I wonder how such advocates would respond to chapter 0 in Scholastic metaphysics!
"What do you mean maths is an example of knowledge that isn't scientific? 2+2 *can* equal 5 . . . And we left scientism alone a long time ago anyway! Haven't you seen us interpret biology?"
1+1+1=1 as an attack on the Trinity, which I will assume it is, is just equivocation. If the idea were that 3 distinct substances equal 1 substance, it might work as a comparison. But the idea is that 3 distinct persons equal 1 substance. That’s not self-contradictory, anymore than 1+1+1 cookies = 1 jar of cookies. In short: one side of the equation has different units than the other, but you’re treating them as the same.
New Atheist Laurence Krauss also believes 2+2 can sometimes equal 5. He is so committed to the idea that he printed 2+2=5 on a t-shirt and used it as a quasi-counter argument against William Lane Craig while debating morality. It was at that precise moment I realised that I had just wasted an hour of my life.
Incidentally, as well as believing 2+2=5, he also believes that something can from nothing as long as the nothing is actually a something.
Don't you believe that 1+1+1 = 1? And don't you believe that something can come from nothing even if nothing is not something (AKA creatio ex nihilo)? And don't you believe that an unmoving locomotive can move a train?
Have you ever considered that some people may think that is hilarious?
"And don't you believe that something can come from nothing even if nothing is not something (AKA creatio ex nihilo)?"
You are equivocating. No one here believes that from nothing something can come -- this is quite explicitly denied by St. Thomas for example. What creation ex nihilo means is that God can create through his power without any preceding matter, but God's power, and only God's power, can bring about created things.
I imagine that "1 + 1 + 1 = 1" is a reference to Trinitarian beliefs.
But at this point, whatever dude, do not let your ignorance get in the way of your silly jabs.
In fact, it is the Thomist who is equivocating on what ex nihilo means. Ex nihilo means "from nothing" and not "from something". Creation cannot come from God's power because God's power is immutable. Anyway, my point was not to show that creatio ex nihilo is impossible, but to remind the readers that something that at first sight may look impossible, like creatio ex nihilo, or the trinity etc. perhaps is possible after all, especially for God. So, I really don't get what Feser is trying to tell us. We know that 2+2 cannot be 5, but to claim we can have the same confidence in e.g. moral issues by using Natural law Theory is not as straightforward.
You, e.g. seem to think that natural law allows you to insult people by calling them ignorant when they don't agree with you. Not every natural law proponent will agree with your interpretation.
"You, e.g. seem to think that natural law allows you to insult people by calling them ignorant when they don't agree with you. Not every natural law proponent will agree with your interpretation."
Calling someone an ignorant is not an insult. Etimologically, ignorant just means someone that ignores. I am simply stating an obvious fact. "Creation cannot come from God's power because God's power is immutable" is an unbelievably ignorant thing to say. If I really wanted to insult you I would add something like stupid or idiot.
And where did you get the idea that I think natural law gives me license to insult anyone? Nowhere. But as is unfortunately common with you, you pull crap out of your ass to try and score some cheap rhetorical points. Your forgiveness is not needed.
Finally, even if one deems there is a parallel in finding the two sets of beliefs ludicrous, there is a difference between what Krauss presents himself to be and then stating some utter absolute nonsense like 2 + 2 = 5 and believing say, the Trinity, since the latter may be more or less difficult to swallow but its defenders explicitly hold that it is *not* contradictory. Whether they are right or not, is not the point; 2 + 2 = 5 is an explicit contradiction. Now maybe Krauss means it in jest, I don't know, but you took him at his word.
The big mistake you are making is that concepts like “2”, “+”, “=“, and “5” are finite concepts that are easily understood by all.
Concepts like “God”, “creation”, “Trinity”, etc. are generally spoken of analogically and are admitted to be incomprehensible.
Even if (per impossible) Christian dogma was contradictory, it would not be obviously so, or if it is obviously contradictory, then it is clear that the person who makes such claims had very little knowledge of the subject at hand.
While I find that most people do not have the competent knowledge of God (and especially Trinitarian theology) to make such claims, the vast majority of people have competent knowledge of arithmetic to see the absurdity of 2 + 2 = 5.
"And where did you get the idea that I think natural law gives me license to insult anyone? Nowhere. But as is unfortunately common with you, you pull crap out of your ass to try and score some cheap rhetorical points. Your forgiveness is not needed."
Well, I apologize. Obviously telling me I "pull crap out of my ass" is simply a commom Thomistic way of being polite. I should have known that.
Anonymous
No, AFAICT I have not been banned and i am not a troll, although some people around here start calling everyone a troll who dares question some ca-called obvious truths.
Greg
Creatio ex nihilo is creation "from" or "out of" nothing by God. God is called a cause but upon closer examination has nothing whatsoever to do with creation.
Scott
The very fact that God tec are spoken of analogically leaves room for interpretation, especially on moral question which are hardly ever black and white.
My point is that it is always very easy (and I would even say "cheap") to accuse someone else's view of being absurd.
I agree with that, but I do not think that it is cheap to accuse someone who claims 2 + 2 = 5 of absurdity. The claims are clear and the conclusion clearly does not follow. The claims are not nearly as clear in other subjects, even if ultimately one finds them contradictory.
If you cannot claim 2 + 2 = 5 is absurd, then you cannot claim anything is absurd. You might as well drop all debate.
The question is what Antonio Spadaro means by saying that in theology 2+2 can equal 5. My guess is that it is a way of saying that things in theology are not (always) black and white. And, while you may disagree with that, it isn't absurd.
Well then the most charitable interpretation is that it is a horrible example, because that 2 + 2 = 5 IS black and white and it is obviously contradictory.
Maybe a better example would be that .99999... = 1. That is prima facie false but upon in depth mathematical analysis turns out to be true. Of course that example is limited as well because the terms are much more comprehensible than God, but at least it is closer to the thrust of a charitable interpretation of what he is saying. I hope that is what he meant, but I am afraid it is not.
The "charitable" interpretation of Spadaro's general teaching is that he is only slmost hopelessly benighted and full of crock, but there is some hope for him because all things are possible with God. As to his specific comment that "2+2=5", if it were necessary or even worthwhile to THINK that we needed a "charitable" interpretation of it individually, instead of ignoring it like we ought to ignore almost everything he says, it would be something like either (a) things are not always what they appear; or (b) a thing isn't merely the sum of its parts (especially, the sum of its material parts). Each of these are in fact true and they are valuable general sayings, thing people often DO say, with validity. If he meant either (a) or (b)), though, Spadaro butchered it by casting it in the form of math, because in doing so he took it out of the context in which its validity works and put it into a context in which it doesn't - almost as if to imply "math itself isn't valid" - which UNDERMINES the truth of (a) and (b) in their proper contexts. So, as metaphor, it's a failure. There is nothing uncharitable about pointing out its failure.
I don't believe that Walter has been banned, and he doesn't typically engage in troll-like behavior. In this thread, though, he picked a particularly poor way to advance a point, one that is rather close to being troll-like. It is probably true that to a careless and silly non-Christian, the doctrine of the Trinity looks like a claim that 1+1+1=1. So? making careful and deep arguments to a careless and silly person is probably completely pointless. Doesn't mean that what the careless person thinks should be granted any weight.
Scott, "Concepts like “God”, “creation”, “Trinity”, etc. are generally spoken of analogically and are admitted to be incomprehensible." So, then, it is generally admitted that you and all such Thomists do not know what you are talking about.
I mean literally, you talk about X but you also say you do not comprehend X.
You have no comprehension of the thing you are asserting, by your own words.
If you cannot comprehend X how do you then consider it reasonable to assert you have a sound argument for X?
It is also incomprehensible that 2+2 should =5. But, if one is to simply accept on faith that self contradictory statements are true then why not believe 2+2=5?
Well, apparently you feel there are certain classes of self contradictory statements that are not allowable, but other sorts of self contradictory statements that are allowable.
As Walter points out the assertion of god's immutability is self contradictory with the assertion of god's creativity. An unchanging god that also creates various different things at various different times is incoherent and incomprehensible, yet you seem to think you have reasoned your way to some great truth of the universe by asserting that mutually exclusive assertions are somehow the case, although incomprehensibly so.
I agree it's not a good example, and indeed .9999... = 1 would be a better one, but I don't think Spadaro is a mathematician. That being said, I do not know what Spadaro actually meant, but if it's something along the lines of "Human beings cannot fully understand what God means by such and such" he is, IMO correct, despite the poor analogy.
"Obviously telling me I "pull crap out of my ass" is simply a commom Thomistic way of being polite."
So the problem is civil discourse, or the lack thereof. Then maybe *not* posting inane parodies of some of people's most cherished beliefs would be a good start. Now you know where you can stuff your outrage at impoliteness: in the same place you withdraw your crap from.
So tell us what else is being parodied? Do they or do they not claim that 2 + 2 some times equals 5? They do. So how is it a parody, much less an inane one? And how are their most cherished beliuefs being parodied? Maybe because 2 + 2 = 5 is an entailemenht of them? Howe exactly? I would assume Fr. Spadaro is just being muddleheaded. If 2 + 2 = 5 does indeed follow from your "most cherished" beliefs, then these beliefs have gone off the deep end.
Good job at posting an inane comment, wherein it is shown that you do not even understand how parodies work. Can we expect any more inanity?
Apparently you did not read to the end. Lindsay claims that these nefarious "colonizers" attempting to undermine mathematics extend their manipulation of meaning to include the definitions of political terms like "racism" and "fascism," and even of the sentence "black lives matter." I grant you that this is not an intentional parody. It is a gruesome caricature of a certain habit of thought on the right. Because surely no one believes this tripe.
My comment was explicitly in response to parody comments of the OP, so for your response to make any sense, your "The whole post" must be referencing the OP.
How you go from whatever James Lindsay says (and I agree with you, he is an ignoramus) as the position of the OP must be another one of your magical feats of reading. Or you did not have the OP in mind but James Lindsay post. In any case your jab is completely misdirected.
This is the reason I referred to what the post is "about" rather than to the post itself. The post itself posits the links as the "answer" to the question it poses. The post is therefore "about" the articles to which it links. Snark about "magical feats of reading" lands more convincingly if it is not deployed in the midst of a misreading.
Ha, the OP "is therefore "about" the articles to which it links." Right. Well, then my snark landed just fine, because I have only "misread" what you "miswrote" in your "magical" feat of "misreading".
Again, if you wish to land a blow about someone's vocabulary, you might try not simultaneously committing a grammatical solecism. Did I just thumbed, indeed.
" ... if you wish to land a blow about someone's vocabulary, you might try not simultaneously committing a grammatical solecism. Did I just thumbed, indeed."
Thanks for linking to my CWR piece on Spadaro. Almost as outrageous as his vapid remark was the fact that some "orthodox" Catholics defended his remark. Nominalism lives!
I've been following James Lindsay on Twitter as part of my "coping with being an excommunicated leftist" strategy, and watching this 2+2=5 fiasco unfold has been absolute *insanity*. The Wokesters have been absolutely obsessed! It's been about two weeks of sophistry now, with no end in sight! The best part was when they decided that this was all part of some sinister, white supremacist alt-right plot when he's an angry liberal! There's zero recognition that the whole thing was basically an Orwellian practical joke.
Been dancing a bit with transgender activists on Twitter today (I'm a masochist for joining), which means being as polite and accommodating as possible, while they heap as much verbal abuse on you as they can, all because you will not scrape and bow and admit that you have "cisgender privilege" over them, the backstabbing, misogynistic traitors.
If Dr. Feser reads this comment: thank you, thank you, thank you for being so mercilessly critical of the left. I've thanked you via email before (and I doubt there are other radical feminists here so it's probably obvious who I am), but I've deprogrammed pretty much completely in the light of recent witch hunts. I'm not sure I'd have been able to deal with the attempts at reeducation if I hadn't had enough exposure to conservative thought to really see the totalitarian side of what was going on. The anti-woke left, where you get monstered and told you're a white supremacist for rejecting queer theory, is not exactly a fun place to be. A lot of the critiques of woke culture are *extremely* useful now that I basically feel like a Trotskyist 24/7.
Ed, while I can understand the desire to respond to the 'woke brigade', what I can't understand is why as a conservative intellectual you've not felt compelled (in 3+ years) to address the absolute embarrassment that is conservatism under Trump and his ilk (everyone from AG Barr to Roger Stone to Guiliani to Michael Cohen and Paul Manafort...seriously it's a murderers' row of corruption, incompetence and buffoonery). Where is the handwringing about conspiracy theories (QAnon), anti-intellectualism, blatant hypocrisy, corruption, etc. while conservatives twist themselves into pretzels in service of the most obvious charlatan to ever hold this much power? Seriously, what the hell?
There aren't enough people already talking about the stupid party (and giving a pass to the evil party)? Big Tech, the universities, the media establishment, these aren't enough people hyperfocused on Trump's every goofy utterance? The real cherry on top of that massive hoard of obsessed drones would be the blog of a relatively obscure philosophy professor?
There is a real advantage to being the underdog in terms of social power: it frees you from confirmation bias.
to address the absolute embarrassment that is conservatism under Trump and his ilk
Well, it is true that conservatives have done some embarrassing things with the Trump years. What is not true is that Trump has done them: Trump isn't conservative. He was a Democrat in the 1970's and 1980's, not a conservative. He wasn't conservative back in 2000 when he first talked about running, and he wasn't in 2012 when he next tried for it. In 2016 he remains what he has been for a long time: a libertarian-leaning populist (probably classical) liberal. People mistake classical liberals for conservatives these days mainly because they are ignorant of how far the Democrat party has moved leftwards from classical liberalism: I think that Humbert Humphrey would be called a moderate conservative these days. And very idea that someone would put Giuliani in the same sentence with conservatism is laughable.
Ed, I think that's quite a debatable point, but I suppose a topic for another day.
TN, I'm not interested in what 'Big Tech' has to say about Trump, I'm interested in what a conservative Catholic intellectual has to say about him, thus why I'm here. I'm especially interested b/c I disagree with Ed that there's some significant imbalance between the parties in their stupidity and evil. Some days I might even argue the conservative side is more cravenly evil. It's definitely not a settled matter. So I don't think Ed's continued one-sided shots at 'the left' are justifiable when 'the right' is just as stupid and evil, if not more so at times, while also having the added dynamic of being the more traditionally conservative and religious side (making their hypocrisy all the more galling to me as a christian).
Tony, I said he's an obvious charlatan...that's exactly why it's so embarrassing that so many 'stalwart' conservatives (everyone from Lindsey Graham and Mitch McConnell to the majority of evangelical christians) have done his bidding and fawned over him with seemingly no questions asked and no cognitive dissonance (or if there is awareness, then a truly terrifying cold + calculated pragmatism). It's particularly hilarious watching old clips of Graham attacking Trump and describing how despicable he is, it goes well beyond the typical 'tear down your opponent until you have to work with them' political maneuvering. The postmortem on this administration and its adherents will not be pretty.
everyone from Lindsey Graham and Mitch McConnell to the majority of evangelical christians...It's particularly hilarious watching old clips of Graham attacking Trump and describing how despicable he is, it goes well beyond the typical 'tear down your opponent until you have to work with them' political maneuvering
I don't know what kool-aid you are drinking: Graham is called one of the most liberal of Republicans, by the ATLANTIC no less.
The post mortem on Trump will be that even though the country had become so degenerate that the conservatives could not field a winning candidate, the liberals were busy tearing themselves to shreds between a moderate liberal Trump and far, far left liberals whose main objectives were to destroy the country the country even faster than Trump, while the center-of-the-road moderates who neither understood conservatism nor liberalism, but had been left holding the Republican flag while the liberals moved leftwards, were so relieved not to have the country wrecked at an even faster pace that they gave honor to Trump for his only being a moderate liberal. (They may have said "conservative" but because they never understood conservatism, they meant "not far, far left liberal".)
"I'm not interested in what 'Big Tech' has to say about Trump, I'm interested in what a conservative Catholic intellectual has to say about him"
Well, there ya go: he thinks one side is stupid and the other side is evil. I'm sorry if you find that unsatisfactory. I'm sorry if you feel like you should get to set the topics on someone else's blog. But if you're really interested in such a discussion, maybe you could try asking about something specific rather than snarky generalizations topped of with a "what the hell".
Sure, & I'm sorry for whatever disability prevents you from performing a Google search. The first result is from yesterday. It even throws you a bone: of course both parties are evil, though the current administration is even more ruthless on this particular score than was its predecessor. I just can't imagine the moral depravity necessary to regard the GOP as anything but evil. I seem to remember a certain Jewish peasant counseling the defense of the poor, the sick, the stranger, the prisoner.
The link you provided just says that Michelle Obama accused Trump of putting kids in cages. It's not very surprising that political rivals make exaggerated accusations about each other, is it? Furthermore, the word "cages" is in quotes indicating that it the description is an interpolation.
So, let me clarify what I'm asking for: what I'm asking for is substantive evidence that supports your claim that some political party is putting kids in cages. If you could please support your claim, that would be great! Thanks!
MM, I am sorry for whatever disability prevents you from reading the stories you link to. The AP News article cited clearly states that nobody was put in a cage, and that the Trump administration neither built the chain-link enclosures used for temporary detention at the border, nor originated the use to which they were put.
If the GOP is evil on this score, so are the Democrats.
Tom Simon, I'm sorry for whatever disability prevents you from reading the phrase in my comment "both parties are evil," a reference to the fact that I also point out in the comment that the article "throws [my interlocutor] a bone" by impugning the Obama administration.
In other words, yes, thanks for saying exactly what I said.
You are right about one thing—a "chain link enclosure" can never function as a cage. Mea culpa. The GOP is angelic.
TN, if you don't know that the current administration is removing children from their families and detaining them in (ahem) "chain link enclosures," I suggest you learn to read. If you want to argue about the definition of a "cage," I suggest you grow a conscience, not to mention a spine.
Why would anyone want smart, evil people to run the country when there is a stupid evil alternative?
Something like this, perhaps:
1. If the stupid party isn't evil, you should vote for the stupid party over the evil party. 2. If the stupid party is evil, you should vote for the stupid party over the non-stupid evil party. (Why would you want people who are better at bringing about evil in the world in power?) 3. The stupid party is either evil or not. 4. Therefore, you should vote for the stupid party (1-3, Dilemma)
Justify your support for evil however you wish. Why would you want to passively accept a state of affairs that forces you to choose between evils, is the only real question.
Spare me the fatuous bluster, MM. I gave you an argument. You owe me a reply, or an honest admission that you're a sophist hack, and a sneak, and a fraud.
I provided that link earlier myself, genius. You think I give a shit about the idiot Democrats? And LOL, your dumb little petitio principii is hardly a logical argument.
After reading the NYT article, I assume that what you mean by “putting children in cages”, is that it is “evil” to hold children in a border detention facility. Is that right?
The article details “squalid” conditions in several border facilities last year. Border patrol officials quoted in the article claimed that they were overrun by large numbers of people and they were not prepared to handle them all (probably because of the Central American caravans last year) and the article says they were tranferring detainees to less crowded locations and setting up temporary facilities. Does that not seem like a plausible explanation? Is there some evidence that compels one to reject that explanation in favor of the contention that Republicans actually just enjoy human suffering?
Would you agree that there is a high degree of grandstanding and exaggeration over this issue? The article claims that people were forced to drink from toilets, but we now know that the facility uses a fixture that has a sink and faucet on top, and a toilet on the bottom (1). Does this kind of prevarication indicate the desire smear one’s opponent is more important than what is true?
The article does not mention it, but the day before this article was published, Trump signed a $4.6 billion dollar relief package “The largest portion of the funding — $2.88 billion — will go to Health and Human Services to provide shelter and care for unaccompanied children.” (ibid) Does this demonstrate the “evil” you are protesting?
No one disagrees that every effort should be made to eliminate inhumane conditions, but if those conditions arose from evil intent is a different question. Or maybe you just think borders are evil? Is that the more fundamental grievance you have?
Of course borders are evil. There should be none. But that isn't the issue. The president has not kept his "intent" secret. I assume you are familiar with his racist rhetoric, which you can't possibly need me to google for you.
But perhaps you are concerned only about Americans. From a report last year:
"Last month, Francisco Erwin Galicia, a Dallas-born teenager, was held in Immigration and Customs Enforcement (ICE) custody for more than three weeks, where he says he lost 26 lb. due to the poor conditions and was not allowed to shower. In March, Customs and Border Protection detained 9-year-old Julia Isabel Amparo Medina, a U.S. citizen, for more than 30 hours when she crossed the border at the San Ysidro port of entry to attend school. These are not isolated incidents. ICE has requested the detention of 3,076 American citizens from October 2002 to December 2018, according to Syracuse University’s Transactional Records Access Clearinghouse."
If you can't see that this is evil—if you prefer to quibble about "intent" despite knowing perfectly well that the administration has indicated its evil intent time & again (please look up Stephen Miller's comments on the issue), then we are at cross purposes, and I wouldn't have us any other way.
There is no defensible moral framework that regards the restriction of freedom of movement as a good, particularly when that freedom of movement is used to flee oppression. If your family is going to be killed in one place, you should be allowed to move to another. If you can't make enough to support your family, you should be allowed to move to where you can. It is barbaric to regard one person as less deserving of the benefits that inhere in living in a certain place simply because he was not born in that place.
In this sense, of course, borders are not evil in and of themselves—as long as they are open to all regardless of circumstance.
If you're wondering if I'm a leftist nut, I should note that I also think the police should be abolished and capitalism should be overthrown.
You wrote: "It is barbaric to regard one person as less deserving of the benefits that inhere in living in a certain place simply because he was not born in that place."
So then you completely support Christopher Columbus.
When the empire of CHAZ colonized downtown Seattle, the first thing they did was establish borders and a police force to enforce the borders with guns. That was "evil" wasn't it?
Look, I tried to take you seriously, but you're just hysterical. Thanks for the discussion.
Oh, touché! To support open borders so that people might free oppression and move to find better opportunity is the *exact same thing* as to support military imperialism! How did I never think of that?
I have not tried to take you seriously, as you have shown from the outset that you are not serious.
James Lindsay has no idea what "deconstruction" means; his notion that "critical social justice theory" is "postmodernist" is laughable. The latter term refers to French theory in the 60s with which Lindsay is unfamiliar, given that he misuses each concept he invokes & misapplies it to present-day struggles against racism where it has no currency whatsoever. You people are delusional.
James Lindsay didnt make up the connection to racism. Academics and educators were literally saying that 2+2 only ever making 4 is literally just the result of the white supremacist male patriarchy.
Sure, the link between deconstruction and the neo-Marxist worldview is rather hard to make, but dont put that on Lindsay. Put that on the deconstructionists and neo-Marxists who borrow from each other and blur their distinctions.
Marxists and deconstructionists are ever at odds, since the former uphold a form of structural determination that the latter attempt to undermine. Marxism and deconstruction are incompatible, as Derrida's late attempt to incorporate Marx inadvertently made clear.
Marx's analysis of how value is produced under capitalism—which is what "Marxism" mainly is—is hardly bull. But of course you've read the three volumes of Capital, so can explain what is wrong with Marx's demonstration of the general forms of differential rents.
"Marxists and deconstructionists are ever at odds"
Strict Marxists maybe see it that way. Neo-Marxists and their useful idiots not so much. There is also a very stark difference between Karl Marx himself and Marxists, then there are neo-Marxists who are critical of both.
Again, Lindsay is simply explaining where they get the idea that our cultural acceptance of 2+2 only making 4 is just the result of the oppressive white male superstructure. Whether he gets it exactly right, his main point is correct that it's an incoherent mish-mash of neo-Marxism and deconstructionism.
Also, I wonder whether your judgements of Lindsay's understanding of these are correct. See here:
MM: Marx's analysis of how value is produced under capitalism—which is what "Marxism" mainly is—is hardly bull.
Actually, everything Marx ever said about economics is bull. The labour theory of value, which is the foundation of his entire system, is so laughably unfounded that it barely even qualifies as wrong.
Not terribly surprised to see this canard repeated. Marx argued against the labor theory of value, a staple of Ricardian economics. You can't have read the relevant passages. What he specifically denies is that the value of a product derives from the quantity of labor required to produce it (both Smith and Ricardo hold versions of this thesis). For Marx, the relevant criterion is the amount of "socially necessary labor time," a society-wide norm to which producers must adhere (if your employers are taking longer than average to produce your product, you're not going to produce as many units in the same period of time as the next fellow, whose employees are producing more units per hour).
But you know all this, because you're intimately familiar with the work of Diane Elston, Moishe Postone, David Harvey, and the many others who have for decades now pointed out that the standard reading (held by some orthodox Marxists, no less) of Marx as holding Ricardo's labor theory of value is wrong.
I'm not sure you've ever been in an economics department (I have a PhD from the University of Chicago), but how about I walk into the New School's and start talking about it?
Of course "most people" would not agree. That hardly means there are no economists in respected economics departments who take Marx's analysis of capitalism quite seriously indeed and would laugh at dismissive characterizations of it. Anwar Shaikh and Duncan Foley at the New School; Ben Fine at the University of London; Andrew Glyn (d. 2007) at Oxford; Michael Piore at MIT; Immanuel Wallerstein (d. 2019) at Yale; John Roemer at Yale; Richard Wolff at U. of Massachusetts; Michael Hudson at U. of Missouri and Bard ... I could list dozens of professors in prestigious economics departments who, if I "walked in to an economics departments and started talking about this stuff" wouldn't bat an eye.
There are a lot of weird, counter-intuitive things in number theory. When I first heard that .999... = 1, I thought it the person telling me was crazy, but there are probably a dozen ways to prove it and they all work. It really causes a person to tread a little more lightly whenever you thing you know something for sure.
Well, you are assigning a meaning to an *infinite* sequence of digits and then carefully check what algebraic manipulations you are allowed to do (not all are valid, which is usually how the above tautology is turned upside down into a would-be proof of a contradiction). And once you realize that is what you are doing, *some* weirdness is to be expected.
That is true. As I'm sure you know, it is not a contradiction, it is because 9 repeating is not a real number. It is still a good trick, and a good lesson in how easy it is to be decieved.
The series diverges trivially; doing invalid algebraic manipulations with series gives the result. A more precise way to get it is by using "non-standard" ways to assign a meaning to such divergent series. There are inumerous such summation methods (usual with famous mathematician names attached like Cesaro summation, Abel summation, Banach limits, etc.) and regularization schemes. The one in question is Ramanujan summation, from the Indian mathematician prodigy Srinivasa Ramanujan.
Thanks for discussing this, it is very interesting.
So is it true to say that one reason the illusion works is because we want to think of it as a convergent series, but, in fact, it is divergent? The same "proof" can be done by sum of an infinite series, but, of course, it just performs the same trick.
We want to think that 999... is really, really close to 1 but just a little less, but, of course it isn't. If 999... were a real number, there would be infinite numbers between 999... and 1.
"We want to think that 999... is really, really close to 1 but just a little less, but, of course it isn't. If 999... were a real number, there would be infinite numbers between 999... and 1."
No. Pick a sequence of decimal digits (in what follows there is nothing special about base 10, you could use any other base) which you view as the would be number .d1d2... We want to interpret the latter as (the notation for) a real number in the closed interval [0, 1] -- I am leaving the integral part aside just for ease of presentation. So what is the standard way? Well, just like an integral number written in decimal notation is really "just" a polynomial in 10, so is such a sequence an infinite series in 1/10, specifically, *by definition* (using LaTeX notation):
.d1d2... = \sum_{n = 1}^{\infty} d_{n}/10^{n}
It is easy to see that the series on the right converges, even absolutely, so no need to use fancy shmancy summation methods, to a number in the closed interval [0, 1] and that is the meaning we assign to the notation on the left. And under this interpretation .999... *just* is identical to 1. There is nothing more mysterious than this.
Since the series converges absolutely, virtually all algebraic operations one is used to are valid. It is not difficult to see that every real number in the closed interval [0, 1] has a representation as such a sequence of decimal digits, but it can have more than one representation -- this is most of the times easily bypassed, e.g. in Cantor's theorem going from this representation to the proof that the closed interval is uncountable.
This is for the standard model of the real numbers (and up to isomorphism + some technical conditions, it is the unique such model). There are non-standard models such as the hyperreals, but they shed no light on this specific matter, so I will leave them alone.
My background is in mathematics, so maybe a few of the steps that are obvious to me are not obvious to you, holler if there is something unclear.
We can't use the identity 0.999... = 9/10 × 1.111... because we don't know yet if multiplication on infinite decimals is well-defined. But we can use the identity 0.999... = 9/10 × ∑_(n=0)^∞ (1/10)^n because it's what an infinite decimal is by definition.
@grodrigues My understanding of 1+2+3.... = -1/12 is that it's a result from analytically continuing the zeta function around the poles. But maybe the way to actually calculate that is through Ramanujan summation... I'm not too familiar with how the zeta function values are actually computed.
Zeta function regularization is another way to obtain the result. I do not know the history of the subject and what came first -- Ramanujan died very young and he was not very fond of writing down rigorous proofs.
Thanks grodrigues! I have a minor in math and enough number theory for a comp sci degree so I follow along . . . sort of. I'll have to work at it more though.
"And under this interpretation .999... *just* is identical to 1. There is nothing more mysterious than this."
On rereading this, it is a bit misleading -- there is a proof that needs to be adduced. But the proof is trivial (in mathematical terms): denote by s(n) the partial sum of the first n terms, which is just 0.99.. with 9 repeated exactly n times. Then:
|1 - s(n)| = 1/10^{n}
Taking the limit n -> +\infty the rhs goes to 0, so therefore so does the lhs. Since all operations in sight commute with taking limits, it follows that 1 = lim_{n -> \infty} s(n) but this is just, by definition, the series I wrote above.
I did some (non-original) work on the Zeta function in my paper comparing proofs of the prime number theorem. Zeta (s) is the sum of 1/[n to the s] on the areas of the complex plane where this is a convergent sum. If you put s equals -1 in the above equation you get the series 1 + 2 +3 which Karl Heniz correctly noted is divergent. However, one can redefine the Zeta function by a series of meramorphic continuations such that the Zeta function has the identical values that it had with the original function where it converged but is now convergent in a much larger region. It turns out that Zeta (-1) = -1/12 as the Zeta function is redefined. This DOES NOT MEAN that 1 + 2 + 3 + + = -1/12. The youtube video Numberphile (which is normally excellent) is wrong about this. Karl Heinz is right. See the youtube by mathologer on this. Ramanujan's intuitive equations were later than Riemann's work on the Zeta function.
"This DOES NOT MEAN that 1 + 2 + 3 + + = -1/12. The youtube video Numberphile (which is normally excellent) is wrong about this. Karl Heinz is right."
If you mean that the lhs is to be interpreted as series, no of course not, and no one, or at least I, have not said otherwise. Summation methods for divergent series are standard rigorous, mathematics, there is nothing "balderdash" about them. For Ramanujan summation for example, see Candelpergher's monograph "Ramanujan summation of divergent series" in the LNM series. These divergent sums also appear in physics, where some sense must be made of them, e.g. in the study of the Casimir effect. The same for the zeta function and associated regularization schemes. You may complain that these summation methods stretch the meaning of the lhs beyond what is reasonable -- that is a fair complaint, and I have nothing to say against or in favor of it.
grodrigues Your reply to Karl Heinz was fine. I never used Ramanujan summation. I have used the summation method where one uses the average of the partial sums but that one does not get you to -1/12 in this particular case.
This was over 33 years ago, so I had to look it up; yes it was Cesaro summation that I had done in some other work. I also had done some work on a tauberian theorem by Wiener in a chapter that I can no longer understand (even though I wrote it!). My point was that there is a gap between saying that the Ramanujan sum of the infinite series is -1/12 and the simple equation that 1 + 2 + 3+ is equal to -1/12.
It is perhaps interesting to note that the three principal convenors of the "New" Discourses website are all committed atheists. And, furthermore they really have nothing "new" to say about anything including of course the nature of Ultimate Reality which is of course Divine. James Lindsay presumes to be a self-appointed expert on quite literally everything. I have listened to some of his online talks - they are uniformly boring
The claim that 2+2=5 is obviously and transparently false. We are therefore free to move on from the truth of the content, which has been definitively dismissed, and concern ourselves with the overall reliability and possible motivations of the speaker. It is permitted to do this, even in philosophy, when we are faced with an argument founded upon a proven lie.
Ideologue is a loaded term. It insinuates that the opponent is basing his or her beliefs exclusively on politics and that they are without merit by definition.
History lesson: social justice warrior existed as a commonly used word in the 90's, and it was universally considered to be a word of praise, even among conservatives. Who was responsible for changing its meaning?
Citation needed. I don’t recall ever hearing or reading the phrase ‘social justice warrior’ in the 20th century, or with any meaning other than its present one. And I moved in the sort of circles where it would have been widely used if it were used at all.
It's literally on the first section of the first page of the first Google search. You're using the ancient usenet chestnut of Check Your Facts. I don't fall for the oldest tricks in the book! Ur gonna have to try harder
And you are using the ancient chestnut of ‘Do My Homework For Me’. You are the one making the claim, not I.
Now, perhaps you need to know that Google does not return the same results for everyone, and it certainly does not return the same results for different search terms. Since you won’t even specify your search term, I refuse to play. Stick that in your pipe and smoke it.
I repeat that I never encountered the term in the 20th century. Perhaps it was in use, but it certainly was not common. The Wikipedia article that you probably are referring to as ‘the first section of the first page of the first Google search’ has one citation, from a Montreal Gazette article dated 1991, in which one hard Leftist was using the phrase to praise another hard Leftist. This is in no way sufficient to justify your position. Nor is relying on an otherwise unsourced reference on Wikipedia.
from a Montreal Gazette article dated 1991, in which one hard Leftist was using the phrase to praise another hard Leftist.
It also has the following quote from an authority on word usage.
Katherine Martin, the head of U.S. dictionaries at Oxford University Press, said in 2015 that "[a]ll of the examples I've seen until quite recently are lionizing the person" As of 2015, the Oxford English Dictionary had not done a full search for the earliest usage.
Also, for saying "yes, people used it in a positive word, but the right kind of people didn't use it as a positive word!" you ought to put on a kilt, eat haggis, and be deported to Scotland for punishment.
Tom Simon's point was that the term "social justice warrior" was not in common parlance before 2000. The majority of people familiar with the phrase "social justice" would not have heard the term "social justice warrior" before 2000.
In 2008 or so, I taught a semester course "Social Justice in the Old Testament" which dealt with numerous issues--poverty, abortion, handicapped people, environment, orphans etc. I am fairly sure that I had not heard the term "social justice warrior" at that time.
@Tim Finlay You ignored the words of Katherine Martin by saying "the term "social justice warrior" was not in common parlance before 2000" and then brought up sone ungeneralizable personal experience. I'm supposed to care... why?
Katherine Martin does not enumerate how often the phrase was used. If there were half a dozen sporadic references then it was not a standard phrase. I would not be surprised if "social justice advocate" was far more common. Exactly what is Tom Simon's crime that he deserves deportation to Scotland?
A major event happened regarding Epic Games and Apple, Inc.
This debacle began when Epic Games introducted a direct payment option for their game Fortnite, which circumvented the rule that all payments must be processed thru Apple and that Apple must get 30% (!) of the sum payment. In return, Apple banned the Fortnite app and subsequently Epic Games filed Epic Games, Inc vs. Apple, Inc in the United States Federal District Court of Northern California that Apple has broken federal antitrust law by operating a monopsony in the form of the official Apple app store on their iOS platform. Epic Games also made a cool parody of the famous 1984 Apple 1984 Superbowl commercial
But there's an old wrinkle in this debacle: in 2001 The United States Court of Appeals for the District of Columbia ruled that Microsoft Corp. broke federal antitrust law by including Internet Explorer as the default web browser and adding restrictions to their operating system to both make it harder to uninstall IE and to install competitors such as Netscape. Because this happened in a different federal circuit from this new lawsuit, it is very likely that a resolution will happen only at the level of the Supreme Court. The result of this either way will be extremely significant.
1. If the SCOTUS rules in favor of Epic Games, it would put all of the major tech companies in danger of antitrust and may even lead to them being broken up.
2. If they rule in favor of Apple, Inc, then it will mark a change in the United States's idea of economic justice from 2001. An action that was considered to be unjust would now be considered just, which would have profound ramifications of how the world economy will operate now.
"Now this was the sin of your sister Sodom: She and her daughters were arrogant, overfed and unconcerned; they did not help the poor and needy. They were haughty and did detestable things before me. Therefore I did away with them as you have seen." (Ezekiel 16:49-50)
Remember this, you Christians: St. Ezekiel said that Sodom and Gomorrah were destroyed specifically for oppressing the poor. If you hush hush these abominable actions under the pretense of "not getting political," you are liable to the same punishment Sodom and Gomorrah suffered and Ezekiel warned would fall on the two kingdoms.
If you hush hush these abominable actions under the pretense of "not getting political,"
What abominable actions are you even talking about? You seem to have pulled this out of thin air. Are you sure it wasn’t some other evil Christian cloud you were ranting at?
Sure they are. Oh, I understand that they're not saying that 2+2 is _always_ equal to 5, nor are they necessarily denying the truth of '2+2=4' in the usual sense, but that under certain circumstances, or when certain situations obtain, or interpreted in particular ways, then, yeah, 2+2=5. And I'm claiming that their arguments are lame, boiling down to nothing much more than equivocation or sometimes confusing universals for particulars. And I'm further saying that they could actually have some fun with quus, which would at _least_ be interesting, but nope.
Fr. Spadaro was making an analogy, and Lindsay was talking about how people were chanig the meaning behind the symbols "2", "5" etc. to make the expression true with a different symbol interpretation, under the standard interpretation of those symbols.
Ed, this may be how Pope Francis got elected. He had two supporters here and another two supporters there and they counted it as five supporters.
ReplyDeleteHe was elected because he had two supporters here and two there plus the Holy Spirit. That makes five indeed.
DeleteWhat's so problematic with Pope Francis, Tim?
DeleteIs it the fact that he's trying to be a much better Christian than most of his predecessors that gets on your nerves?
@Anonymous
DeleteTim can speak for himself, but I'm assuming that the answer is no for the obvious reason that you set up a straw man.
Is it the fact that you cannot rebut the real reason Tim has disdain for Francis that you have to make something up?
I wonder how such advocates would respond to chapter 0 in Scholastic metaphysics!
ReplyDelete"What do you mean maths is an example of knowledge that isn't scientific? 2+2 *can* equal 5 . . . And we left scientism alone a long time ago anyway! Haven't you seen us interpret biology?"
"2+2 *can* equal 5"
DeleteSure, if 1+1+1=1, then why not?
Sound's like someone is dividing the substance.
DeleteI was going to respond that moron 'star' but I realized this wasn't about the Most Holly Trinity so I didn't.
Delete1+1+1=1 as an attack on the Trinity, which I will assume it is, is just equivocation. If the idea were that 3 distinct substances equal 1 substance, it might work as a comparison. But the idea is that 3 distinct persons equal 1 substance. That’s not self-contradictory, anymore than 1+1+1 cookies = 1 jar of cookies. In short: one side of the equation has different units than the other, but you’re treating them as the same.
DeleteWilliam,
DeleteOk, so you acknowledge that god is not simple, fine.
It is at least coherent to say 1/3 + 1/3 + 1/3 = 1. Fine, if that is your assertion I cannot call it incoherent in that respect.
Indeed, you may call god a jar of cookies, as it were. Fine, god has parts, this cookie, that cookie, and that other cookie.
New Atheist Laurence Krauss also believes 2+2 can sometimes equal 5. He is so committed to the idea that he printed 2+2=5 on a t-shirt and used it as a quasi-counter argument against William Lane Craig while debating morality. It was at that precise moment I realised that I had just wasted an hour of my life.
ReplyDeleteIncidentally, as well as believing 2+2=5, he also believes that something can from nothing as long as the nothing is actually a something.
That's hilarious! 🤣
DeleteDon't you believe that 1+1+1 = 1?
DeleteAnd don't you believe that something can come from nothing even if nothing is not something (AKA creatio ex nihilo)?
And don't you believe that an unmoving locomotive can move a train?
Have you ever considered that some people may think that is hilarious?
...so a priest, an imam, and a rabbi walk into a bar, and the bartender says, "is this some kind of a joke?"...
Delete@Walter Van der Acker:
Delete"And don't you believe that something can come from nothing even if nothing is not something (AKA creatio ex nihilo)?"
You are equivocating. No one here believes that from nothing something can come -- this is quite explicitly denied by St. Thomas for example. What creation ex nihilo means is that God can create through his power without any preceding matter, but God's power, and only God's power, can bring about created things.
I imagine that "1 + 1 + 1 = 1" is a reference to Trinitarian beliefs.
But at this point, whatever dude, do not let your ignorance get in the way of your silly jabs.
grodrigues
DeleteIn fact, it is the Thomist who is equivocating on what ex nihilo means. Ex nihilo means "from nothing" and not "from something". Creation cannot come from God's power because God's power is immutable.
Anyway, my point was not to show that creatio ex nihilo is impossible, but to remind the readers that something that at first sight may look impossible, like creatio ex nihilo, or the trinity etc. perhaps is possible after all, especially for God.
So, I really don't get what Feser is trying to tell us. We know that 2+2 cannot be 5, but to claim we can have the same confidence in e.g. moral issues by using Natural law Theory is not as straightforward.
You, e.g. seem to think that natural law allows you to insult people by calling them ignorant when they don't agree with you. Not every natural law proponent will agree with your interpretation.
But, I forgive you, grodrigues.
@Walter van der Acker:
Delete"You, e.g. seem to think that natural law allows you to insult people by calling them ignorant when they don't agree with you. Not every natural law proponent will agree with your interpretation."
Calling someone an ignorant is not an insult. Etimologically, ignorant just means someone that ignores. I am simply stating an obvious fact. "Creation cannot come from God's power because God's power is immutable" is an unbelievably ignorant thing to say. If I really wanted to insult you I would add something like stupid or idiot.
And where did you get the idea that I think natural law gives me license to insult anyone? Nowhere. But as is unfortunately common with you, you pull crap out of your ass to try and score some cheap rhetorical points. Your forgiveness is not needed.
Finally, even if one deems there is a parallel in finding the two sets of beliefs ludicrous, there is a difference between what Krauss presents himself to be and then stating some utter absolute nonsense like 2 + 2 = 5 and believing say, the Trinity, since the latter may be more or less difficult to swallow but its defenders explicitly hold that it is *not* contradictory. Whether they are right or not, is not the point; 2 + 2 = 5 is an explicit contradiction. Now maybe Krauss means it in jest, I don't know, but you took him at his word.
Isn't Walter a known and "banned" troll?
Delete- John
'Ex' can mean both 'from' and 'out of'. Creation ex nihilo is creation out of nothing, not creation from no cause.
DeleteWalter,
DeleteThe big mistake you are making is that concepts like “2”, “+”, “=“, and “5” are finite concepts that are easily understood by all.
Concepts like “God”, “creation”, “Trinity”, etc. are generally spoken of analogically and are admitted to be incomprehensible.
Even if (per impossible) Christian dogma was contradictory, it would not be obviously so, or if it is obviously contradictory, then it is clear that the person who makes such claims had very little knowledge of the subject at hand.
While I find that most people do not have the competent knowledge of God (and especially Trinitarian theology) to make such claims, the vast majority of people have competent knowledge of arithmetic to see the absurdity of 2 + 2 = 5.
grodrigues
Delete"And where did you get the idea that I think natural law gives me license to insult anyone? Nowhere. But as is unfortunately common with you, you pull crap out of your ass to try and score some cheap rhetorical points. Your forgiveness is not needed."
Well, I apologize. Obviously telling me I "pull crap out of my ass" is simply a commom Thomistic way of being polite. I should have known that.
Anonymous
No, AFAICT I have not been banned and i am not a troll, although some people around here start calling everyone a troll who dares question some ca-called obvious truths.
Greg
Creatio ex nihilo is creation "from" or "out of" nothing by God. God is called a cause but upon closer examination has nothing whatsoever to do with creation.
Scott
The very fact that God tec are spoken of analogically leaves room for interpretation, especially on moral question which are hardly ever black and white.
My point is that it is always very easy (and I would even say "cheap") to accuse someone else's view of being absurd.
Walter,
DeleteI agree with that, but I do not think that it is cheap to accuse someone who claims 2 + 2 = 5 of absurdity. The claims are clear and the conclusion clearly does not follow. The claims are not nearly as clear in other subjects, even if ultimately one finds them contradictory.
If you cannot claim 2 + 2 = 5 is absurd, then you cannot claim anything is absurd. You might as well drop all debate.
Scott
DeleteThe question is what Antonio Spadaro means by saying that in theology 2+2 can equal 5. My guess is that it is a way of saying that things in theology are not (always) black and white.
And, while you may disagree with that, it isn't absurd.
Walter,
DeleteWell then the most charitable interpretation is that it is a horrible example, because that 2 + 2 = 5 IS black and white and it is obviously contradictory.
Maybe a better example would be that .99999... = 1. That is prima facie false but upon in depth mathematical analysis turns out to be true. Of course that example is limited as well because the terms are much more comprehensible than God, but at least it is closer to the thrust of a charitable interpretation of what he is saying. I hope that is what he meant, but I am afraid it is not.
The "charitable" interpretation of Spadaro's general teaching is that he is only slmost hopelessly benighted and full of crock, but there is some hope for him because all things are possible with God. As to his specific comment that "2+2=5", if it were necessary or even worthwhile to THINK that we needed a "charitable" interpretation of it individually, instead of ignoring it like we ought to ignore almost everything he says, it would be something like either (a) things are not always what they appear; or (b) a thing isn't merely the sum of its parts (especially, the sum of its material parts). Each of these are in fact true and they are valuable general sayings, thing people often DO say, with validity. If he meant either (a) or (b)), though, Spadaro butchered it by casting it in the form of math, because in doing so he took it out of the context in which its validity works and put it into a context in which it doesn't - almost as if to imply "math itself isn't valid" - which UNDERMINES the truth of (a) and (b) in their proper contexts. So, as metaphor, it's a failure. There is nothing uncharitable about pointing out its failure.
DeleteI don't believe that Walter has been banned, and he doesn't typically engage in troll-like behavior. In this thread, though, he picked a particularly poor way to advance a point, one that is rather close to being troll-like. It is probably true that to a careless and silly non-Christian, the doctrine of the Trinity looks like a claim that 1+1+1=1. So? making careful and deep arguments to a careless and silly person is probably completely pointless. Doesn't mean that what the careless person thinks should be granted any weight.
Scott,
Delete"Concepts like “God”, “creation”, “Trinity”, etc. are generally spoken of analogically and are admitted to be incomprehensible."
So, then, it is generally admitted that you and all such Thomists do not know what you are talking about.
I mean literally, you talk about X but you also say you do not comprehend X.
You have no comprehension of the thing you are asserting, by your own words.
If you cannot comprehend X how do you then consider it reasonable to assert you have a sound argument for X?
It is also incomprehensible that 2+2 should =5. But, if one is to simply accept on faith that self contradictory statements are true then why not believe 2+2=5?
Well, apparently you feel there are certain classes of self contradictory statements that are not allowable, but other sorts of self contradictory statements that are allowable.
As Walter points out the assertion of god's immutability is self contradictory with the assertion of god's creativity. An unchanging god that also creates various different things at various different times is incoherent and incomprehensible, yet you seem to think you have reasoned your way to some great truth of the universe by asserting that mutually exclusive assertions are somehow the case, although incomprehensibly so.
Scott
DeleteI agree it's not a good example, and indeed .9999... = 1 would be a better one, but I don't think Spadaro is a mathematician.
That being said, I do not know what Spadaro actually meant, but if it's something along the lines of "Human beings cannot fully understand what God means by such and such" he is, IMO correct, despite the poor analogy.
@Walter van der Acker:
Delete"Obviously telling me I "pull crap out of my ass" is simply a commom Thomistic way of being polite."
So the problem is civil discourse, or the lack thereof. Then maybe *not* posting inane parodies of some of people's most cherished beliefs would be a good start. Now you know where you can stuff your outrage at impoliteness: in the same place you withdraw your crap from.
The whole post is literally about an inane parody of some of people's most cherished beliefs.
Delete@MM:
DeleteDid not know that the claim 2 + 2 = 5 is among any, let alone some, people's cherished beliefs. Is it among yours? That would explain a lot.
Uh huh. That is indeed the only belief parodied in the post. Good job.
Delete@MM:
DeleteSo tell us what else is being parodied? Do they or do they not claim that 2 + 2 some times equals 5? They do. So how is it a parody, much less an inane one? And how are their most cherished beliuefs being parodied? Maybe because 2 + 2 = 5 is an entailemenht of them? Howe exactly? I would assume Fr. Spadaro is just being muddleheaded. If 2 + 2 = 5 does indeed follow from your "most cherished" beliefs, then these beliefs have gone off the deep end.
Good job at posting an inane comment, wherein it is shown that you do not even understand how parodies work. Can we expect any more inanity?
Apparently you did not read to the end. Lindsay claims that these nefarious "colonizers" attempting to undermine mathematics extend their manipulation of meaning to include the definitions of political terms like "racism" and "fascism," and even of the sentence "black lives matter." I grant you that this is not an intentional parody. It is a gruesome caricature of a certain habit of thought on the right. Because surely no one believes this tripe.
Delete@MM:
DeleteMy comment was explicitly in response to parody comments of the OP, so for your response to make any sense, your "The whole post" must be referencing the OP.
How you go from whatever James Lindsay says (and I agree with you, he is an ignoramus) as the position of the OP must be another one of your magical feats of reading. Or you did not have the OP in mind but James Lindsay post. In any case your jab is completely misdirected.
This is the reason I referred to what the post is "about" rather than to the post itself. The post itself posits the links as the "answer" to the question it poses. The post is therefore "about" the articles to which it links. Snark about "magical feats of reading" lands more convincingly if it is not deployed in the midst of a misreading.
Delete@MM:
DeleteHa, the OP "is therefore "about" the articles to which it links." Right. Well, then my snark landed just fine, because I have only "misread" what you "miswrote" in your "magical" feat of "misreading".
Your extended vocabulary has me in awe. Did you just thumbed a thesaurus?
DeleteAgain, if you wish to land a blow about someone's vocabulary, you might try not simultaneously committing a grammatical solecism. Did I just thumbed, indeed.
Delete" ... if you wish to land a blow about someone's vocabulary, you might try not simultaneously committing a grammatical solecism. Did I just thumbed, indeed."
Delete" ... a grammatical solecism ..." LOL
" Did I just thumbed ..."
Yeah.
Thanks for linking to my CWR piece on Spadaro. Almost as outrageous as his vapid remark was the fact that some "orthodox" Catholics defended his remark. Nominalism lives!
ReplyDeletewheat and tares will grow together until harvest
DeleteI've been following James Lindsay on Twitter as part of my "coping with being an excommunicated leftist" strategy, and watching this 2+2=5 fiasco unfold has been absolute *insanity*. The Wokesters have been absolutely obsessed! It's been about two weeks of sophistry now, with no end in sight! The best part was when they decided that this was all part of some sinister, white supremacist alt-right plot when he's an angry liberal! There's zero recognition that the whole thing was basically an Orwellian practical joke.
ReplyDeleteBeen dancing a bit with transgender activists on Twitter today (I'm a masochist for joining), which means being as polite and accommodating as possible, while they heap as much verbal abuse on you as they can, all because you will not scrape and bow and admit that you have "cisgender privilege" over them, the backstabbing, misogynistic traitors.
DeleteIf Dr. Feser reads this comment: thank you, thank you, thank you for being so mercilessly critical of the left. I've thanked you via email before (and I doubt there are other radical feminists here so it's probably obvious who I am), but I've deprogrammed pretty much completely in the light of recent witch hunts. I'm not sure I'd have been able to deal with the attempts at reeducation if I hadn't had enough exposure to conservative thought to really see the totalitarian side of what was going on. The anti-woke left, where you get monstered and told you're a white supremacist for rejecting queer theory, is not exactly a fun place to be. A lot of the critiques of woke culture are *extremely* useful now that I basically feel like a Trotskyist 24/7.
Lately, as time allows, I've been listening to Katlyn Borysenko and Keri Smith. Probably nothing new to you, but an education for me.
DeleteI was thinking of getting Debra Soh's new book
DeleteOrwell was one of the most interesting and insightful liberals ever. Even his Road to Wigan Pier was interesting.
DeleteSpadaro must be in charge of the Vatican bank.
ReplyDeleteEd, while I can understand the desire to respond to the 'woke brigade', what I can't understand is why as a conservative intellectual you've not felt compelled (in 3+ years) to address the absolute embarrassment that is conservatism under Trump and his ilk (everyone from AG Barr to Roger Stone to Guiliani to Michael Cohen and Paul Manafort...seriously it's a murderers' row of corruption, incompetence and buffoonery). Where is the handwringing about conspiracy theories (QAnon), anti-intellectualism, blatant hypocrisy, corruption, etc. while conservatives twist themselves into pretzels in service of the most obvious charlatan to ever hold this much power? Seriously, what the hell?
ReplyDeleteYou're describing the Stupid Party. I've always been clear that I prefer the Stupid Party to the Evil Party.
DeleteAnd what about critizing the Stupid Party and calling for a decent alternative?
DeleteAre you sure that the Stupid Party is not an Evil Party as well?
Deleteif Trump loses the election in November we will soon be sorely missing the "Stupid Party".
DeleteThere aren't enough people already talking about the stupid party (and giving a pass to the evil party)? Big Tech, the universities, the media establishment, these aren't enough people hyperfocused on Trump's every goofy utterance? The real cherry on top of that massive hoard of obsessed drones would be the blog of a relatively obscure philosophy professor?
DeleteThere is a real advantage to being the underdog in terms of social power: it frees you from confirmation bias.
to address the absolute embarrassment that is conservatism under Trump and his ilk
DeleteWell, it is true that conservatives have done some embarrassing things with the Trump years. What is not true is that Trump has done them: Trump isn't conservative. He was a Democrat in the 1970's and 1980's, not a conservative. He wasn't conservative back in 2000 when he first talked about running, and he wasn't in 2012 when he next tried for it. In 2016 he remains what he has been for a long time: a libertarian-leaning populist (probably classical) liberal. People mistake classical liberals for conservatives these days mainly because they are ignorant of how far the Democrat party has moved leftwards from classical liberalism: I think that Humbert Humphrey would be called a moderate conservative these days. And very idea that someone would put Giuliani in the same sentence with conservatism is laughable.
Ed, I think that's quite a debatable point, but I suppose a topic for another day.
DeleteTN, I'm not interested in what 'Big Tech' has to say about Trump, I'm interested in what a conservative Catholic intellectual has to say about him, thus why I'm here. I'm especially interested b/c I disagree with Ed that there's some significant imbalance between the parties in their stupidity and evil. Some days I might even argue the conservative side is more cravenly evil. It's definitely not a settled matter. So I don't think Ed's continued one-sided shots at 'the left' are justifiable when 'the right' is just as stupid and evil, if not more so at times, while also having the added dynamic of being the more traditionally conservative and religious side (making their hypocrisy all the more galling to me as a christian).
Tony, I said he's an obvious charlatan...that's exactly why it's so embarrassing that so many 'stalwart' conservatives (everyone from Lindsey Graham and Mitch McConnell to the majority of evangelical christians) have done his bidding and fawned over him with seemingly no questions asked and no cognitive dissonance (or if there is awareness, then a truly terrifying cold + calculated pragmatism). It's particularly hilarious watching old clips of Graham attacking Trump and describing how despicable he is, it goes well beyond the typical 'tear down your opponent until you have to work with them' political maneuvering. The postmortem on this administration and its adherents will not be pretty.
everyone from Lindsey Graham and Mitch McConnell to the majority of evangelical christians...It's particularly hilarious watching old clips of Graham attacking Trump and describing how despicable he is, it goes well beyond the typical 'tear down your opponent until you have to work with them' political maneuvering
DeleteI don't know what kool-aid you are drinking: Graham is called one of the most liberal of Republicans, by the ATLANTIC no less.
https://www.theatlantic.com/politics/archive/2014/06/how-lindsey-graham-stomped-the-tea-party/372521/
The post mortem on Trump will be that even though the country had become so degenerate that the conservatives could not field a winning candidate, the liberals were busy tearing themselves to shreds between a moderate liberal Trump and far, far left liberals whose main objectives were to destroy the country the country even faster than Trump, while the center-of-the-road moderates who neither understood conservatism nor liberalism, but had been left holding the Republican flag while the liberals moved leftwards, were so relieved not to have the country wrecked at an even faster pace that they gave honor to Trump for his only being a moderate liberal. (They may have said "conservative" but because they never understood conservatism, they meant "not far, far left liberal".)
Anon,
Delete"I'm not interested in what 'Big Tech' has to say about Trump, I'm interested in what a conservative Catholic intellectual has to say about him"
Well, there ya go: he thinks one side is stupid and the other side is evil. I'm sorry if you find that unsatisfactory. I'm sorry if you feel like you should get to set the topics on someone else's blog. But if you're really interested in such a discussion, maybe you could try asking about something specific rather than snarky generalizations topped of with a "what the hell".
Ah yes: removing children from their parents and putting them in cages is stupid, not evil. 2 + 2 = 6!
DeleteMM, could you provide a link with evidence that children are put in cages?
DeleteSure, & I'm sorry for whatever disability prevents you from performing a Google search. The first result is from yesterday. It even throws you a bone: of course both parties are evil, though the current administration is even more ruthless on this particular score than was its predecessor. I just can't imagine the moral depravity necessary to regard the GOP as anything but evil. I seem to remember a certain Jewish peasant counseling the defense of the poor, the sick, the stranger, the prisoner.
Deletehttps://apnews.com/2663c84832a13cdd7a8233becfc7a5f3
MM,
DeleteThank you for your concern for my health!
The link you provided just says that Michelle Obama accused Trump of putting kids in cages. It's not very surprising that political rivals make exaggerated accusations about each other, is it? Furthermore, the word "cages" is in quotes indicating that it the description is an interpolation.
So, let me clarify what I'm asking for: what I'm asking for is substantive evidence that supports your claim that some political party is putting kids in cages. If you could please support your claim, that would be great! Thanks!
MM, I am sorry for whatever disability prevents you from reading the stories you link to. The AP News article cited clearly states that nobody was put in a cage, and that the Trump administration neither built the chain-link enclosures used for temporary detention at the border, nor originated the use to which they were put.
DeleteIf the GOP is evil on this score, so are the Democrats.
Tom Simon, I'm sorry for whatever disability prevents you from reading the phrase in my comment "both parties are evil," a reference to the fact that I also point out in the comment that the article "throws [my interlocutor] a bone" by impugning the Obama administration.
DeleteIn other words, yes, thanks for saying exactly what I said.
You are right about one thing—a "chain link enclosure" can never function as a cage. Mea culpa. The GOP is angelic.
TN, if you don't know that the current administration is removing children from their families and detaining them in (ahem) "chain link enclosures," I suggest you learn to read. If you want to argue about the definition of a "cage," I suggest you grow a conscience, not to mention a spine.
DeleteMM,
DeleteSo you will not substantiate your claim that some political party is putting kids in cages.
Jesus Christ, TN. If you folks really want to know what is going on at the border, you can check the news:
Deletehttps://www.nytimes.com/2019/07/02/us/politics/border-center-migrant-detention.html
It's depraved, I repeat, to deny that this is evil. Would you like me to look up the relevant passages in the Gospels for you, too?
Why would anyone want smart, evil people to run the country when there is a stupid evil alternative?
DeleteSomething like this, perhaps:
1. If the stupid party isn't evil, you should vote for the stupid party over the evil party.
2. If the stupid party is evil, you should vote for the stupid party over the non-stupid evil party. (Why would you want people who are better at bringing about evil in the world in power?)
3. The stupid party is either evil or not.
4. Therefore, you should vote for the stupid party (1-3, Dilemma)
Justify your support for evil however you wish. Why would you want to passively accept a state of affairs that forces you to choose between evils, is the only real question.
DeleteSpare me the fatuous bluster, MM. I gave you an argument. You owe me a reply, or an honest admission that you're a sophist hack, and a sneak, and a fraud.
Deletehttps://www.usnews.com/news/politics/articles/2020-08-18/ap-fact-check-michelle-obama-and-the-kids-in-cages?fbclid=IwAR2e5a0DC24bEOom6IyCpjEqvbOaM5BtS1PSEnODPDGewQC2x3N6qrTMmy0
DeleteI provided that link earlier myself, genius. You think I give a shit about the idiot Democrats? And LOL, your dumb little petitio principii is hardly a logical argument.
DeleteMM,
DeleteAfter reading the NYT article, I assume that what you mean by “putting children in cages”, is that it is “evil” to hold children in a border detention facility. Is that right?
The article details “squalid” conditions in several border facilities last year. Border patrol officials quoted in the article claimed that they were overrun by large numbers of people and they were not prepared to handle them all (probably because of the Central American caravans last year) and the article says they were tranferring detainees to less crowded locations and setting up temporary facilities. Does that not seem like a plausible explanation? Is there some evidence that compels one to reject that explanation in favor of the contention that Republicans actually just enjoy human suffering?
Would you agree that there is a high degree of grandstanding and exaggeration over this issue? The article claims that people were forced to drink from toilets, but we now know that the facility uses a fixture that has a sink and faucet on top, and a toilet on the bottom (1). Does this kind of prevarication indicate the desire smear one’s opponent is more important than what is true?
The article does not mention it, but the day before this article was published, Trump signed a $4.6 billion dollar relief package “The largest portion of the funding — $2.88 billion — will go to Health and Human Services to provide shelter and care for unaccompanied children.” (ibid) Does this demonstrate the “evil” you are protesting?
No one disagrees that every effort should be made to eliminate inhumane conditions, but if those conditions arose from evil intent is a different question. Or maybe you just think borders are evil? Is that the more fundamental grievance you have?
(1) https://www.factcheck.org/2019/07/confusion-at-the-border/
Of course borders are evil. There should be none. But that isn't the issue. The president has not kept his "intent" secret. I assume you are familiar with his racist rhetoric, which you can't possibly need me to google for you.
DeleteBut perhaps you are concerned only about Americans. From a report last year:
"Last month, Francisco Erwin Galicia, a Dallas-born teenager, was held in Immigration and Customs Enforcement (ICE) custody for more than three weeks, where he says he lost 26 lb. due to the poor conditions and was not allowed to shower. In March, Customs and Border Protection detained 9-year-old Julia Isabel Amparo Medina, a U.S. citizen, for more than 30 hours when she crossed the border at the San Ysidro port of entry to attend school. These are not isolated incidents. ICE has requested the detention of 3,076 American citizens from October 2002 to December 2018, according to Syracuse University’s Transactional Records Access Clearinghouse."
If you can't see that this is evil—if you prefer to quibble about "intent" despite knowing perfectly well that the administration has indicated its evil intent time & again (please look up Stephen Miller's comments on the issue), then we are at cross purposes, and I wouldn't have us any other way.
Why are borders evil?
DeleteThere is no defensible moral framework that regards the restriction of freedom of movement as a good, particularly when that freedom of movement is used to flee oppression. If your family is going to be killed in one place, you should be allowed to move to another. If you can't make enough to support your family, you should be allowed to move to where you can. It is barbaric to regard one person as less deserving of the benefits that inhere in living in a certain place simply because he was not born in that place.
DeleteIn this sense, of course, borders are not evil in and of themselves—as long as they are open to all regardless of circumstance.
If you're wondering if I'm a leftist nut, I should note that I also think the police should be abolished and capitalism should be overthrown.
MM,
DeleteYou wrote: "It is barbaric to regard one person as less deserving of the benefits that inhere in living in a certain place simply because he was not born in that place."
So then you completely support Christopher Columbus.
When the empire of CHAZ colonized downtown Seattle, the first thing they did was establish borders and a police force to enforce the borders with guns. That was "evil" wasn't it?
Look, I tried to take you seriously, but you're just hysterical. Thanks for the discussion.
Oh, touché! To support open borders so that people might free oppression and move to find better opportunity is the *exact same thing* as to support military imperialism! How did I never think of that?
DeleteI have not tried to take you seriously, as you have shown from the outset that you are not serious.
*flee
DeleteAny books you recommend to address this kind of postmodernism?
ReplyDeleteJames Lindsay has no idea what "deconstruction" means; his notion that "critical social justice theory" is "postmodernist" is laughable. The latter term refers to French theory in the 60s with which Lindsay is unfamiliar, given that he misuses each concept he invokes & misapplies it to present-day struggles against racism where it has no currency whatsoever. You people are delusional.
DeleteJames Lindsay didnt make up the connection to racism. Academics and educators were literally saying that 2+2 only ever making 4 is literally just the result of the white supremacist male patriarchy.
DeleteSure, the link between deconstruction and the neo-Marxist worldview is rather hard to make, but dont put that on Lindsay. Put that on the deconstructionists and neo-Marxists who borrow from each other and blur their distinctions.
Marxists and deconstructionists are ever at odds, since the former uphold a form of structural determination that the latter attempt to undermine. Marxism and deconstruction are incompatible, as Derrida's late attempt to incorporate Marx inadvertently made clear.
Delete(Not to mention that there are hardly any practicing deconstructionists today.)
DeleteI think the most important thing is that both Marxism and deconstructionism are bull.
DeleteMarx's analysis of how value is produced under capitalism—which is what "Marxism" mainly is—is hardly bull. But of course you've read the three volumes of Capital, so can explain what is wrong with Marx's demonstration of the general forms of differential rents.
Delete"Marxists and deconstructionists are ever at odds"
DeleteStrict Marxists maybe see it that way. Neo-Marxists and their useful idiots not so much. There is also a very stark difference between Karl Marx himself and Marxists, then there are neo-Marxists who are critical of both.
Again, Lindsay is simply explaining where they get the idea that our cultural acceptance of 2+2 only making 4 is just the result of the oppressive white male superstructure. Whether he gets it exactly right, his main point is correct that it's an incoherent mish-mash of neo-Marxism and deconstructionism.
Also, I wonder whether your judgements of Lindsay's understanding of these are correct. See here:
https://newdiscourses.com/2020/07/complex-relationship-between-marxism-wokeness/
MM: Marx's analysis of how value is produced under capitalism—which is what "Marxism" mainly is—is hardly bull.
DeleteActually, everything Marx ever said about economics is bull. The labour theory of value, which is the foundation of his entire system, is so laughably unfounded that it barely even qualifies as wrong.
Not terribly surprised to see this canard repeated. Marx argued against the labor theory of value, a staple of Ricardian economics. You can't have read the relevant passages. What he specifically denies is that the value of a product derives from the quantity of labor required to produce it (both Smith and Ricardo hold versions of this thesis). For Marx, the relevant criterion is the amount of "socially necessary labor time," a society-wide norm to which producers must adhere (if your employers are taking longer than average to produce your product, you're not going to produce as many units in the same period of time as the next fellow, whose employees are producing more units per hour).
DeleteBut you know all this, because you're intimately familiar with the work of Diane Elston, Moishe Postone, David Harvey, and the many others who have for decades now pointed out that the standard reading (held by some orthodox Marxists, no less) of Marx as holding Ricardo's labor theory of value is wrong.
Imagine being a Marxist in 2020
Delete"Marx's analysis of how value is produced under capitalism—which is what "Marxism" mainly is—is hardly bull."
DeleteWalk into an economics department and start talking about this stuff. Please.
Yet such wacky leftist rags as The Economist and The Financial Times continue to assert his relevance.
Deletehttps://www.ft.com/content/cf6532dc-4c67-11e8-97e4-13afc22d86d4
I'm not sure you've ever been in an economics department (I have a PhD from the University of Chicago), but how about I walk into the New School's and start talking about it?
Deletehttps://www.newschool.edu/nssr/story/anwar-shaikh-publishes-analysis-of-modern-capitalism/
Yes I have, are you claiming that most people would agree with you? Because such views are quite heterodox.
DeleteOh, and is your PhD in economics?
DeleteOf course "most people" would not agree. That hardly means there are no economists in respected economics departments who take Marx's analysis of capitalism quite seriously indeed and would laugh at dismissive characterizations of it. Anwar Shaikh and Duncan Foley at the New School; Ben Fine at the University of London; Andrew Glyn (d. 2007) at Oxford; Michael Piore at MIT; Immanuel Wallerstein (d. 2019) at Yale; John Roemer at Yale; Richard Wolff at U. of Massachusetts; Michael Hudson at U. of Missouri and Bard ... I could list dozens of professors in prestigious economics departments who, if I "walked in to an economics departments and started talking about this stuff" wouldn't bat an eye.
DeleteThe last time I saw a huge pile of dump like this I was at a barnyard
ReplyDelete1 = .999...
ReplyDeleteX = .999...
10X = 9.999...
9X = 9
X = 1
.999... = 1
T N,
DeleteHaha! We had the same idea. Yes that is a much better example than 2 + 2 = 5. At first glance, it looks absurd, but it turns out to be true.
Scott,
DeleteIsn't that weird?
There are a lot of weird, counter-intuitive things in number theory. When I first heard that .999... = 1, I thought it the person telling me was crazy, but there are probably a dozen ways to prove it and they all work. It really causes a person to tread a little more lightly whenever you thing you know something for sure.
T N:
DeleteWell, you are assigning a meaning to an *infinite* sequence of digits and then carefully check what algebraic manipulations you are allowed to do (not all are valid, which is usually how the above tautology is turned upside down into a would-be proof of a contradiction). And once you realize that is what you are doing, *some* weirdness is to be expected.
grodrigues,
DeleteThat is true. As I'm sure you know, it is not a contradiction, it is because 9 repeating is not a real number. It is still a good trick, and a good lesson in how easy it is to be decieved.
Surprised no one's brought up 1+2+3+4+... = -1/12 ;)
DeleteTN's "counter-intuitive" result is Kosher, since he is describing an algebraic process.
Deletesum(n) from 1 to infinity = -1/12 is balderdash because it rests on averages, which is a no-no for a mathematician.
@Karl Heintz:
DeleteThe series diverges trivially; doing invalid algebraic manipulations with series gives the result. A more precise way to get it is by using "non-standard" ways to assign a meaning to such divergent series. There are inumerous such summation methods (usual with famous mathematician names attached like Cesaro summation, Abel summation, Banach limits, etc.) and regularization schemes. The one in question is Ramanujan summation, from the Indian mathematician prodigy Srinivasa Ramanujan.
grodrigues,
DeleteThanks for discussing this, it is very interesting.
So is it true to say that one reason the illusion works is because we want to think of it as a convergent series, but, in fact, it is divergent? The same "proof" can be done by sum of an infinite series, but, of course, it just performs the same trick.
We want to think that 999... is really, really close to 1 but just a little less, but, of course it isn't. If 999... were a real number, there would be infinite numbers between 999... and 1.
T N:
Delete"We want to think that 999... is really, really close to 1 but just a little less, but, of course it isn't. If 999... were a real number, there would be infinite numbers between 999... and 1."
No. Pick a sequence of decimal digits (in what follows there is nothing special about base 10, you could use any other base) which you view as the would be number .d1d2... We want to interpret the latter as (the notation for) a real number in the closed interval [0, 1] -- I am leaving the integral part aside just for ease of presentation. So what is the standard way? Well, just like an integral number written in decimal notation is really "just" a polynomial in 10, so is such a sequence an infinite series in 1/10, specifically, *by definition* (using LaTeX notation):
.d1d2... = \sum_{n = 1}^{\infty} d_{n}/10^{n}
It is easy to see that the series on the right converges, even absolutely, so no need to use fancy shmancy summation methods, to a number in the closed interval [0, 1] and that is the meaning we assign to the notation on the left. And under this interpretation .999... *just* is identical to 1. There is nothing more mysterious than this.
Since the series converges absolutely, virtually all algebraic operations one is used to are valid. It is not difficult to see that every real number in the closed interval [0, 1] has a representation as such a sequence of decimal digits, but it can have more than one representation -- this is most of the times easily bypassed, e.g. in Cantor's theorem going from this representation to the proof that the closed interval is uncountable.
This is for the standard model of the real numbers (and up to isomorphism + some technical conditions, it is the unique such model). There are non-standard models such as the hyperreals, but they shed no light on this specific matter, so I will leave them alone.
My background is in mathematics, so maybe a few of the steps that are obvious to me are not obvious to you, holler if there is something unclear.
Say there grod, those are some pretty impressive copy and paste skills on display, I mean, whooo, I am totally impressed.
DeleteWhich site did you copy your material from? Just wondering.
0.999... is a geometric series multiplied by 9/10. It's the geometric series for r=1/10. This value is inside of the radius of convergence, so
Delete0.999... = 9/10 × ∑_(n=0)^∞ (1/10)^n
= 9/10 × 1/(1-1/10)
= 9/10 × 1/(9/10)
= 1
We can't use the identity 0.999... = 9/10 × 1.111... because we don't know yet if multiplication on infinite decimals is well-defined. But we can use the identity 0.999... = 9/10 × ∑_(n=0)^∞ (1/10)^n because it's what an infinite decimal is by definition.
@grodrigues My understanding of 1+2+3.... = -1/12 is that it's a result from analytically continuing the zeta function around the poles. But maybe the way to actually calculate that is through Ramanujan summation... I'm not too familiar with how the zeta function values are actually computed.
Delete@Anonymous:
DeleteZeta function regularization is another way to obtain the result. I do not know the history of the subject and what came first -- Ramanujan died very young and he was not very fond of writing down rigorous proofs.
Thanks grodrigues! I have a minor in math and enough number theory for a comp sci degree so I follow along . . . sort of. I'll have to work at it more though.
DeleteI wrote:
Delete"And under this interpretation .999... *just* is identical to 1. There is nothing more mysterious than this."
On rereading this, it is a bit misleading -- there is a proof that needs to be adduced. But the proof is trivial (in mathematical terms): denote by s(n) the partial sum of the first n terms, which is just 0.99.. with 9 repeated exactly n times. Then:
|1 - s(n)| = 1/10^{n}
Taking the limit n -> +\infty the rhs goes to 0, so therefore so does the lhs. Since all operations in sight commute with taking limits, it follows that 1 = lim_{n -> \infty} s(n) but this is just, by definition, the series I wrote above.
I did some (non-original) work on the Zeta function in my paper comparing proofs of the prime number theorem. Zeta (s) is the sum of 1/[n to the s] on the areas of the complex plane where this is a convergent sum. If you put s equals -1 in the above equation you get the series 1 + 2 +3 which Karl Heniz correctly noted is divergent. However, one can redefine the Zeta function by a series of meramorphic continuations such that the Zeta function has the identical values that it had with the original function where it converged but is now convergent in a much larger region. It turns out that Zeta (-1) = -1/12 as the Zeta function is redefined. This DOES NOT MEAN that 1 + 2 + 3 + + = -1/12. The youtube video Numberphile (which is normally excellent) is wrong about this. Karl Heinz is right. See the youtube by mathologer on this. Ramanujan's intuitive equations were later than Riemann's work on the Zeta function.
Delete@Tim Finlay:
Delete"This DOES NOT MEAN that 1 + 2 + 3 + + = -1/12. The youtube video Numberphile (which is normally excellent) is wrong about this. Karl Heinz is right."
If you mean that the lhs is to be interpreted as series, no of course not, and no one, or at least I, have not said otherwise. Summation methods for divergent series are standard rigorous, mathematics, there is nothing "balderdash" about them. For Ramanujan summation for example, see Candelpergher's monograph "Ramanujan summation of divergent series" in the LNM series. These divergent sums also appear in physics, where some sense must be made of them, e.g. in the study of the Casimir effect. The same for the zeta function and associated regularization schemes. You may complain that these summation methods stretch the meaning of the lhs beyond what is reasonable -- that is a fair complaint, and I have nothing to say against or in favor of it.
grodrigues
DeleteYour reply to Karl Heinz was fine. I never used Ramanujan summation. I have used the summation method where one uses the average of the partial sums but that one does not get you to -1/12 in this particular case.
@Tim Finlay:
Delete"I have used the summation method where one uses the average of the partial sums but that one does not get you to -1/12 in this particular case."
Césaro summation? Césaro summation cannot handle series that diverge to infinity.
This was over 33 years ago, so I had to look it up; yes it was Cesaro summation that I had done in some other work. I also had done some work on a tauberian theorem by Wiener in a chapter that I can no longer understand (even though I wrote it!). My point was that there is a gap between saying that the Ramanujan sum of the infinite series is -1/12 and the simple equation that 1 + 2 + 3+ is equal to -1/12.
DeleteIt is perhaps interesting to note that the three principal convenors of the "New" Discourses website are all committed atheists. And, furthermore they really have nothing "new" to say about anything including of course the nature of Ultimate Reality which is of course Divine.
ReplyDeleteJames Lindsay presumes to be a self-appointed expert on quite literally everything. I have listened to some of his online talks - they are uniformly boring
Of course, this is completely irrelevant to the truth of the content.
DeleteThe claim that 2+2=5 is obviously and transparently false. We are therefore free to move on from the truth of the content, which has been definitively dismissed, and concern ourselves with the overall reliability and possible motivations of the speaker. It is permitted to do this, even in philosophy, when we are faced with an argument founded upon a proven lie.
DeleteIdeologue is a loaded term. It insinuates that the opponent is basing his or her beliefs exclusively on politics and that they are without merit by definition.
ReplyDeleteHistory lesson: social justice warrior existed as a commonly used word in the 90's, and it was universally considered to be a word of praise, even among conservatives. Who was responsible for changing its meaning?
Citation needed. I don’t recall ever hearing or reading the phrase ‘social justice warrior’ in the 20th century, or with any meaning other than its present one. And I moved in the sort of circles where it would have been widely used if it were used at all.
Delete
DeleteIt's literally on the first section of the first page of the first Google search. You're using the ancient usenet chestnut of Check Your Facts. I don't fall for the oldest tricks in the book! Ur gonna have to try harder
And you are using the ancient chestnut of ‘Do My Homework For Me’. You are the one making the claim, not I.
DeleteNow, perhaps you need to know that Google does not return the same results for everyone, and it certainly does not return the same results for different search terms. Since you won’t even specify your search term, I refuse to play. Stick that in your pipe and smoke it.
I repeat that I never encountered the term in the 20th century. Perhaps it was in use, but it certainly was not common. The Wikipedia article that you probably are referring to as ‘the first section of the first page of the first Google search’ has one citation, from a Montreal Gazette article dated 1991, in which one hard Leftist was using the phrase to praise another hard Leftist. This is in no way sufficient to justify your position. Nor is relying on an otherwise unsourced reference on Wikipedia.
Try harder or don’t bother trying at all.
from a Montreal Gazette article dated 1991, in which one hard Leftist was using the phrase to praise another hard Leftist.
DeleteIt also has the following quote from an authority on word usage.
Katherine Martin, the head of U.S. dictionaries at Oxford University Press, said in 2015 that "[a]ll of the examples I've seen until quite recently are lionizing the person" As of 2015, the Oxford English Dictionary had not done a full search for the earliest usage.
Also, for saying "yes, people used it in a positive word, but the right kind of people didn't use it as a positive word!" you ought to put on a kilt, eat haggis, and be deported to Scotland for punishment.
Tom Simon's point was that the term "social justice warrior" was not in common parlance before 2000. The majority of people familiar with the phrase "social justice" would not have heard the term "social justice warrior" before 2000.
DeleteIn 2008 or so, I taught a semester course "Social Justice in the Old Testament" which dealt with numerous issues--poverty, abortion, handicapped people, environment, orphans etc. I am fairly sure that I had not heard the term "social justice warrior" at that time.
Delete@Tim Finlay You ignored the words of Katherine Martin by saying "the term "social justice warrior" was not in common parlance before 2000" and then brought up sone ungeneralizable personal experience. I'm supposed to care... why?
DeleteKatherine Martin does not enumerate how often the phrase was used. If there were half a dozen sporadic references then it was not a standard phrase. I would not be surprised if "social justice advocate" was far more common. Exactly what is Tom Simon's crime that he deserves deportation to Scotland?
DeleteA major event happened regarding Epic Games and Apple, Inc.
ReplyDeleteThis debacle began when Epic Games introducted a direct payment option for their game Fortnite, which circumvented the rule that all payments must be processed thru Apple and that Apple must get 30% (!) of the sum payment. In return, Apple banned the Fortnite app and subsequently Epic Games filed Epic Games, Inc vs. Apple, Inc in the United States Federal District Court of Northern California that Apple has broken federal antitrust law by operating a monopsony in the form of the official Apple app store on their iOS platform. Epic Games also made a cool parody of the famous 1984 Apple 1984 Superbowl commercial
But there's an old wrinkle in this debacle: in 2001 The United States Court of Appeals for the District of Columbia ruled that Microsoft Corp. broke federal antitrust law by including Internet Explorer as the default web browser and adding restrictions to their operating system to both make it harder to uninstall IE and to install competitors such as Netscape. Because this happened in a different federal circuit from this new lawsuit, it is very likely that a resolution will happen only at the level of the Supreme Court. The result of this either way will be extremely significant.
1. If the SCOTUS rules in favor of Epic Games, it would put all of the major tech companies in danger of antitrust and may even lead to them being broken up.
2. If they rule in favor of Apple, Inc, then it will mark a change in the United States's idea of economic justice from 2001. An action that was considered to be unjust would now be considered just, which would have profound ramifications of how the world economy will operate now.
"Now this was the sin of your sister Sodom: She and her daughters were arrogant, overfed and unconcerned; they did not help the poor and needy. They were haughty and did detestable things before me. Therefore I did away with them as you have seen." (Ezekiel 16:49-50)
DeleteRemember this, you Christians: St. Ezekiel said that Sodom and Gomorrah were destroyed specifically for oppressing the poor. If you hush hush these abominable actions under the pretense of "not getting political," you are liable to the same punishment Sodom and Gomorrah suffered and Ezekiel warned would fall on the two kingdoms.
If you hush hush these abominable actions under the pretense of "not getting political,"
DeleteWhat abominable actions are you even talking about? You seem to have pulled this out of thin air. Are you sure it wasn’t some other evil Christian cloud you were ranting at?
What abominable actions are you even talking about?
DeleteApple, Inc's market capture.
All of these arguments for why 2+2=5, but no one tries a Kripke style quus argument? Lame. These Jacobins need to up their philosophy game.
ReplyDeleteYou do realize that neither Fr. Spadaro nor the people Lindsay is criticizing are actually claiming 2 + 2 = 5?
DeleteSure they are. Oh, I understand that they're not saying that 2+2 is _always_ equal to 5, nor are they necessarily denying the truth of '2+2=4' in the usual sense, but that under certain circumstances, or when certain situations obtain, or interpreted in particular ways, then, yeah, 2+2=5. And I'm claiming that their arguments are lame, boiling down to nothing much more than equivocation or sometimes confusing universals for particulars. And I'm further saying that they could actually have some fun with quus, which would at _least_ be interesting, but nope.
DeleteFr. Spadaro was making an analogy, and Lindsay was talking about how people were chanig the meaning behind the symbols "2", "5" etc. to make the expression true with a different symbol interpretation, under the standard interpretation of those symbols.
DeleteExactly. It's called equivocation, and it's lame.
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