeting a head of state. This piece is from right-leaning aggregator American Thinker, but it makes some insightful, nonpartisan points.

    Israel's prime minister Bibi Netanyahu addressed Congress today. Kamala did not attend.

    Many Democrats, particularly those on the left, are upset with Israel at the moment and want to make a point of insulting the leader of one of America's strongest allies. That is their right. About half of Congressional Dems chose not to attend.

    But Kamala is running for president. She COULD have risen above her partisanship and seized the opportunity to represent herself as the head of State at a moment when there is a power vacuum at the top. (Biden gave speech tonight. I've seen more convincing hostage videos).

    Imagine Kamala had gone to the airport to meet Bibi. If she had, every newspaper in the world would have published a front page photograph of Harris, representing the United States, greeting a close ally. One she has differences with, to be sure ... but she'd be seen as rising above politics to perform the duties of a head of State.

    Everyone in the world would have seen her as the acting US president.

    Instead, here's what she did. She decided to go express her partisanship and boycott Bibi. Instead, she went off to give a speech to a council of black sororities.

    The article makes the point, amplifying the reports that she doesn't put in the work, that she doesn't actually want to be bothered with doing the work of being president. She just wants the title and the perks.

    In the end she leaned into the you-go-girl feminism that's driving her recent popularity; at the expense of an incredible missed opportunity to present herself to the world as the acting president of the United States.

    She demonstrated her terrible political instincts and her unsuitability to be the leader of the free world. She is not up to the job. She doesn't know what the job is. In her mind she's still a leftist making a political point, not a head of State.

    This was a very telling episode to understand Kamala Harris.

    3) Jamal Trulove.

    A black man in San Francisco was wrongly convicted of a murder. As Wiki puts it:

    After he was framed by police for the 2007 murder of an acquaintance, Trulove was convicted in 2010, sentenced to 50 years to life, and imprisoned for six years.

    A California appeals court overturned his conviction in 2014 and he was retried in 2015 and acquitted. In 2016 he sued the city of San Francisco. In April 2018 a jury found the two officers accused of framing him guilty of fabricating evidence and failing to disclose exculpatory evidence. In 2019 the San Francisco Board of Supervisors voted to approve a settlement of $13.1 million.
    — Wiki

    The prosecutor on that case was Kamala Harris.

    It's very worth noting that Wikipedia does not mention her involvement in this case. Wouldn't it be useful for readers to know that a candidate for president framed a black man for murder and fought against his exoneration?

    That's why Wikipedia is not to be trusted on political issues. You see this kind of thing over and over.

    A detailed account of the case appears here. San Francisco Is Paying For Jamal Trulove’s Wrongful Conviction. Will Kamala Harris?.

    At last week’s Democratic primary debate, Harris rightly won plaudits for confronting Joe Biden on his history of opposing busing. But Harris cannot escape her past as San Francisco DA and California attorney general, which includes wrongful convictions like Trulove’s and inaction in other cases of law enforcement misconduct, including an informant scandal that consumed the Orange County DA’s office and its sheriff’s department. If Harris does not reckon with her failures in the criminal legal system, she could find herself in Biden’s position at the next debate: defending the indefensible. — Appeal

    4) A Facebook meme is going around to the effect that as California Attorney General, Harris put 1500 black men in jail for smoking pot.

    In fact-checking this before I repeated it here, I found a "debunking": Misleading claim says Harris jailed 1,500 Black men for marijuana

    The article went on to admit that she imprisoned 1974 people for weed ... but that some of them might not have been black men. Some were women or whites.

    You call that a debunking?

    After she was no longer Attorney General, she told black radio host Charlamagne tha God that "I have. And I inhaled – I did inhale. It was a long time ago. But, yes"

    That's Harris in a nutshell. When she wants to look tough on crime, she throws pot smokers in prison. When she wants to look cool, she tells a black radio host she smoked weed.

    She stands for nothing. She has no beliefs, no principles, and no convictions. She says and does whatever she thinks will bring momentary advantage to her ambition.

    5) BLM agrees with Bret Stephens.

    People who've followed Harris's career know her record of incarcerating black men. That's why today, Black Lives Matter came out against her un-democratic coronation.

    Black Lives Matter demands that the Democratic National Committee (DNC) immediately host an informal, virtual snap primary across the country prior to the DNC convention in August. We call for the Rules Committee to create a process that allows for public participation in the nomination process, not just a nomination by party delegates. The current political landscape is unprecedented, with President Biden stepping aside in a manner never seen before. This moment calls for decisive action to protect the integrity of our democracy and the voices of Black voters. — BlackLivesMatter

    They go on to enumerate complaints similar to ones I've made recently. That the DNC rigged their primaries. That "the DNC Party elites and billionaire donors bullied Joe Biden out of the race."

    Black women tend to like Kamala. Black men often don't. I don't have the statistics but there are a lot of black people coming out against Kamala online today. In her disastrous 2020 campaign (that ended in 2019), she polled badly with blacks.

    6) Two striking instances of Orwellian retconning of her past.

    - A study by GovTrack, "an organization that tracks congressional voting records," showed that in 2019 Kamala Harris was the most liberal Senator.

    Today, that web page is gone. "But the web page with the ranking, which was widely covered in news reports during the 2020 election, was recently deactivated. The link now displays a "Page Not Found" message. The Internet Archive shows the page was deleted sometime between July 10 and July 23, with some on X claiming the page was still up on July 22."

    - In 2021 Biden had a crisis on the border, the result of his overturning all of Trump's policies that were keeping a lid on the problem. Biden appointed Kamala border czar. She did nothing at all except humiliate herself in an interview with Lester Holt. When he called her on her lie that she'd been to the border, she said "I haven't been to Europe, either." Classic Kamala. Great with a scripted line, but defensive and careless when speaking off the cuff. You know the clip. People were shocked when they saw it. Liberals especially. They had no idea.

    The border is therefore a legitimate line of criticism from the Republicans. So what are the leftist media doing? Denying she was ever the border czar. If you claim Kamala was ever the border czar, you're repeating Republican propaganda.

    Axios ran a story today (Wednesday) that Harris "never actually had" the title of border czar.

    Of course numerous critics quickly pointed out that they had indeed claimed exactly that. Axios said, "After being called out, Axios issued an editor’s note to acknowledge that “Axios was among the news outlets that incorrectly labeled Harris a ‘border czar’ back in 2021.""

    Of course they were not incorrect in 2021. They were caught lying today when they claimed she wasn't the border czar. There are dozens of news videos showing Dem politicians and MSM reporters calling her the border czar at the time.

    This Orwellian retconning is exactly what Winston Smith, the protagonist of 1984, did for a living. He made news accounts of the past conform to the ever-changing party narrative of the present. In the digital age it's all too easy.


    Well that's my curated list of Kamala miscellany this evening.

    It's possible that Hollywood and the media will sanitize her past, coronate her, and get her over the top. She could win. I still give her a 25% chance. She's having a Brat summer dontcha know.

    Or, the Kamala scam could blow up the way the Biden scam did, and the American people will hand the Democrats a defeat for the ages.

    In which case they'll blame it on racism and sexism and learn nothing.
  • US Election 2024 (All general discussion)
    Some are saying the earth is flat.Echarmion

    A lot more are calling it a coup than are claiming the earth is flat. What would you call it? The Dems lied for three years to hid Biden's infirmity, then stabbed him in the back. When Nancy Pelosi comes to you and says, "We can do this the easy way or the hard way," and a letter is put out that you clearly didn't write, that's a coup.

    Biden did make a brief appearance today. So the narrative has gone from "Sharp as a tack" to "Remarkably lifelike." Still no idea who is running the country.

    Of course the MSM spin is that Joe is a patriot for gracefully putting his country first. Caesar stepped down gracefully the same way.
  • 0.999... = 1
    I'll settle for that. It's a very marginal point, anyway.Ludwig V

    Ok glad we got to the bottom of that!

    Both this argument and the one about evidence are actually aimed at the same point. Once you have introduced probability as an interpretation/application of the formal function, it is very difficult to ignore reality - metaphysics.Ludwig V

    Ok.

    I have read about this, but didn't realize that's what you meant. It's an interesting take on the idea that we construct mathematics - and some other things as well. However, if it is fiction, it is not the same kind of fiction as literary fiction. However, fake means pretending to be something you are not. Neither is doing that.Ludwig V

    Fictionalism is a useful point of view. Avoids having to defend what math "means."

    I'm sure that many of them - especially the loonies - are virtue signallers. It doesn't follow that they all are. There is a real issue here.Ludwig V

    Oh you baited me about the eco-loons. I'm all for clean air and water. I'm also for modern civilization. The point is to strike a sensible balance, not to throw tomato soup on paintings.

    There's a line of thought in eco circles that accepts that the world will not be able to make the changes quickly enough to make much difference. I think that's right. The thing is, the disruption and costs of serious climate change will be greater than the costs of changing now. If we could change now, and do it right, the disruption could be kept to a minimum. There'll be lots of work in the new industries.Ludwig V

    We'll all toil in the windmill factories? I think I better quit while I'm behind here. Eco hysteria is a luxury belief. Green policy hurt third world is one random link I found.

    Fusion could do it, and it seems to be getting closer. Fission leaves waste. There used to be a lot of concern about what to do with it. I think the plan now is to bury it and leave it alone - for 100,000 years. You can't say those guys are not ambitious.Ludwig V

    The ITER project had another setback. Nine more years delay, another five billion dollars over budget. Fusion would be nice if they can make it work. The fission waste is a problem, but you can't run the world on windmills.

    Don't worry. The last Government passed a new law, restricting free speech to ensure that all protest can easily be ignored. I doubt that the new Government will prioritize repealing it. The people who've been imprisoned will become martyrs - and the whole thing will escalate.Ludwig V

    I support free speech. Blocking roads is not speech.

    Oh, yes, it's all over the media. From here, it seems that the chaos will continue and spread. I don't think it will end with the election, either.Ludwig V

    I hope things don't get too much worse. At the moment nobody knows if we have a president.
  • US Election 2024 (All general discussion)
    Trump has a now very familiar problem with the reality situation.BC

    He's the old one now. Kam at least has put some youth into our political process. It'll be interesting to see how this plays out.
  • Mathematical truth is not orderly but highly chaotic
    The albums 'Conversations With Myself' and 'Further Conversations With Myself'.TonesInDeepFreeze

    Thank you. "Today I learned."
  • US Election 2024 (All general discussion)
    What difference does it make to the country? The net result is the same.Echarmion

    Whatevs.
  • Mathematical truth is not orderly but highly chaotic
    So did Bill Evans.TonesInDeepFreeze

    Help me out. The jazz player?
  • 0.999... = 1
    I'm not saying that if to-day is Sunday, the probability that yesterday was Saturday is anything other than 1. Of course not. I'm saying that because today is Sunday, probability doesn't apply to the proposition that yesterday was Saturday.Ludwig V

    I don't see why not. If a bookmaker had to set odds on the proposition, he'd assign it as 1. Anyway let's agree to disagree.


    That bet is money in the bank, so long as the odds show a profit. But who would take the other end of it?Ludwig V

    Nobody. That's why it's got probability zero!

    I suppose you might find a taker who would give you your money back. But that would be an empty ritual. There's a good reason why bookies close their books when the race is over.
    More politely, where there is no risk, there is no bet.
    Ludwig V

    Hmmm. "No action." As a bit of a gambler back in the day, I understand that!! Probabilities 0 and 1 are no action. Not a valid bet! So I can sort of relate to your point.


    Ah, this is a different can of worms. "Credence" is degree of belief, isn't it? And belief concedes the possibility of falsehood. So that makes sense.
    But when there is no possibility of falsehood, we do not speak of belief; we speak of knowledge. So if you assign a credence to "Yesterday was Saturday", you are allowing the possibility that it wasn't. But if you assign a credence of 1, you are excluding that possibility.
    In my book, credence doesn't apply.
    Ludwig V

    I better quit while I'm behind here.

    I think "preferable" is better than "should". I'm happy with that.Ludwig V

    Right. To account for situations where we can't possibly have any evidence, or know what's going on, but we have a subjective opinion and degree of belief anyway.

    H'm. That's a new take on mathematics.Ludwig V

    Fictionalism. It's all fake. But interesting and useful, so why not do it anyway and enjoy it.

    https://plato.stanford.edu/entries/fictionalism-mathematics/


    I can understand the idea that axioms and definitions can be posited in a spirit of exploration. The point in that case is to work out the implications of certain ideas. But the axioms and definitions, even if they are, in some sense, provisional, need to be clear and consistent, don't they?Ludwig V

    Clear, with some study. And consistent, well we often can't even prove our axioms are consistent. Nobody knows for sure if the axioms of set theory are consistent.

    And paraconsistent logic is a thing these days. Logic in which we can allow a certain well-controlled amount of contraction.

    https://en.wikipedia.org/wiki/Paraconsistent_logic

    Anyway, you're not telling me that the axioms and definitions of probability theory are in some sense provisional, are you?Ludwig V

    Provisional. Explain what you mean by that word. They're seemingly sensible, but they immediately lead to anomalies like the famous non-measurable set and the Banach-Tarski paradox.

    The probability axioms are highly useful and natural, but they bite.

    https://en.wikipedia.org/wiki/Vitali_set

    It looks as if I have got you started. There are real and serious issues at stake in these disagreements. (You didn't mention climate change.)Ludwig V

    I think the eco-loons are self-centered virtue signalers . Every time you make energy production harder you starve a few hundred thousand third-worlders to death. The Green agenda is starting to crack in Europe. We all like clean water and air, but destroying our economy in the name of "the planet" is suicidal and cruel. The billionaires flying their private jets to climate conferences give the game away. The Obamas own beach front property in two states. They must not be too worried about the seal level rising.

    I'm for nukes. Environmentally clean and abundant energy to run our world. Some of the eco-loons would have us living in grass huts. Of course THEY wouldn't live in grass huts. The rest of us would.

    I see in England that they threw a few highwayblockers in prison for 4-5 years. Did you see the story? A good start, I say. And the next time some trust fund vandal glues their hands to a museum floor, just leave them there.

    https://abcnews.go.com/International/wireStory/british-climate-protesters-plotted-highway-shutdown-record-harsh-112069763

    Aren't you glad you asked :-)

    The biggest problem is that the parties have given up listening to each other. Meanwhile, Putin and Xi Jinping with Kim Jong Un and Ali Khameini are calculating that the West is so divided that they can re-make the world in their own image. There's a serious need for some waking up on all sides. Perhaps one day, the threat will be so great that we'll be forced to recognize that the things that we share are more important than the things we disagree about. I hope we don't wake up too late.Ludwig V

    Is the Biden coup getting much play where you are? He published a letter saying he's dropping out of the race. But there's no video or photos of him signing the letter, and he hasn't been seen for five days. I have no doubt the global competition is taking note. The leader of the free world is the victim of a coup by his own political party.
  • Infinity
    Thus, were set theory removed mathematicians would perish.jgill

    I said no such thing. If the freeway didn't exist, I'd take the old dirt road that people used before they built the freeway. I'd still get where I'm going. Set theory is the modern general framework for most math. That doesn't mean math couldn't get along without it. But if you want to do math these days, you have to use the language of set theory simply because everyone else does.

    I think not. But mathematics would not be nearly as robust as it is today. My humble opinion.jgill

    Yes ok. But people are into alternatives these days. Category theory and homotopy type theory are two big alternative foundational frameworks. It's all a matter of historical development.

    Back in the late 1960s my advisor remarked on the separation of the nitty gritty at ground level and the efforts to fly high and look down on mathematics, an abstract perspective to see how the various parts fitted together and document how parts from one branch were like parts form another. He gave me a choice and I felt far more comfortable working in the lowlands, (particularly after learning a bit about algebraic topology). I came into the profession exploring convergence and divergence of analytic continued fractions and related material. Pretty much an extension of the efforts during the 1700s and 1800s to solidify those properties of series. Grubby stuff, but I still enjoy grovelling in it. :cool:jgill

    Sounds like fun.
  • Even programs have free will
    According to the page on the subject, determinism and predeterminism are "closely related":Tarskian

    After reading all that i was a little unclear on pre- versus regular old determinism. The text passages are the kind of philosophical writing that always makes my eyes glaze.

    If you believe that everything has a reason, it does not mean that you also know that reason. Predictability requires indeed both.Tarskian

    Hmmm, determinism doesn't mean that everything has a "reason." If you have some Rube Goldberg machine and you start it, it's perfectly deterministic. But it doesn't have any "reason." It's just one thing causing the next thing.
  • US Election 2024 (All general discussion)
    An apt comparison, but even rabid jackals, never mind healthy ones, form 'packs' or 'tribes'. As in 'a pack of wild dogs'. Jackals are canids.BC

    Not entirely sure I caught that. Was I right or wrong to analogize the media to a pack of rabid jackals?

    I'm always struck by the way the narrative turns on a dime. One day, news videos of Joe's decrepitude and senescence are cheap fakes. The next day everyone turns and stabs the guy in the back. It's ugly to watch.

    The question should be, "Is he too cognitively impaired to BOTH run for president and be president?" There's a big difference between managing the job for the 5 months and managing the job for 53 more months, should he have been reelected.BC

    It's a good question if he's doing the job today. Missing in action for five days. He signs a letter dropping out of the race and he's too ill to have his picture taken. But he's perfectly fine to do his job?

    I was in favor of him NOT running for another term before the famous debate. Both Biden and Trump are too old, and Trump has even more cognitive problems, particularly with the reality situation, than Biden.BC

    If the Dems had just held competitive primaries, Biden's problems would have been exposed and they'd have a younger and stronger candidate right now who was actually chosen by the Democratic voters, and not by the party insiders.

    As to whether Trump or Biden are farther gone, we can agree to disagree. I will agree that Trump's lost a couple of steps from eight years ago. Look at what he's endured. Whether you think he's guilty or not, all those court cases must have taken a lot out of him.

    This is not the first election where people had to hold their nose and vote for the candidate they hate a little less thanthe other one.

    Kamela has more than enough on her plate successfully campaigning, never mind trying to become an experienced incumbent in just a few months.BC

    I can see your point. But I still think that incumbency is very powerful. And if Joe is in as bad shape as he appears to be, it would be better for the country and certainly better for Kamala to just 25A the guy and be done with it. Or have Nancy get Joe to resign the presidency. Report is that she told Joe he could drop out of the race "the easy way or the hard way." Nancy seems to be the one running things in the Dem party.
  • Mathematical truth is not orderly but highly chaotic
    Better deep in knowledge and shallow in misunderstanding. Better deep in love and shallow in hate.TonesInDeepFreeze

    Choke me in the shallow water before I get too deep. -- Edie Brickell.

    Then you're discussing with the wrong person.TonesInDeepFreeze

    I have some darned fine conversations with myself.

    You may prefer whatever you want; there's no need for forgiveness for preferring whatever you like; meanwhile, I prefer to show how you are wrong in saying that 'true' is not defined entirely with the notion of interpretations and not the notion of axioms.TonesInDeepFreeze

    You are free to do so, of course.
  • US Election 2024 (All general discussion)
    What happened to Sanders during 2016 was pretty wild. Hands down he would have won, but, the Clinton's wanted it their way and look what we got...Shawn

    Biden made that same point the other day, noting that the same kind of Dem chicanery that they're using on him is how they ended up losing to Trump in 2016. And speaking of Joe, where is he? Hasn't been seen for five days since posting his resignation letter on an X account run by staffers, on letterhead missing the presidential seal, and bearing a signature that appears not to match his signatures on several recent executive orders.

    If this happened in a corrupt foreign country it would look like a coup. Since it's happening right in front of our faces in our own country, a lot of people take it all at face value. I do not personally believe anything going on lately, from the Trump assassination attempt to Joe dropping out of the race but remaining our invisible president, is to be taken at face value.
  • US Election 2024 (All general discussion)
    Some are calling it a coup. Certainly if you saw this plot play out in some corrupt foreign country you'd call it what it is. Biden hasn't been seen in five days. I heard that he called in to Kamala's rally, but his remarks were brief and he sounded cogent. It may well have been a deep fake. The technology is very good.

    The last thing he said was that he is in the race to win it. Then we saw him creaking slowly up a flight of airplane stairs, and then someone posts his resignation letter on his X account, which is known to be run by staffers and not personally used by Joe. An image is flying around social media of his signature on his four recent executive actions, which do not match the signature on his letter. The letter does not bear the presidential seal. No photograph or video exists of him signing it. Then he disappeared totally for five days, officially recovering from covid.

    This raises another question. If he's too sick to even have his picture taken signing a letter, is he too sick to fulfill his presidential duties. In November, 201, Biden was placed under general anesthesia fo his colonoscopy, and Kamala officially assumed presidential authority for an hour an a half or so.

    If Biden is too impaired, even temporarily, to perform the duties of his office, the public has a right to know. And if he's not impaired, why haven't we even seen a still photograph of him in five days, let alone live video.

    Some people online are snarkily asking for proof of life, which is what you typically demand of kidnappers to show that their hostage is still alive before you pay the random. And it's not a bad question. Where is Joe, and who is acting as president? Is he even alive? And if he is too cognitively impaired to run for president, how on earth can he continue to BE president? With two war going on? Who's in charge?

    It's entirely possible that he has no idea that he's dropped out of the race. Nothing is being told to us, and the Democrats are so happy to be rid of their Biden problem they aren't asking any questions.

    Kamala's got the Dems thrilled. It's very similar to her 2020 campaign launch in Oakland, California, in 2019. She drew 20,000 people and immediately became the rock star candidate. Calling Biden a racist and selling "That little girl was me" T-shirts turned out to be her high point. The next debate she got taken apart by Tulsi Gabbard, and never recovered. She dropped out in 2019, never even making it to the first primary election. She was polling badly in her home state of California.

    That's Kamala. On paper she looks terrific, checks all the right boxes. The more people get to know her the less they like her. Also she has a big negative. She owns all of the Biden-Harris administration's problems. The inflation, the wars, the immigration disaster. Especially the latter, as Biden appointed her immigration czar and she was an utter failure, only managing to humiliate herself telling Lester Holt, "I've never been to Europe," when he challenged her on not going to the border. That's Kamala. She flusters and screws up when she has to go off-script under even mild pressure.

    Biden was polling badly on the issues before the public saw his humiliation at the debate. It's Biden's policies the public doesn't like, and Harris owns those policies herself.

    If she gets traction the Dems will go all-in behind her. If not, they'll give her the hook and trot out the next contestant. They have four weeks from today till the start of their convention.

    I do congratulate the Dems for getting their act together and settling on a provisional candidate they can all live with. I can see why they don't want an open convention. Too much risk and potential chaos. Kamala's nice and safe for now. She appeals to a lot of Dems. She delivers scripted lines and speeches very well. And she can stay up past 4pm, a big upgrade from Biden.

    But what did happen to Biden? The Dems propped him up for three years, then rigged their own primaries to get him nominated with only token opposition (anyone remember Dean Phillips?) and now they throw him over when he's polling badly. Reportedly Nancy Pelosi went to Joe and said he could go "the easy way or the hard way." This is the guy who got fourteen million votes in the Democratic primaries, and allegedly eighty one million in the 2020 general election. No American has ever cast a single vote for Kamala Harris for president.

    I don't want to hear anyone ever again telling me that Donald Trump is a threat to Democracy. The Democratic party wouldn't know democracy if it bit them in the donkey. The back-room honchos decide what they want, and screw their own voters. 2016, 2020, and now 2024. Will the public punish the Democrats for lying to us about Biden's condition for four years and now running a coup to install a candidate chosen by the inner party and not their voters? Whether or not it ultimately succeeds, it's not democracy. It's not the will of the people.

    A lot of people hate Trump and Kam has some strengths. She's got a great angle, a former DA who prosecuted sex crimes versus sexual assaulter Trump. She's strong on abortion. She will be a tough candidate if she can overcome her known issues. I'd give her a 25% chance to win. It could happen.

    In other news, the condemnation of Kimberly Cheatle is savage and bipartisan after her train wreck testimony today. We still don't know how many shots were fired, what directions they came from, who killed the 20 year old. Usually when a crime occurs, the cops hold a press conference and tell us what they know. Why are we being stonewalled on the attempted assassination of Trump, not even allowed to hear the most basic facts? I caught some of the hearings this morning, it was bad. Even Dems Ro Khanna and AOC lit into her for incompetence and stonewalling.
  • US Election 2024 (All general discussion)
    What happened to Sanders during 2016 was pretty wild. Hands down he would have won, but, the Clinton's wanted it their way and look what we got...Shawn

    Yes it's funny that the other day Biden himself said, "That's how we got Trump in 2016," meaning the Dems letting the party insiders override the will of the voters. He still has political instincts. It's very unclear whether the Democrats have improved their situation or not.
  • 0.999... = 1
    Fair enough. We're obviously not going to reach agreement. For what it's worth, my diagnosis is that we disagree about the boundaries of the relevant context. For you, the assignment of 1 to the probability of an outcome which has actually occurred, is sufficiently defined by the context of probability theory. For me, it isn't.

    I'm perfectly happy with our agreement (?) that it can be described as empty. That bothers me, but not you.
    Ludwig V

    Well ... letting the matter drop would be for the best. But ... can you explain to me how today being Sunday, the probability that yesterday was Saturday is anything other than 1?

    I mean, suppose that you had to place a bet on the proposition. What do you think the odds should be?

    That is, if today is Sunday, what is your credence that yesterday was Saturday?

    I can understand, roughly, why you (plural) believe that and there's a sense in which I agree. I just don't think it is the whole story.Ludwig V

    Well, nothing is the WHOLE story. Life is complicated.

    Yes, I do. But I also think that credence should be influenced by evidence.Ludwig V

    You have already stipulated to the opposite. You have, if I have understood you correctly, agreed that it's NICE if credence is influence by evidence; but sometimes there's not enough evidence or I'm not qualified to evaluate the evidence. Then I must NECESSARILY form a subjective degree of belief without benefit of evidence. It's your use of "should" that I object to. I could live with "preferable," but not "should."

    I hope you weren't just appealing to a vote. But if you mean that I should take more seriously the opinion of others who can be expected to know what they are talking about, then your question is valid. My view is not at all standard. That doesn't bother me. What does bother me is that the orthodox view is comprehensible and so not irrational. I'll have to reconsider.Ludwig V

    If you were a betting man, what would you bet that today being Sunday, that yesterday was Saturday? What is your credence for that proposition? How should a bookmaker set the odds?

    Yes, I can see that. If you'll forgive me, I think that mathematicians and especially logicians tend to be to keen to get to the formalization and too quick to move from setting up the formalization to exploring it. I get stuck on the question what the value is of beliefs that have no connection with the world. To believe something is to believe that it is true.Ludwig V

    Don't you like fiction? Do you have the same complaints about the novel Moby Dick ("He tasks me. He heaps me.") and the game of chess; one a work of fiction, and the other a meaningless formal game with entirely made-up rules?

    I agree with that. I went looking for the UN policy statement about this, but couldn't find it. But I did find a string of warnings about the dangers. Whatever went on in the US, disagreement was not suppressed everywhere.Ludwig V

    In the US it was ugly. People lost their medical licenses for expressing scientific skepticism. Teachers, workers of all kinds lost their jobs. People lost friends. The mass formation, as some called it, was terrifying. For the first time I truly understood Nazi Germany. Excuse the argumentum ad Hitlerum. I saw how a society goes mad. I was immune by personality. I kept my head down, and since I'm not much involved in public society, I didn't have to risk anything. I just waited it out. But I'm wary of my fellow Americans now in a way I previously wasn't.

    Certainly. Their problems are different, but nonetheless based on their history. Like the Brexiteers, they want to have their cake and eat it. The difference is that their ambivalence is the question of Russia. The problem exists, but less acutely, for the whole of the mainland. Geography is inescapable, even in these times.Ludwig V

    Immigration is an issue on both sides of the pond. Liberty versus top-down control. The wokesters versus the people who never voted for the woke policies. The double standard of justice, a kid jailed fo making bicycle marks on a Pride crosswalk, while Antifa defaces statues. Don't get me started. LOL.

    Quite so. I forgot about the Lusitania.Ludwig V

    I saw a really good tv movie that cut between the action on board ship, on the German U-boat, and in the halls of the British admiralty. I read up a little afterward. A distinguished jurist was appointed to lead the inquiry. Afterward he called it, "a dirty business," and retired. They screwed the captain to cover up Admiralty complicity.
  • Mathematical truth is not orderly but highly chaotic
    That is a deep misunderstanding.TonesInDeepFreeze

    Better deep than shallow.

    I discussed this with myself and determined I'm right.

    I prefer not to argue the point, if you'll forgive me.

    Also, look at it this way:

    Given a set of axioms G and a different set of axioms H, it may be the case that the class of models for G (thus for all the theorems from G) is different from the class of models for H (thus for all theorems of H). So let's say S is a member of G or a theorem from G, and S is inconsistent with H. Then, yes, of course, S is true in every model of G and S is false in every model of H.

    But, given an arbitrary model M, whether S is true in M is determined only by M.
    TonesInDeepFreeze

    I'll read and consider his when I get a chance. Thanks for posting it.
  • US Election 2024 (All general discussion)
    Joe has to resign the presidency, the sooner the better. There's are negative and positive reasons.

    The negatives are that as long as he's President, Karine Jean-Pierre is going to be asked:

    1) If Joe Biden is too cognitively impaired to run for President; then isn't he too cognitively impaired to BE President? And since Joe is clearly not running the country and hasn't been for some time, who has been and IS running the country? Obama? Jill "Edith Wilson" Biden? And remember, the media smell a wounded politician like a herd of rabid jackals. Have you noticed the tone shift in the White House briefing room lately? KJP is under attack like she's never experienced before.

    2) Is Joe going to preemptively pardon son Hunter, brother James, and other members of his family, for Federal felonies they may be subject to regarding the Biden family's decades of grift, bribery, and influence peddling involving foreign countries? This family business is a well known open secret in Washington, and is denied by the Dems in exactly the same way that they denied Biden's progressive cognitive impairment. Meaning, they'll deny it everyone finds out about it, then they'll all pretend to be shocked and they'll savage him. So he has to issue the pardons before he leaves office, and he might as well get it over with fast.

    But there's a huge positive and beneficial reason he should resign the presidency first thing tomorrow morning.

    It makes Kamala the incumbent. The "historical" incumbent. Incumbency by itself is a huge advantage, easily worth five or ten percent of the vote. And just as in 2008, centrist-minded Republicans might have said, well, McCain's a corrupt wamongering jerk, war hero nothwithstanding; and I don't want to have to think of myself as a closet racist. So I'll vote for Obama. A lot of votes went that way. If you were any kind of independent or centrist who was not a doctrinaire Republican, you voted for Obama for the historical symbolism of a black man becoming President in this country.

    Kamala would get those same independents. She'd energize all the women in this country. As bad a politician as she is, she could win on symbolism. Symbolism has a lot of power among us humans, like the Trump bloody fist flag photo.

    So I say that if Biden pardons his family and drops out tomorrow morning, that is the Dems' best shot at an electoral victory in 2024. Get it all over wish and by election day the public will have forgotten Biden entirely. The longer this fiasco goes on, the more the American people are reminded every single day of the massive fraud the Democrats ran on the nation. The sooner they get past that the better.

    Personally I hope he doesn't do it. Let the press ask KJP every day. Let the party civil war continue. Already Pelosi and the Obama have not endorsed Kamala, calling for an open process. Under the circumstances a non-endorsement is equivalent to an anti-endorsement. The Clintons and the Bidens are behind a Kamala coronation, for the third consecutive DNC back-room deal rammed down the throats of their own voters. Saving democracy indeed.

    Now you can see why the Dems forced Bobby Jr. to leave the Democratic party. Else he'd be the heir apparent and the DNC hates Bobby Jr.

    I'm just curious, I get that some people just hate Trump. But aren't the liberals getting sick and tired of getting shafted by the DNC? They could have held a competitive primary this year, Joe's condition would have been exposed, and Gavin or Gretchen would be a strong candidate. The Dems did this to themselves. And to the fourteen million Democratic primary voters who voted for Joe, while the media were telling them Joe's sharp as a tack. Aren't any liberals righteously angry about all this chicanery going back to 2016 and 2020 and now 2024? The DNC does not give a hoot about the will of their own voters, or "democracy." The centrist warmongers pick their candidate no matter what their voters think. How long will Dem voters just fall into line behind whatever corrupt hack the central party coronates? After Trump is gone and Trump hate is no longer a factor, what will hold the Dem party together?
  • Mathematical truth is not orderly but highly chaotic
    It is not the case that 'mathematical truth' means ''axioms plus an interpretation'TonesInDeepFreeze

    If you fix an interpretation and change the axioms, you'll get different truths. This is obvious. Not worth arguing about.
  • Mathematical truth is not orderly but highly chaotic
    It doesn't matter whether S is an axiom or not. The definition doesn't mention 'axiom'.TonesInDeepFreeze

    You should go back to what I originally said that you objected to, and you will see that I am right.
  • Mathematical truth is not orderly but highly chaotic
    I don't know what that means.TonesInDeepFreeze

    If your statement S is an axiom, you will understand my point.
  • Mathematical truth is not orderly but highly chaotic
    The truth of a sentence is per interpretation, not per axioms.TonesInDeepFreeze

    Hmm. You could fix the interpretation and change the axioms to show that truth depends on the axioms plus the interpretation. That's not the usual way of thinking about it but I believe it could be shown.

    Some sentences are true in all models. Some sentences are true in no models. Some sentences are true in some models and not true in other models.

    Axioms are sentences. Some axioms are true in all models (those are logical axioms). Some axioms are true in no models (those are logically false axioms, hence inconsistent, axioms). Some axioms are true in some models and not true in other models (those are typically mathematical axioms).

    The key relationship between axioms and truth is: Every model in which the axioms are true is a model in which the theorems of the axioms are true. And every set of axioms induces the class of all and only those models in which the axioms are true.
    TonesInDeepFreeze

    Ok.

    (1) I would avoid the word 'valid' there, since it could be misunderstood in the more ordinary sense of 'valid' meaning 'true in every model'. What you mean is 'well-formed'. But, by definition, every sentence is well-formed, so we only need to say 'sentence'.TonesInDeepFreeze

    Yes you're right.

    (2) If by 'independent' you mean 'not determined to be true, and not determined to be false', then there are no such sentences. Per a given model, a sentence is either true in the model or false in the model, and not both.TonesInDeepFreeze

    Yes ok.

    That depends on what things are truths.

    If a truth is a true sentence, then there are exactly as many truths as there are true sentences, which is to say there are denumerably many

    If a truth is "state-of-affairs", such as taken to be a relation on the universe, then, for an infinite universe, there are more "truths" then sentences.
    TonesInDeepFreeze

    Yes that's a bit of murkiness in the paper the OP linked. But Chaitin and the paper author seem to take truth in the latter sense.
  • 0.999... = 1
    The use of "probability=1" is defined in the context of the table (function), that is, in context where a range of possible outcomes is given, one of which will turn out to be the outcome. Outside that context, it's use is not defined. Or rather, its use is defined as "= true". That is quite different from "probability (A v B vC..) = 1" meaning "the total of the probabilities of A v B v C... is 1", that is, its use in defining the range of the probabilities of the outcomes. So it serves no purpose, apart from confusing me.Ludwig V

    We should go back to agreeing to disagree, since your understanding of probability 1 is contrary to, well, everyone else's. Is this a standard philosophical view? IMO you are choosing to confuse yourself about something very simple.


    Meaning is a slippery word. One might want to object that the meaning of the word "table" is an object in the world. But we make the words and we use them.Ludwig V

    There's no meaning in symbols. That was the thesis. Mine and Searle's, at any ratet.

    I would put it stronger, but it is true that credence is not necessarily based on conclusive evidence, and may be not be based on evidence at all.Ludwig V

    Then you agree with my point. Credence could be influenced by evidence but need not be.

    You're right. Most of what we know, we know at second hand. If we had to prove everything ourselves from scratch, we would be very limited. Standing on the shoulders of giants and even midgets is essential. Philosophers like to brush that aside and only pursue the gold standard. There shouldn't be any problem about assigning a credence to what we are told by others. I would count it as evidence. Why not?Ludwig V

    They might have little or no evidence themselves. Credence is just what people believe, evidence or not. If you redefine evidence as "what my friends believe," that way lies mob rule.

    Quite so. We react instantaneously and without conscious thought to most of what's going on around us. We would never keep up if we had to sit down and reason everything out.Ludwig V

    Right. Hence credence. I think you are agreeing with me. Credence is a nice concept because we can apply the rules of probability to it, but we needn't know anything about the world to have subjective beliefs.

    But, if I've got any sense, I will give more credence to credences assigned by someone who knows what they're talking about over credences assigned by someone who doesn't. That's reasonable, surely?Ludwig V

    Sure.

    Well, the opposition in the UK were certainly not silenced. Their voices were heard throughout. The problem is that without an estimate of what would have happened without lockdowns, we have no way of assessing their success. It's has always been regularly used with Ebola outbreaks, so it must have its uses. But those incidents have been relatively contained. I think the scope and duration of the COVID lockdowns was the problem.Ludwig V

    Ok well I should terminate my own thread hijack about this subject. But a quick lookup showed that Ebola lockdowns were only in two regions. The covid lockdowns were virtually global and were not a good idea.

    It's not that simple. Every time you sign a treaty, you give up some sovereignty. It's a question of balance - quid pro quo.Ludwig V

    Some Europeans are getting restless, are they not?

    It's long and peculiar story. There'll be lots of stuff on the internet if you want to look it up. The problem was that it needed free access to both UK and Republic markets. While both were in the EU, it wasn't a problem. But when the UK left, it was not possible for them to continue free trade with both and yet could not give up either. It was obviously insoluble from the beginning, but nobody bothered until the reality hit.
    They seem to be reasonably satisfied with the most recent arrangements, but they are a bit of a lash-up.
    Ludwig V

    Ok, I should look that up.

    I'll bet. It's a very beautiful place. The whole island is - outside Belfast.Ludwig V

    Yes I'd love to go back.

    Well, there's always been a counter-narrative. The left wing have never liked him. There was the Sidney Street siege, Gallipoli, the famine in Assam in 1943, and pet research projects that wasted a lot of money and it took a lot of persuading to get him to accept the invasion of France. No financial scandal that I know of, which makes a nice change. I think most people accept he made a critical difference in WW2.Ludwig V

    He all but fired the torpedo himself at the Lusitania to get the US into WWI. The Admiralty records are sealed to this day.
  • Infinity
    5 views per day. The title doesn't resonate with many apparently (including me). Nevertheless, an important movement.jgill

    Virtually every professional mathematician lives in the world created by this movement. Nobody notices because it's like fish not noticing water. It's just the familiar founding of analysis in set theory.
  • Mathematical truth is not orderly but highly chaotic
    Thank you. This is similar to the group theory example. It makes more sense now.jgill

    Glad that helped.


    My favorite game on the internet is guessing the number of page views per day for math and other topics. I guessed 126 here, whereas it is 111. Close, but no cigar.jgill

    That's interesting. Which page views? I think you've mentioned in the past that you look at papers written or something like that.
  • 0.999... = 1
    This is a bit embarrassing. I was using a bit of philosophical jargon, which seems to be out of date. You must have been wondering how empty sets were relevant. The expression derived from the logical positivists who classified tautologies as empty or trivial because, although they are not false, they do not assert anything. For them, proper, non-empty, statements were those that could be verified or falsified. The idea is used in Peter Unger's book Empty IdeasLudwig V

    That makes perfect sense. I understand you now! Yes I was thinking of the empty set. Perhaps what you're describing I might call, "invalid," or an error condition in programming. In programming, an operation can succeed; or it can fail; or it can blow up entirely and throw an error condition.

    A tautology that doesn't assert anything is kind of a dead end in the reality tree, if I may wax poetic. If we're processing it, it's an error. It doesn't have any meaning.

    Is that about right?

    But if that -- then I still don't get it! Probability 1 says that something is certain to happen. If I add 1 plus 1, I am certain to get 2. If we have a slow computer, we put in 1 plus 1 today, and we are certain, with probability 1, that the computer will output 2 tomorrow. What's wrong with that?

    Note that I introduced time into math, by imagining we're doing math on a slow computer!

    Unger’s argument is that thinkers used to put forward arguments whereby “if what they said was true then reality was one way. If it was untrue then it was another way .... They were sticking their necks out.”
    See Review of Unger "Empty Ideas (I don't recommend the book. For all that the review talks about philosophy being fun, which I approve of, this book is hard going for rather small rewards.) I don't agree with this application of the argument, but the idea can be useful.
    Ludwig V

    Since you don't recommend the book I will not dispatch a clone to read it!

    But surely, putting 1 + 1 into a computer and expecting to get back 2, is not an empty idea! I don't see that.

    Some examples may help.
    1) An obvious case is "This sentence is true".
    2) If I assert that snow is white, it is empty for me to assert in addition that I believe that snow is white.
    3) Tarski's redundancy theory of truth (which, in case you don't know, is popular among philosophers) says that "snow is white" is true iff snow is white.
    4) The probability of p = 1 iff p is true iff p
    Ludwig V

    I took a MOOC in mathematical philosophy, and the prof showed us that "Snow is white" is true if snow is white. That was several years ago, and to this day I don't really get it.

    But anyway, mathematicians are trained to get used to empty objects. There's the empty set, and the empty topological space, and so forth. You get used to accepting vacuous arguments. So I don't see empty ideas as a problem. An empty idea is still and idea. The empty set is a set.

    Yes. But I thought that unintended consequences were events in the empirical world.Ludwig V

    That was about something interesting but I forgot and didn't feel like tracing back :-)

    We're using "meaning" in slightly different ways. The paradigm case of a symbolic system for me is language, and that has meaning - if it didn't, it wouldn't be a symbolic system. A symbol is created by setting up rules for the use of an arbitrary character or object. So the rules of chess set up rules for the use of the various elements of the game. I'm inclined to say that establishes the meaning of the symbolic characters within the game, and I would agree that that meaning is "in the minds of" the players and spectators.Ludwig V

    When the knight is captured it doesn't feel good or bad. The player may feel good or bad. I'm back to the Chinese room. Searle says the room doesn't know what any of the Chinese sentences mean. So if you agree meaning is in the mind, that's what I believe also.

    I also agree with you that the significance of the game (e.g. its interpretation as a war game, suggested by the names of some of the pieces, or the value attached to titles like "grandmaster") is not established by the rules of the game. So there are layers of meaning (or significance), depending on context.Ludwig V

    Yes, it would be the same game if you called the knight the frisbee.

    Yes, I'm agreeing with you. But I want to distinguish between the two by saying that credence should be based on evidence or at least plausibility and that fantasy has neither of those. That's all. How else would one separate them?Ludwig V

    I say that it is NICE if my credence is based on some evidence. Maybe I put some work into forming my opinion.

    But maybe I just didn't have the time to get a Ph.D. in quantum field theory in order to have any credence at all that there are quarks. I believe there are quarks, 100%. I believe in that particular science. But I would be hard pressed to lay out the mathematical theory. I don't know the evidence. I only know that if Sean Carroll tells me there are quarks, I believe him. Actually Veritasium has an awesome video on quarks, that's where I learned that mass comes from the binding energy that keeps the quarks from flying apart.

    I believe what I just wrote. I have zero evidence for any of it. Binding energy is analogized by a rubber band, that's what I know about it.

    I hope I'm making my point. We are all obliged to place high credences on many things that we can't possibly have the slightest idea about. The electric grid will be up tomorrow. How the hell do I know? Did I personally inspect every faulty transformer that's about to blow, and take down half the county with it?

    Here is my thesis. For every proposition P, I have a credence credence(P), whether I know the first thing about the topic or not. I think there's a 10 percent chance the Royals whacked Diana. I've seen enough hit man movies to know that when you die in a car crash, it might or might not have been an accident!

    Point being that I have a credence, which I found by simply thinking about it for a moment, about a situation in which I can't possibly know the first thing, and actually I haven't looked into it much. So I know nothing. But I have an opinion!

    Isn't having opinions about things that we know nothing about, one of the most human things we do?


    Yes, I remember the JFK story. I was once, briefly, an auditor (annual accounts for companies and other institutions). They drummed into me that when something was wrong, cock-up was more likely than conspiracy. But that doesn't prevent suspicions.Ludwig V

    The US government was up to its eyeballs in chicanery that would have shocked the naive America of the 50s and 60s. Assassinating foreign leaders. Interfering in foreign elections. Running sick mind control experiments. Business partners with the Mafia in plots to kill Castro. Controlling what the news media reported. I agree that just because they covered up the assassination, doesn't mean they did it. Doesn't mean they didn't, but doesn't mean they did. But under the law they are accessories after the fact, and just as legally accountable as the actual perpetrators.

    Likewise this week. The Biden admin, Mayorkas and that clown Cheatle, are embarrassed at their gross incompetence on display. By the way I am not one that says Cheatle is a clown because she's female. I say she's a clown because she's an idiot. Whether she actually believed that nonsense about the sloped roof preventing an agent from being up there, she was stupid enough to say so in front of a camera. That's a firing offense for any bureaucrat. Because it totally destroys the public's trust.

    The days of dogmatic nationalization of the means of production are long gone. Nowadays, at least in the UK, it's a pragmatic issue and we have a number of half-way houses and regulators for specific areas.
    But isn't the free market a collective social institution? One of the basic functions of the state is to supervise and enforce contracts, and the companies and other collectives that operate in the market are themselves collective institutions - and they aren't accountable to voters.
    Ludwig V

    It's a continuum, to be sure. Individual versus the collective.

    There was a lot of back-stabbing in the aftermath of the referendum. It was not pretty. But I don't think any of the Prime Ministers intended that. Brexiteers told everyone that the EU could be adjusted to suit what they wanted. The EU were reluctant to do so - and why should they? It's not as if public opinion in
    the EU thought Brexit was a good idea. Brexiteers labelled any compromise as "stabbing Brexit in the back"; it seems they didn't grasp what negotiation is all about. The only people who were stabbed in the back were the Northern Irish who were thrown under a bus by Boris Johnson.
    Ludwig V

    That last bit I didn't know anything about, the Northern Irish.

    I went on a business trip to Cork once, it was so lovely.


    I voted remain, but had serious doubts about the ultimate EU project ("ever closer union"). Europhiles didn't pay enough attention to the longer-term history of the UK (since, say, 1700).Ludwig V

    I don't like the idea of giving up national sovereignty to such an undemocratic institution as the EP. "Brussels" has become a pejorative and not just the name of a city.

    Forgive me, but I can't think of anyone, malevolent or not, who actually benefited from the lockdowns apart from the vulnerable groups - older people, people with health issues. I plump for miscalculation, in spite of the UN warnings, so by British politicians.Ludwig V

    I would say at the least, that many of the authoritarian types in our society took advantage of the situation, in a manner not supported by the science. And anyone who pointed that out, was cancelled, had their career ruined, their jobs or professional licenses taken away.

    I do not regard that as miscalculation. I regard that as evil, cynical calculation.

    Yes. The conservatives thought they could go back to the way things were before the war. The voters wanted a fresh start. They got it - even the conservatives had to accept the new ways. It took them 50 years to unpick it and they're still not done.Ludwig V

    Well the recent batch of conservatives have been useless. May was terrible. Was Johnson next? Then Sunak? They're what we call RINOs, Republicans in Name Only. Squishy liberals with no convictions calling themselves conservatives. Well here's to Starmer, he's got his work cut out.

    Well, people were kind to him for quite a long time. But that's changing now.Ludwig V

    Is that right? Is there Churchill revisionism about?
  • Infinity
    I don't know, but there are lots of US/Brit differences, the common one being the "o/ou", which most are familiar with. I'm Canadian so I'm stuck in between, getting it from both sides. For us, the 'proper' way is the Brit way, which my spellcheck hates. I have the keyboard option for Canadian English, but it seems to default to US. There are some interesting nuances, such as the practice/practise difference. We would use "practise" as a verb, an activity, but if a professional like a doctor, or lawyer, sets up a practice, we have the other form as a noun. It's not a very useful distinction, and difficult to figure out when you're writing, so screw it! What's the point in such formalities?Metaphysician Undercover

    You managed to entirely misunderstand my answer.

    Since judgement is apparently a Britishism, I accept that and have no trouble with it; no more than I have with colour. I speak perfect English. I left my spanner on the bonnet of the lorry!

    So I did NOT realize that judgement with an e is a Britishism. I just thought it was the same common misspellings that's on my personal list of stuff that annoys me.

    And now that I know it's a Britishism, the next time I'm about to chide someone for misspelling judgment, I'll first ask them if they're British; and if they are, I'll belay that chide.

    Is that any more clear?
  • Mathematical truth is not orderly but highly chaotic
    Ordinarily I would not give it much thought, but this thread seems to focus on math truth beyond virtue of proof. You seem to know what that is all about. Can you provide a very simple definition of this sort of truth in math? I suppose the definition of a triangle is truth without proof. Truth by definition. But what makes a string of symbols true? Model theory? I thought I understood a parallel idea when I quoted the group theory example from StackExchange, but I guess not. Are axioms true by virtue of definitions?jgill

    Ok I'll do my best.

    When we manipulate symbols, we use syntax rules. There's no "meaning" associated with the symbols except the meaning in our minds. The symbol manipulations are entirely mechanical, they could be worked out by a computer program. In fact there's much contemporary research on computers doing proofs. Mathematicians are starting to use https://en.wikipedia.org/wiki/Proof_assistant]proof assistants and proof formalizer software. It's a big field, going on ten or twenty years now.

    But ok, there's the mechanical symbol manipulation. Syntax.

    Now we want to talk about semantics, or meaning. So we cook up, if we can, a model or interpretation of the symbols. The variables range over such and so set. The operation symbols mean such and so. For example, we might have the formal axioms of integer arithmetic, say the ring axioms. And then there is a model, the set of integers.

    Now -- and this is actually a very deep point, I do not pretend to begin to understand the nuances -- things are said to be either true or false in the model.

    So truth and falsity, semantic concepts, are always relative to a particular model. The integers and the integers mod 5 both satisfy the same ring axioms, but 1 +1 + 1 + 1 + 1 = 0 is false in the integers; and true in the integers mod 5.

    That's what we mean by truth. Mathematical truth is always:

    Axioms plus an interpretation.

    If I say, "Our planet has one moon," as a purely syntactic entity, it's a valid sentence. But it's neither true nor false.

    If I interprete "Our planet" as Earth, it's true. If I interpret it as Jupiter, it's false.

    So. Given a collection of axioms; and an interpretation of the axioms, which is (1) a domain over which the symbolic variables range; and (2) a mapping from the symbols to objects in the model.

    When you do that, then each valid sentence in the language of the axioms is then either true or false in the model. (It could be independent, too, but we're not concerned with that here).

    Now the paper in the OP makes the point that there are more mathematical truths than there are symbol strings to express them. So most mathematical truths don't have proofs we can write down. In fact we can't even express most mathematical truth.

    This is already long enough so let me know if this is the answer you were looking for. In the end it's related to Tarski's truth thing and Godel's incompleteness theorem and Turing's Halting problem -- though I recently learned that in fact he did NOT talk about what we call the Halting problem in his famous 1936 paper. So all this stuff was "in the air" in the 1930s. A guy named Chaitin came along later and recast all of this in terms of information theory. How "incompressible" a string is as a measure of its randomness. Using those ideas he proved Godel's incompleteness theorems from a different point of view.

    From that, you can show that mathematical truths are essentially random. True for no reason than we could ever write down. That's what all this is about.

    But you must understand, none of this is of the least importance to the vast majority of working mathematicians. You're not missing anything.
  • Infinity
    Sorry, the devil made me do it. For some reason, out of all the words that have multiple spellings British/American mainly, people on this forum complain about judgement/judgment. Why is this worthy of a correction? You didn't correct me when I spelled color colour.Metaphysician Undercover

    Oh that's interesting. Is judgement with the extra 'e' a Britishism? I was not aware of that.

    This discussion has degenerated. Let's evacuate.Metaphysician Undercover

    Ok.
  • Mathematical truth is not orderly but highly chaotic
    True or False?: The Earth is a planet. Answer: True (by virtue of classification)

    True or False?: The square of the hypotenuse in a right triangle equals the sum of the squares of the two sides. Answer: True (by virtue of proof)

    True or False?: The Continuum Hypothesis is true. Answer: Well, let's see . . . .
    jgill

    Interesting to hear you arguing against the concept of truth. Well moral relativism is the ethos of the age, I suppose.