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
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
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
I see from the reports that the soup did actually damage the paint of the frame, so I was wrong about that. — Ludwig V
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
I'm not sure what you expect me to say. — Ludwig V
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
But does it show that wind farms should be abolished? — Ludwig V
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
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
He wasn’t removed at all. He decided not to run. — Wayfarer
Yes, Meaning is as ill-defined as metaphysics. It's usually easier not to mention it. — Ludwig V
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
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 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
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
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
herClean 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
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
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
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
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 remember that everyone agreed that GW Bush was a fucking idiot. But noone called it treason. — Echarmion
No surprise here: our economy and politics are run by overlapping elites. — BC
Anytime you want jazz album recommendations, just ring. — TonesInDeepFreeze
Jazz is one thing I know a lot about, unlike logic. — TonesInDeepFreeze
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
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
They stabbed him in the chest, not the back. It was very visible and very public. Nothing hidden or conspiratorial about it. — Echarmion
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
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
I had to go and look that up, but that's absolutely crazy. Mob level shit. — Tzeentch
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
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
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
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
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
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
Some are saying the earth is flat. — Echarmion
I'll settle for that. It's a very marginal point, anyway. — Ludwig V
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
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
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
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
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
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
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
Trump has a now very familiar problem with the reality situation. — BC
The albums 'Conversations With Myself' and 'Further Conversations With Myself'. — TonesInDeepFreeze
What difference does it make to the country? The net result is the same. — Echarmion
So did Bill Evans. — TonesInDeepFreeze
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
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
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
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 think "preferable" is better than "should". I'm happy with that. — Ludwig V
H'm. That's a new take on mathematics. — Ludwig V
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
Anyway, you're not telling me that the axioms and definitions of probability theory are in some sense provisional, are you? — Ludwig V
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
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
Thus, were set theory removed mathematicians would perish. — jgill
I think not. But mathematics would not be nearly as robust as it is today. My humble opinion. — jgill
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
According to the page on the subject, determinism and predeterminism are "closely related": — Tarskian
If you believe that everything has a reason, it does not mean that you also know that reason. Predictability requires indeed both. — Tarskian
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
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
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
Kamela has more than enough on her plate successfully campaigning, never mind trying to become an experienced incumbent in just a few months. — BC
Better deep in knowledge and shallow in misunderstanding. Better deep in love and shallow in hate. — TonesInDeepFreeze
Then you're discussing with the wrong person. — TonesInDeepFreeze
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
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
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
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
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
Yes, I do. But I also think that credence should be influenced by evidence. — Ludwig V
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
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
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
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
Quite so. I forgot about the Lusitania. — Ludwig V
That is a deep misunderstanding. — TonesInDeepFreeze
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
It is not the case that 'mathematical truth' means ''axioms plus an interpretation' — TonesInDeepFreeze
It doesn't matter whether S is an axiom or not. The definition doesn't mention 'axiom'. — TonesInDeepFreeze
I don't know what that means. — TonesInDeepFreeze
The truth of a sentence is per interpretation, not per axioms. — TonesInDeepFreeze
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
(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
(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
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
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
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
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
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
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
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
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
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
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
I'll bet. It's a very beautiful place. The whole island is - outside Belfast. — Ludwig V
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
5 views per day. The title doesn't resonate with many apparently (including me). Nevertheless, an important movement. — jgill
Thank you. This is similar to the group theory example. It makes more sense now. — jgill
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
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 Ideas — Ludwig V
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
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
Yes. But I thought that unintended consequences were events in the empirical world. — Ludwig V
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
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, 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
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 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
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
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
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
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, people were kind to him for quite a long time. But that's changing now. — Ludwig V
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
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
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
This discussion has degenerated. Let's evacuate. — Metaphysician Undercover
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