I just have to disagree with this.

You don't have to have the ability to make a bijection to have size, a < b does give a size comparison and size doesn't somehow evaporate without a bijection. The ability to measure accurately something exactly simply isn't a precursor for size to exist. You are creating your own math so good luck with that.

If the size is unmeasurable then it is not a size. Size has to be an integer. — Devans99

Aha!

This is the definition that you base your thinking. An integer shows size, yes, but size doesn't have to be an integer! Just to take one definition:

In mathematical terms, "size is a concept abstracted from the process of measuring by comparing a longer to a shorter"

Let's remember (again) the heap of rock pebbles. A heap is more than one, but it's not exact. Yet it can perfectly perform the task of defining size. Just as you can have a < b < c , which naturally do define size, but don't give 'exact sizes' like the bijection a +1 = b. Now a < b < c isn't a bijection, yet it does define obviously size!

(And we already had the discussion about how impossible is it to count the natural numbers from 1 to googolplex. Of course, the concept of size is often applied to ideas that have no physical reality, just like in mathematics.)

I'll define infinity as ‘A number bigger than any other number’ then it is clear that there can be only one such number - if there was a second infinity then both would have to be larger than the other - a contradiction - so there can be only one infinity. — Devans99

So, could it be then there would be Absolute Infinity?

An infinite set is unmeasurably bigger than a finite set. An infinite set therefore has no size. — Devans99

Ok, let's think about what you said here.

So infinite sets are unmeasurably bigger. Fine, they are bigger, we agree with this.

How then couldn't you simply say that infinite sets have an unmeasurably bigger size? Meaning that they do have a size, but the size is obviously unmeasurable, because (accurate) measuring is something that you can do in the finite realm.

Not only is it possible, it is a fact. Yes, we have secret knowledge and we exert influence over human affairs. Any given ordinary individual may not like the way things are working out, but they are ignorant of our objectives. And they are going to stay ignorant, because we are not going to reveal what our objectives are.

We advise you to discontinue this line of inquiry, for your own good. — Bitter Crank

Finally Bitter Crank shows his real face!

We should shut up and continue debating about other non-important issues...

- An infinite set does not have a cardinality property: cardinality or size implies the ability to measure something. Infinity is by definition unmeasurable so infinite sets have no cardinality/size property — Devans99

But isn't an infinite set bigger than any finite set? Doesn't that imply size, even if obviously you cannot measure it like a finite set?

And what is your problem with the reductio ad absurdum proof of there not being a bijection between the natural numbers and the reals?

I would not use bijection to arrive a conclusion about a sets size; bijection claims that there are the same number of rationals as naturals so it is clearly wrong (naturals are a proper subset of the rationals so bijection is giving a wrong results). — Devans99

How do you come to this conclusion? Give a proof that this isn't so. Because the proof of this being so is for me quite understandable (if I remember it correctly): you can well order the rationals, hence there is a bijection between the rationals and the natural numbers.

To all of us: discussion with Devans99 is a waste of time. — tim wood

Yeah maybe, you cannot just say that set theory is wrong. It would be similar that I would simply declare quantum physics wrong in physics. You would actually need to give a proof of it in mathematics.

We've been issuing passports since about 1912 (taking the Brits) and the rest of Europe a bit later. — Benkei

I think official documents equivalent to passports have been used since Ancient Egypt. The Chinese used them extensively. Passports have been used here since the time of Finland being the Grand Dutchy of Russia and Finns traveling to Russia and Russians traveling to Finland needed a passport starting from 1819. During that year a bureau for Passports was established in St. Petersburg for Finland.

A French passport from 1602:

Csalisbury's totally accurate description of you above (and me) are so spot on that it's now just entertainment for others for us to continue this extremely stereotypical debate.

Despite ssu 's continued spurning of the Koch Brother's extremely well-documented influence in politics via "covert operations" the objective of which is to "bring about social change" through a "vertically and horizontally integrated" strategy, starting "from idea creation to policy development to education to grassroots organizations to lobbying to litigation to political action". Often known as the "Kochtopus", the ultimate end goal has been to deregulate their industry and maximize their profits by promoting libertarian talking points. There's no conspiracy, it's merely capitalists using their capital to ensure they can continue to generate more capital by shifting what the public is discussing — Maw

Your utter inability to see how exactly similar your argumentation is to the right-wing hysterical outrage against Soros, even with similar figures of speech like reference to an octopus with it's tentacles everywhere and 'covert operations', is so telling that it's funny. Just change the names and change it from libertarian talking points to liberal/leftist talking points and it's exactly what you find among Breitbart following Trump fans.

Like to berries... or more correctly two strangling octopuses:

The steps are fairly simple. Call yourself a provocateur and tour college campuses with lectures titled "Why Do Lesbians Fake So Many Hate Crimes", or "The Dangerous Faggot". — Maw

Don't forget sending emails like 'urging Yale University students to think critically about an official set of guidelines on costumes to avoid at Halloween'. Oh those devious ways the evil alt-right gets innocent students to play along and get that angry response they have planned for!

Of course the campus nonsense hasn't been picked up in mainstream news as it hasn't become Trump's trump card like the kneeling NFL players or flag burning at the time of Bush senior (if I remember correctly), but that doesn't apparently matter.

Maw, here, is standard issue Internet Leftist rage, tapped into a flagrant sense of intellectual and moral superiority. SSU, here, is standard issue erstwhile-centrist-liberal-now-battling-left-excesses-thereby-inexorably-becoming-right-as-leftists-just-get-more-and-more-ridiculous. i'm standard issue 'this is all just spectacle' buttressing my 'above it allness' at the expense of engagement. — csalisbury

All well defined, have to say.

(Of course I've never seen myself as a centrist liberal at all, but as coming from a socialist nanny-state that Bernie Sanders praises sometimes and not from North America, that definition can be understood)

Yet what you are implying is that someone funding an institute project that publishes something is then directly supporting the factual arguments of any article written in the project. Billionaires give to a lot of things money and their decision is just to whom they give the money.

Isn't that a bit overreaching conclusions? It is really similar like the conspiraty-theorists in the right.

I'll take an example: George Soros has given money to associations that some are close to Black Live Matters. And OMG! All the hubbub around that in the right. It is similar to think that the Koch brothers are funding articles about Camille Paglia.

This conspiracy bullshit of billionaires meddling through journal articles (because they have given money to the institutions) is simply silly.

First, the article takes Paglia as an example, but it also takes professor Samuel Abrams. To infer then that Paglia is vouched by Koch Brothers is a long shot. So long, that it goes to the Alex Jones -type of conspiracy. That is my point.

If you want to describe the 'evil workings' of the Koch brothers, then far better to talk about the actual project they are funding, which I referred above.

Bullshit.

If you want your 'alt-right' culprit, it would be the editor of the Atlantic, Jeffrey Goldberg:

Today The Atlantic begins a year-long reporting project, “The Speech Wars,” exploring questions of American free expression and public discourse. The project will unfold across TheAtlantic.com, in video, and through live events, beginning with an event next week in San Francisco looking at the debate about free speech on campuses, on tech platforms, and in politics.

“The Speech Wars” is born out of The Atlantic’s legacy of covering threats to free expression, freedom, and justice—beginning with the magazine’s founding in 1857 as a nonpartisan journal that argued for the cause of abolition—and more urgently by the public’s increasing sectarianism and declining tolerance for challenging points of view.

“The Atlantic is, and always has been, a marketplace for competing ideas,” said Jeffrey Goldberg, editor in chief of The Atlantic. “We need to understand why so many factions and individuals across America have traded dissent and useful argument for intolerance and illiberalism.”

“The Speech Wars” will seek to understand where free speech is in danger and where it has been abused. With social media and the internet enlivening the marketplace of ideas—and giving every citizen access to the public square—we should be living in a golden age of free expression. The opposite is now true: over the past two decades, liberals and conservatives have increasingly come to believe their ideological opposites aren’t just misguided, but dangerous. The Atlantic’s reporting will explore all of these complicated realities, offering a range of reports and essays from staff writers and contributors.

See The Atlantic Begins “The Speech Wars” Reporting Project

Are the Koch Brothers vouching for Camille Paglia? Are they funding her?

Or would it be Tom Nichols, the writer of the article?

Or the actually, the Atlantic???

The Atlantic published another article on Camille Paglia paid for by the Koch Brothers. Just incredible. — Maw

Koch Brothers paying for articles about Camille Paglia?

An article mentioning among other things Paglia and you are saying the Koch Brothers are vouching for Paglia??? This is as silly as the Soros hysteria on the right.

This illustrates a subtle strategy for some right wingers who have counted on being protested and/or uninvited at college campus and leveraging that by writing articles — Maw

Oh brother, this is starting to sound as delusional as some Alex Jones following Trump supporter.

Yeah, obviously it has been the white supremacist alt-right that has lured the innocent students to protest/deplatform people at campuses in order to get more clicks. :joke:

I never did figure out why nuclear was so vilified in Germany? Was this Kraftwerk's doing? — Wallows

I think that the anti-nuclear power stance comes from the issue that people are simply so ignorant that they link nuclear energy to nuclear weapons. Of course there was a huge peace movement in Germany during the Cold War as obviously Germans understood that they would be the central battlefield in a possible outbrake of WW3. Back then even Germany itself had an arsenal tactical nuclear weapons (which sounds astounding now). You can argue that it's easy to be against everything nuclear when you oppose deployment of nuclear weapons. And do remember the absolute hysteria of Fukushima. The actual earthquake and tsunami were of little importance after Fukushima happened: who cares how many died (15 000+) if there is a nuclear power plant accident!

That ignorant scepticism we will see in reality if an actual energy producing fusion reactor will be built, I'm sure of it. A lot of people will be sceptical of nuclear fusion power.

On the other hand coal has been used for ages, it employs a lot of people in Germany and with nuclear we have the image of in our minds of Hiroshima and radiation a silent killer that we cannot smell or notice. With coal? Well, just to cook food every day with an open fire is very dangerous to your health. But of course who wouldn't know the nice comforting smell of smoke from a fire?

There were a lot more than 50 "liquidators" at Chernobyl exposed to massive doses of radiation, doses falling into the rapid fatal-effects range. — Bitter Crank

As I said, the UN/WHO have come to the conclusion that 4 000 people likely will die of the accident. Equivalent to 27% of Americans that die annually thanks to pollution from coal plants.

The popular anti-nuclear stance is more of a religion of ignorance and stupidity that simply rejects any objective understanding of the reality of energy production and energy policy. And the spineless politicians go with the flock to appease the clueless voters. Who cares about the actual effects as everything can be spun.

Just take Angela Merkel's decision in 2011 (after Fukushima) to close down all German nuclear plants by 2022, which was hailed as great news by the typical idiots. So what was the actual result of closing down the nuclear plants? German has to use more coal energy. Wind and solar power, although having been increased, have not been able to replace nuclear energy. Hence if Germany's carbon emissions shrank during from 1990 to 2010, after 2011 it has increased it's carbon emissions and has been busy opening new coal plants. Last year the German energy minister has admitted that the country will fail to meet it's ambitious targets to cut carbon emissions for 2020. Germany still produces roughly 40% of it's energy from coal. And of course, coal generated electricity is imported from Poland. Partly thanks to the hysteria against nuclear energy.

And it has still 7 nuclear power plants working, that should be closed in three years.

The longer we stay in overshoot, the worse the ecological consequences are and the harder it will be for 7 / 10 billion people to bring things into stability when we decide to make the effort, and at some point it's impossible and a large die-off will result regardless of our knowledge. — boethius

We won't stay long in the overshoot in my view.

One has to understand that there will be a peak of human population, and then it will decrease. This happens because of the rise of prosperity. Young people alive can quite well see "Peak Population" and then deal with the problems resulting from declining global population. Yet even that might not be so devastating: just look at how bad things are in Japan now.

Or could we simply turn it around, and say the world causes us to react mathematically? No need to talk about inventions and discoveries. — Richard B

The use of logic makes mathematics as it is. I think it is reasonable to say that logic gives us the mirror how we make sense of the World around us.

Animal reasoning and extra-terrestial intelligent life may be different from ours, but it is hard to see that there wouldn't be similarities. For example our base-10 number system is quite random, we just have ten fingers and ten toes to easily to count with. Yet that there would not exist some numeral system for finite arithmetic or that there wouldn't be arithmetic would be quite spectacular.

. I think The Simpsons and Chernobyl have soured me on the whole nuclear deal. I can be bribed to change my mind though... — 0 thru 9

How about this graph?

Yeah, there's a new series coming out from HBO about Chernobyl. — Wallows

Interesting, surely will be dramatic (even if the story isn't untold, but well documented). Yet in order to put things into perspective, I would urge people to review the United Nations report from 2005 on the Chernobyl disaster, link: CHERNOBYL: THE TRUE SCALE OF THE ACCIDENT

Those who don't bother to read the thing, here's a quote:

A total of up to 4,000 people could eventually die of radiation exposure from the Chernobyl nuclear power plant (NPP) accident nearly 20 years ago, an international team of more than 100 scientists has concluded.

As of mid-2005, however, fewer than 50 deaths had been directly attributed to radiation from the disaster, almost all being highly exposed rescue workers, many who died within months of the accident but others who died as late as 2004.

And let's put this into perspective on just how many are killed by coal fired nuclear plants YEARLY:

(Forbes) According to all studies on the subject, coal kills over ten times more people than any other energy source per kWh produced, mainly from fine toxic particulates emitted from coal plants. And coal kills ten times more people in the developing world than in America, simply because they lack regulations like our Clean Air Act.

In fact, our Clean Air Act is the single piece of legislation that has saved the most American lives in history. It is why coal kills over 300,000 people in China each year, but only about 15,000 Americans per year.

(See Forbes article Pollution Kills More People Than Anything Else)

So there you have it. The worst possible nuclear accident ever will kill roughly a third that are killed just in the US in one year thanks to coal power.

And of course there are sane opinions about the subject:

I agree. But do you think is possible to give a concrete meaning (or measure) to what it means for a theorem to be "beautiful"?
I mean: if a large group of people is able to distinguish a beautiful mathematical theory from an ugly one, probably there exists a measure of "beautifulness" independently from the person that judges. — Mephist

Usually the most beautiful mathematical object (or theorem, proof etc.) is the most simple and the most applicable to various fields of mathematics. In other words, it has equivalent findings in other forms.

For the ugly one you have to have a laudatur in math from the university and knowledge of the distinct field of math to understand what the gibberish is all about. And usually it has not applications.

In a way, a beautiful mathematical object, be it a theorem, proof or whatever, is something that could be given as an example of how interconnected and logical, 'beautiful', mathematics itself is.

I would say something like the Fibonnaci sequence is an example of mathematical beauty: simple and quite useful in various fields.

From the evidence of the thread I see:

1) The curmudgeonly unfortunately-not-yet-mummified Scruton losing one of his sidelines as a government advisor for some ill-judged use of language with the accusations against him appearing to be at least partly trumped up.
2) Camille Paglia being unsuccessfully assailed by some students exercising their free speech rights to punish her use of her ivory tower to fire thoughtless missives against sexual assault victims.
3) Talking turd Alex Jones falling foul of social media company guidelines that, like our guidelines, result in the banning of minor talking turds on a regular basis.

The ideological warfare seems to be getting along fine and fears of peace seem greatly exaggerated. — Baden

:up:

I would add the 'ideological war' isn't truly detrimental or dangerous either as neither side is really thinking of implementing a Final Solution to get rid of the other side. We're still talking.

What's interesting about Buckley is that he's illustrative of how normal conservatism and the alt-right cannot be so neatly separated. Mainstream conservatism has routinely platformed and turned a blind eye towards white supremacy until it is no longer because tenable to do so (e.g. when the language because too explicit). — Maw

And again, what in the quote is about white supremacy?

Xenophobia doesn't imply white supremacist thought. You might argue it the other way around, but again, not everybody is a white nationalist on the right. It would be similar to calling every social democrat a marxist and arguing that the two ideologies are inherently the same ideology.

I've come to the simple conclusion that people tolerate foreigners and ethnic minorities when these people provide money and hence are beneficial to the society as a whole. Contribution gives the acceptance. Period. It's universal and has a long historical background.

You see, nobody hates tourists. Yet if the tourists wouldn't spend their money, wouldn't contribute to the society by creating jobs etc, but would be begging in the streets and sleeping in the parks, they would be hated everywhere and wouldn't be welcome at all. Hence if it seems that a minority isn't giving it's share to the society, but seems to be free riding the system, immediately the xenophobic views emerge. How real this is actually, is often a good topic for debate, but once it's truly obvious for everybody, the notion is totally different: if the foreigners are literally taking wealth away from the society, then you have the younger generations up in arms against the foreigners are then simply called a foreign occupiers. You call it an occupation and the foreigners the enemy. And when a country is really occupied by another one and this creates a conflict, nobody in their right mind is calling the insurgents xenophobes.

Do ethnic minorities and foreigners make easy scapegoats? Of course. But this unfortunate thing is not at all confined to one single race. The above has absolutely nothing to do with white supremacy as the fact is totally applicable to other societies than white European or North American. The feeling and behavior is quite universal even for those who are non-whites. And the above is very important to understand because otherwise one can make the error of thinking that one set of people are 'open to foreigners and multicultural' while then another society is a bunch of bigoted xenophobes.

one can imagine several low cost PR INTENDED benefits: it looks progressive, it seems slightly fashion forward, it probably appeals to a certain 'hip' demographic, and so on. — Bitter Crank

Yep. Sports Illustrated can pat themselves on the back for those progressive multiculturalism points earned.

The floor is yours, Frank A.

Logic gives so much systemic and rigorous structure to mathematics that it's quite reasonable for us to argue that mathematical truths are discovered.

The given proofs or the mathematical approach taken to establish a mathematical proof can be quite subjective and rely on the person doing the proof and what he or she has been interested in, yet mathematics as a whole is such a beautiful system that the truths aren't just inventions.

Oh yes, this trainwreck is going to hell in a handbasket. We are all doomed.

How long have we been doomed for now?

Two hundred years? More?

But now it's really going. Just now, Honestly.


Have you noticed that people of a different era could already talk of you as a cyborg? Of course, the machines you use aren't attached to your body, but still. Spending your time in communication with total strangers through various machines calledthe internet and using all those computer algorithms and electronic widgets in your life. It's not just coming, that horrible future is already here. Has been for quite some time.

I can imagine the time when we would be writing actual letters in candle light: "Dear Mr. Bitter Crank, on the letter you sent me last October..."

Scruton and Paglia are not academics, they're wannabe celebrities. — unenlightened

Both are professors, one graduate of Yale, another graduate and PhD from Cambridge and both have long extensive academic careers.

But if they have been active in social media, unenlightened here thinks somehow they are not academics.

Latest privileged white academic in the firing line for having incorrect views is Camille Paglia. It was only a matter of time I guess. — jamalrob

I think we should set up an Outrage Bingo - the right-wing targeted version.

Other ones just waiting their turn to be 'Scrutonized' would have to be Christina Hoff Summers and professors Amy Wax and Janice Fiamengo. And all the horrible people in the Intellectual Dark Web.

In my opinion, we as humans have to escape the illusion everyone lives in, try to see the bigger picture and maybe remember where life started, because strictly speaking we are all related to each other, it does not matter if you believe in science or in any religion. We are a “being family”. Empathy has gotten lost or it may have never been around in the first place. Therefore I am not happy with our world even though I grew up in Switzerland where you can say the welfare is extremely high. No one has to suffer in terms of essential needs and everyone gets help if its needed. — lucafrei

And that's exactly your problem.

You don't see the positive side in the World as you have grown up what many would see as the model of a peaceful prosperous country where various ethnic groups speaking different languages live in harmony (or at least we don't hear about any ethnic strife in Switzerland). No news is good news. And the Swiss don't get much into the news. The only bad things you hear from Switzerland is that there is a drug problem (but which country wouldn't have one).

Why don’t we think about how the human family can live together in peace, sharing knowledge and thoughts? Imagine we include the brilliance of every human individual and put this together. I see humanity working with nature, as if they were one, I see humanity exploring space, making new discoveries, extending their knowledge. I see humanity as one nation but still with different cultures. — lucafrei

Yet isn't that actually happening? American astronauts have still gone to the International Space Station with Russian rockets. Doesn't that at least tell something?

It is an inherent aspect of Western culture to be critical about the way things are. We have that what could be called Angst. We are restless about the problems we perceive the World having and we have this urge to solve them. Or at least to speak about them. The globe isn't in a near Mayhem. We portray it to be so as to highlight the importance of the present.

We wouldn't be happy if our time now would be just the backwater of the far more interesting 20th Century to future historians, who don't see much happening in the 21st Century (especially compared to the awesomely exiting 22nd Century and the epic 20th Century).

If I may ask: What unspeakable things did Trump do to your family? — fishfry

Unspeakable?

Well, I wouldn't want to start speaking about why the US President has these photos where his own daughter poses as a young girlfriend to my own children. Likely this sex offender will be exposed later in history books.

If you're going to criticize what I said, you should read me more carefully. What I said is that a border wall does not solve *all* important problems — Relativist

What I was criticizing was that Tiff wasn't talking about Trump's wall, she was talking about what was happening in Arizona. It's actually a good thing sometimes to put these things into some kind of context. Sure, Trump uses scare tactics as often as he can and in the way only Trump can. Yet immigration is an issue, especially when you look at this from the perspective of US policy and take into account the near history with the Obama and Bush administrations. Deportations increased in each of the first four years President Obama was in office, topping 400,000 in fiscal year 2012. Obama oversaw more deportations than George W. Bush did, just as Bush oversaw more than Bill Clinton did. Just for comparison, Trump deported last year 256 000 people.

The situation obviously isn't good in Central America and is very bad with the situation in Venezuela. Mexico still is muddling through, but if it would go downhill from the present, the situation would be very bad quite easily.

I also said that his rhetoric MIGHT have contributed to the current influx of asylum seekers ("better come now before the wall goes up or the border is closed"). I'm not claiming to know this for a fact, but it is certainly a possibility. — Relativist

Well, I think we had the similar idea/meme going viral in Europe in 2015-2016 that the borders would be closed without any rhetoric similar to Trump, and indeed that did happen. The EU did tighten it's border security and the mass migration at the scale that we saw earlier did end.

Definately a must read. And those who won't read it, the most important part:

Yet you are silent. Because, after all, what are you supposed to say? He’s the president of the United States.

You feel this happening. It bothers you, at least to some extent. But his outrageous conduct convinces you that you simply must stay, to preserve and protect the people and institutions and values you hold dear. Along with Republican members of Congress, you tell yourself you are too important for this nation to lose, especially now.

You can’t say this out loud — maybe not even to your family — but in a time of emergency, with the nation led by a deeply unethical person, this will be your contribution, your personal sacrifice for America. You are smarter than Donald Trump, and you are playing a long game for your country, so you can pull it off where lesser leaders have failed and gotten fired by tweet.

Of course, to stay, you must be seen as on his team, so you make further compromises. You use his language, praise his leadership, tout his commitment to values.

And then you are lost. He has eaten your soul.

Now that's the kind testimony the US needs.

Regarding the Border Wall: let’s remember the H.L. Mencken saying - ‘for every complex problem there is a solution that is clear, simple, and wrong.’ — Wayfarer

:up:

OK fair point, but my meaning was if sufficient stones existed, the a googolplex of stones would be possible. — Devans99

So now it would be possible. But it isn't possible.

The set of natural numbers exists in our heads only — Devans99

Numbers exist in our heads only. And likely some animals use a mathematical system of "nothing, 1,2,3, many.) which is a totally functional system if you don't have an issue with or the need to count to something more than three. So likely this whole system of counting isn't only limited to humans. Yet in the physical realm there is no number 54. 54 doesn't exist physically. So it doesn't exist.

I've tried to make my point with the example of googolplex of anything that you cannot make the basis of mathematics in what physically exists in the universe or otherwise you end up with a totally illogical idea of finite numbers exist until they don't.

Mathematical proofs are done in the realm of mathematics and logic. Mathematical entities are not proven by starting to look at what we have observed by science and physics to exist. This is a very typical confusion I have noticed people have.

Hence the set of natural numbers exists in Mathematics. And it is an infinite set. And there is the axiom of infinity. And just disagreeing with this won't get you anywhere. You have to prove what is illogical in the mathematical system.

We classify ourselves as carbon-based intelligent beings. — BrianW

We define part of the living to be intelligent. As what we know to be living is carbon based, we have this assumption all living is carbon based. We might be wrong, but we simply have then to have the counter example that shows the assumption to be false.

I'm not sure what you mean? Two googolplex of stones can exist IMO. — Devans99

At this level, it is estimated that the there are far less than a googol of atoms in the observable universe. As stones consist of more than one atom, obviously two googolplex of stones cannot exist.

My view is that paradoxes indicates that there is an error in the explicit/implicit assumption underlying the problem. — Devans99

I agree with this. We makes assumptions that are contradictory to each other. So what are we lacking? That's the interesting question.

A paradox is just a contradiction so it is a form of proof via contradiction that infinite sets do not have sizes / infinity does not exist. — Devans99

I have to disagree with you in this one. The set of natural numbers N does exist in the Mathematical realm. It is an infinite set as it surely isn't a finite set of numbers.

Trump has claimed he "wouldn't be surprised" if George Soros was funding the "invading" immigrant caravan which was the manufactured story leading up to the mid-term election - The idea that non-whites are "replacing" whites is a key component of white nationalism ideology. — Maw

Yep. And Trump loves conspiracy theories.

Yet the vast majority of people thinking that borders shouldn't be totally open aren't white nationalists.

At what point is what I am saying believable? When CNN says we have a problem at our border? — ArguingWAristotleTiff

No.

Understand how this goes, Tiff.

First and foremost, if ANYTHING you say can be interpreted as giving credibility to Trump, people are going to dismiss you... because you are basically supporting then what they hate, Trump. You see Americans simply cannot escape the bipolar political discourse in the country. I would argue that this may be becoming reality in other countries too, but still for example here it's not present as the political parties have to create coalition governments, which tones down the rhetoric immensely. Yet the American media has every intention to uphold this bipolarization. Since the presidential elections are coming, this mass psychosis will get hold of many Americans and rightly the time is called the silly season. The two-party state depends on Americans believing that the other party is inherently bad and the only thing to do is to vote for the other one.

Just look at how Relativist answered to you:

There are problems that are manifested at the border, but a border wall does not solve it because asylum seekers can enter through legal points of entry. Trump's rhetoric has done more harm than good — Relativist

So basically Relativist agree's that there are problems at the border, but then comes the Freudian slip: Trump's border wall doesn't work, Trump's rhetoric is bad. Now I didn't notice you saying that Trump's idea of a wall is great and that you support Trump's rhetoric. In fact you were not talking about Trump at all. In my view you haven't been a staunch defender of Trump or the Republicans any way. And so this shows how people approach these issues: nothing is an objective discussion about the situation, everything is a political statement that supports your political side.

Yes. In a sense, there is a circle of vice ( the vicious) where the bullied (victims) can become the bullies. — Amity

I'd say those that portray themselves as defending the victims are the one's that really are the bullies.

If one is simply vexed over the issue of free speech then this story regarding a children's speech pathologist in Texas who was fired because she refused to sign a pledge stating that she would not engage in any economic boycott of Israel should be more alarming. — Maw

You forget to mention that she has had success in her lawsuit (or the pressure group Council on American-Islamic Relations, which filed the lawsuit on her behalf), so maybe the legal system is still working in Texas. See Texas speech pathologist celebrates temporary free-speech win, hopes it inspires. Amawi, an US citizen and a person of Palestinian origin, has stated in her lawsuit that she has “seen and experienced the brutality of the Israeli government against Palestinians.” So obviously she takes it seriously.

If one is indeed vexed over the issue of free speech, one can debate the actions of the Texas legislator with having laws that state that certain state agencies shouldn't contract with and invest public funds in companies that boycott Israel.

Just as I said myself earlier, this is an example of how free speech is curtailed, just in this occasion on the opposite side of the political spectrum. It's quite common that some Muslim criticizing Israeli policy is labeled as an anti-semite. But of course for the political tribalist, only their own one side matters, they are the one's unjustly and viciously attacked while as any complaints from the other side are totally fictional, delusional and simply wrong (as the accusations are totally justified). Or they couldn't care less.

54 stones can exist. An infinite number of stones cannot. — Devans99

Stones can exist. Yet Again you have the same illogical idea here: two googolplex of stones cannot exist. And where in reality exists this '54'?

Potential Infinity (limits in calculus) is useful. — Devans99

Congratulations! You've made it to Aristotle with accepting potential infinity.

Set theory is rife with paradoxes because of infinity. — Devans99

The whole error is then to deny the existence of the paradoxes and think that everything in mathematics is fine and dandy if we a) don't approach this question or b) ban it.

The existence of the paradoxes show simply that our understanding of infinity is still lacking. Mathematics as a system isn't finished. We have still these issues with it that we cannot understand, just like the Greeks had problems with irrationals and at least for some time had this idea that all numbers were rational.

That's my view: paradoxes aren't a problem to be solved, but something that shows that the base of mathematics isn't yet finished. Paradoxes are more likely to be answers to be understood. And it's linked to our understanding of the infinite.