I’d still like to believe that there are principled evangelicals, although I must admit scepticism. — Wayfarer

I still know that there are principled Americans, even if they are a small minority perhaps.

After all, this “character counts” and “personal integrity” and “political leadership” was central to what a lot of… evangelicals argued when Bill Clinton was president. And now that it’s Donald Trump, they’ve decided to push that aside, which means that morality for them was a means to an end, not an end. It was something to be used as a political weapon.

Well, I got disappointed at how the Democrat supporters, voters and politicians who were against Bush (or Cheney's) policies after 9/11 had no trouble with Obama continuing Dubya's "War on Terror" and him increasing the drone strikes, even killing underage American citizen just because his father had been a terrorist propagandist.

So the way how Americans change their views once "their man" is in charge is very common and just tells how partisan Americans are.

Does or should Hotelling's Law apply to potential democratic candidates-who would want to win, quite obviously-against Trump in 2020? — Wallows

No matter how much you research the voter base and political trends, there happens all the time surprises that the pollsters and campaign professionals never saw coming.

Hotelling's law simply is an outcome of how risky it is to choose a totally new approach, design something utterly new and totally different from others. Yes, it maybe a huge hit (which then competitors will copy), but then again one might be wrong and it's a total fiasco.

It is a bit similar to the famous Beauty Contest -example of John Maynard Keynes (when describing how the stock market works). The judges don't choose the girl that they find most attractive, they choose what they think the other judges think is the most attractive girl. Hence if every judge thinks that all the other judges are total morons that have utterly no idea of beauty, they might choose a girl nobody's particularly fond of.

Can you put Hotelling's observation to politics? Sure, but it is also a bit different. One might say that the American voter has been "angry" and "dissappointed" at present politicians and the two parties since... the 70's or earlier? (Forever?) And that want for something else, desire for change, might pick up a Trump or a Ross Perot every once in a while from the "normal" types of politicians.

this concept was edifying for me in understanding why have the Democrats in the US, since Reagan, have tended to be very conservative in nature, at least to foreign eyes. — Wallows

Should be still noted that the US has a right-wing and a centrist-right wing party that share power.

Another fact contributing to this is simply the fact that dems are at a disadvantage in the US to pursue progressive and socialist policies, given the Cold War and the vilification of socialism since then (although times are changing). — Wallows

The US basically didn't have a strong 20th Century type socialist movement at all. The Democratic Party is a Social Democratic Party, it has only a leftist wing that can well call itself leftist in the European way.

Does or should Hotelling's Law apply to potential democratic candidates-who would want to win, quite obviously-against Trump in 2020? — Wallows

Going against a sitting President is always difficult and a risk-averse approach might not be the most successful as in order to win you have to get excitement around the candidate. Now Trump isn't the most popular President for sure, yet at least the Democrats don't look at him to be a pushover. Which is good as the condescending attitude that the media (and the Democratic party) had right from the start towards Trump was the most important reason, in my view, that Trump came to be so popular.

I can’ t fathom how any self-described Christian could approve of Trump if they know anything about him. — Wayfarer

Easy. the white, evangelical/born-again Christians favour 75% the GOP. They just hate the godless Democrats, that's why. Trump is far more better than Hillary for them.

Isn't the City of London basically a city-state inside Greater London already?

You know, the City of London Corporation headed by the Lord Mayor of London, and all the money protected by the arrangement.



They'll surely survive.

I just re-read and realized that you may have been implying that I was being condescending towards those Americans who do not have a good grasp upon how monetarily corrupt the government of the United States of America has become in the past forty or fifty years. — creativesoul

No system can assume that 1) everybody has a clear understanding about the issues and, above all, 2) that they would agree on what issues are right or wrong.

The people ought be able to trust that elected officials will act on their behalf. That is their job. There's nothing wrong with trusting elected officials. — creativesoul

That is true. Yet it should be noted that 'acting on their behalf' is actually a complicated matter. Serving the country or serving the people is different from serving a customer as in the private sector.

Nah, not utopia. Just a situation where those who wield the power over less fortunate people be knowledgable and do so with great care about the consequence that their actions have upon those people's lives and livelihoods. — creativesoul

It's a researched fact that this isn't so in the US, that it's simply 'money talks', yet with the rise of lobbying this isn't a thing only affecting the US, but an universal phenomenon. Just how actually would our representatives take more care about 'less fortunate' people isn't so simple either as it has been a central political issue since, well, antiquity.

The United States of America is not a democracy. Rather, it is a republic. — creativesoul

Ah this line again. Cliche b... as you said earlier as those 'pure democracies' without any minority protection basically don't exist.

:yikes: My bad.

Scotland, part of the UK for 300 years, could sever its union. — Bitter Crank

Not likely. Those Pseudo-English don't have the stomach to get independent. Heck, their pro-independence politicians don't have the guts to make Scotland independent. And the English are so nice after all.



I'd say this is more of a trick of the media to get us following the media-circus around the issue.

Surrealist paintings themselves are nice.

Yet I find the surrealist painters to be annoying charlatans that try desperately to be more than they are.

Carrington painted without any interest in communicating with her audience.She just painted the images that came to her. She didn't expect to become a famous artist because gender bias in the art world so strong in her lifetime, so her art was first and foremost personal to her. — frank

Yet she was a hang around member of the Bloomsbury group. (Lucky to you that she had friends that came famous like her.)

I have no problem with this. My point was that logic is necessary in all sciences. Of course, the amount of empirical data and the role of hypotheses varies widely. The point of my classical mechanics example was that it is a closed, axiomatic structure, within which one may deduce theorems in the same way that one deduces them in math. Still it is not math, and it is not true in any absolute sense. — Dfpolis

I agree, yet when modeling reality, it's apparent that there are approximations and generalizations etc. that simply don't make sciences as rigorously logical as mathematics. For starters, every measurement is an approximation. Logic is of course necessary. I studied myself economics and economic history and noticed that a lot of variables are rudimentary models of very complex phenomena, like 'inflation', 'GDP' or 'aggregate demand', and that one shouldn't forget it when calculating math formulas with them.

That is precisely the notion I reject. — Dfpolis

Ok, then I think I've misunderstood your point.

I am saying that axioms are no different than any other claims. They are either justifiable, or not. Either adequate to reality (true) or not. Mathematics cannot be exempted from epistemological scrutiny just because it has a canonical, axiomatic form. — Dfpolis

Perhaps now I understand your point. (I'm btw happy with pragmatism: usefulness is far more important than we typically think.) So if I understood you correctly, when you talk about 'unscientific' math that is "merely a game, no different in principle than any other game with well-defined rules" is that it's actually not applicable and/or the axioms simply aren't in line with reality. Like astrophysics using a helical model of the universe simply might not be useful...especially if the universe simply isn't optimally modeled using a helix.

The standard mathematicians answer would be "Well, it could be useful someday". Modelling the universe using a helix might have those not yet known nice 'mathematical properties' that future physicists make better models and can avoid today's problems. And some mathematicians are totally happy with the "math-is-just-various-kinds-of-rules" approach and declare every kind of math as worthy as long as it's logically correct.

I have no idea what you mean by "totally local." Are you claiming that the concept <incommensurability> came to be independently of any experience of reality? History would seem to rebut this. — Dfpolis

Logical (not local). No, I'm not saying that. What I'm saying that a field that has developed from the need to count and calculate to solve real world problems doesn't have it's axiomatic foundations solely on arithmetic as it has also incommensurability and uncomputability. So the foundations aren't so narrow that everything starts from simple arithmetic.

Some comments about your classification. You define in the first class to be math that has axioms rooted in our experience and reality.

Most axioms are abstracted from our experience of nature as countable and measurable. — Dfpolis

Yet we can have logical problems with those too: Zeno's paradoxes and the huge debate over infinitesimals have shown that we stumble to the problems of infinity from quite normal experiences. (And those who think limits have solved all the questions, well, how about the Continuum Hypothesis then?)

There's still a lot that we don't know.

Knowing what that change would take includes knowing that it takes the average American citizen to have knowledge about the inner workings of government that they quite simply do not have. It would take American voters knowing what the problems actually are and believing that they are able to do something about it. — creativesoul

A condescending attitude towards your fellow citizens doesn't help. Or you don't believe in democracy?

Reaching for some utopia or what, creativesoul?

Fair enough.

The cost of theft is much higher than the purchase price. — creativesoul

Not to the thief. Hence a stolen car has a lower price than a car bought in the dealership.

It's equivalent to feeling powerless about the issue. One can feel powerless to change a situation that s/he does not like in the least without ever being ok with it. — creativesoul

Why on Earth would you feel powerless? That's the whole problem here. Or has the Supreme Court made it illegal to vote for some other party than the two?

If people don't like the two party system, why then vote the parties? You really think that your vote is "wasted" by voting a third party? When there is a will, there's a way. It's simply idiotic to assume that current political situation cannot be changed. Yet when there isn't that will, I guess the simple answer is that you are OK with the system.

I'm less certain that Americans are ok with monetary corruption in government, and more certain that there is an overwhelming majority of citizens who do not believe that there is anything that can be done about it. — creativesoul

When people believe nothing cannot be done about something, that is equivalent of being OK with the issue. I can whine about the Finnish summer having too many mosquitoes, but my dislike of mosquitoes isn't going to change anything. And if someone purposes physically draining all swamps in Finland I strongly disagree with that ludicrous idea, even if I'm not a supporter of the green party.

The bi-partisan system is corrupt... both sides. — creativesoul

The stagnant structure of the two party system creates the environment for deeply entrenched corruption as the two parties simply share power in the US: they know that they can at worst be for 8 years in the opposition until the voters want "change". Add to this the revolving door to the private sector, hopping from being a lobbyist to being a government official, being a career politician is a good paying job.

And of course, investment in corruption pays off well, because the price of something stolen is always far cheaper than something legal. What is worse is that the corruption is made totally legal. Your really have to be an idiot or far too greedy to get into trouble in the system.

That is certainly the modern usage, but not the only one. Traditionally, scientia meant an organized body of knowledge -- organized in terms of explanations reducible to first principles. So, I would say that mathematics is a science in the sense of being an organized body of knowledge -- and that knowledge is an understanding of reality. — Dfpolis

So in the way as history is a science? Some in the natural sciences would shudder at the idea, but I'm totally OK with it.

Second, "logical system" needs more explanation. All sciences proceed logically. I suspect that you mean a "closed system," i.e. one that simply elaborates an axiom se — Dfpolis

No. I think it is you who define "logical" or "logical system" in an extremely narrow way and as logical meaning as a "closed system". The way I see here math to be logical that simply every mathematical truth has to be logical. It doesn't state AT ALL that everything in math has to begin from a small finite set of axioms. What Hilbert was looking for was something else, especially with things like his Entscheidungsproblem.

The classical mechanics they developed is still useful and taught today, but it is not true. Unjustified foundations necessarily give unjustified conclusions. — Dfpolis

Ok, there's your problem right above. What you are making is a hugely reductionist argument that everything has to be deduced from the same axioms. If something doesn't fit to be the universal foundation, in your terms it has to be false and whole fields have to be false. Classical mechanics works just as classical geometry works. There being quantum mechanics or geometries of spheres etc. simply don't refute one another and make the other untrue or false. What is only wrong is the reductionist idea that everything can be deduced from one system or the other.

Math isn't like this. Mathematics has for example incommensurability, which is totally logical.

It seems some think that enlarging his base is exactly the point. — Amity

More of the same is enlarging your base? Interesting.

To depict the democrats to be woke socialists who'll ruin the country is very conventional GOP politics, so if Ms Douglas assumes this to be appeasing the moderates... that's a quite an interesting definition on what moderates are.

Except for not one, not two, not three, but at least four, regular NYT Op-Ed columnists written just in the last month or so (and in fact both Bret Stephens and David Brooks had to write immediate follow ups that were just as bad as their originals). Similar articles have been written about in the Washington Post and The Atlantic. — Maw

Maw, just look at how the vitriolic discourse has gone and will (in reality) go. To argue about getting the moderates or a democratic candidate getting the Trump voters is theoretically logical, but in real terms I wouldn't be so sure.

Above all, the democratic candidate will have to win the candidacy, and is there the winning strategy be to go lure the moderate Republicans?

This is what I am disputing. Standards of poverty are not absolute, but relative, and hence, arbitrary. I can't deal making absolute judgments based on arbitrary evidence.

You do it. — god must be atheist

Povetry stats are typically made using a relative measure, of being some percent of the median income. Yet there is the measure of absolute povetry, you know. And you can have an indicator for income is below a necessary level to maintain basic needs, basic living standards (food, shelter, housing).

Then there is also the term extreme povetry: Extreme poverty is typically defined as a state in which a person lacks access to all, or several, of the goods needed for meeting basic needs.

And I think the World Bank has used the 1$ per day income as an stat for quite some time. Now it's 1,9$. Actually the stat is one of the very happy stats about our time:



Special thanks to China and India for giving up socialism!

What's also funny (read: absurd, tragic, rip my eyeballs out) is that NO ONE is telling the GOP be more moderate in order to appeal to more voters. — Maw

NO ONE is telling in either of the two parties to be more moderate. That (being moderate) is seen as a losing strategy.

Let's face the reality: Trump didn't believe he was going to win and he surely doesn't believe at all that he could enlarge his base. Hence he focuses on his hardcore supporters and hopes (or simply assumes) that other Republicans will have to follow, or that the democrats will push other Republicans to vote for him. Hence the portrayal of democrats being socialists who hate America. The "Send her back"-chant is the new normal, typical Trump with the reverses now, but you'll hear it later. For his hardcore supporters Trump truly needs to be outrageous.

Basically corruption has been made quite legal in the US and Americans are totally OK with it. Just like they are with the most expensive health care system in the World. Corruption has likely increased a bit with Trump.

Or at least with inept players as Trump's son-in-law, the corruption is even more evident and straight forward than with others. What was telling is that Trump was himself so surprised that his "drain the swamp" comment got so much response. Trump supporters simply pin totally ludicrous hopes to the guy and are basically unified about their hatred of the democrats. And since any kind of critical view of the doings of the Trump administration is "pinko-liberal media propaganda", anything will go.

Especially if the country stays out of recession.

Trump is a symptom. — creativesoul

Yet it's obvious that what is infected is the Republican party. It simply cannot shake the Trump disease.

I just came back from a trip with my family to Washington DC and New York (my son wanted to visit the US to the horror of his mother). Visited Capitol Hill and waited in line to see from the gallery the House of Representatives in session. When we got there only a few members were talking their time to the empty seats as it was a Friday, but the message of a Republican member still showed how far US politics has gone. This older Republican politician (don't know his name) started his attack on the FBI on how politicized it has become (yet remembered to mention Hoover as a historical example) and how it's leadership went solely after then the Republican candidate. (Yes, who would remember anymore Comey's October surprise?)

It was sobering to listen (with your own ears) what US politics has become during the age of Trump. Also what was noteworthy how the safety procedures have tightened after 9/11 as I had visited last time the place in the 1990's. At least people, even foreigners, can go and listen to what is said.

It does not seem different enough to vitiate my point. In any lifetime, or finite number of lifetimes, we can only go through a finite number of axiom sets. So, there are true axioms we cannot deduce. Or, am I missing your point? — Dfpolis

It's a subtle point only. Mainly that if for every consistent formal system there exists specific true but unprovable statements, that doesn't actually mean that there are true but unprovable statements in every formal system.

Again, in math we aren't confined to what is physically possible (physically countable, physically computable), as we use infinity so much everywhere in math.

So, you will have to explain why my criticism is "totally out of whack." — Dfpolis

Fair enough.

First of all, with 'scientific' we describe that we are using the scientific method, an empirical way to make objective observations, experiments, tests or measurements, about reality, the physical world as you mention, to solve if our hypothesis are correct or not. Mathematics is logical system. Applicability of mathematics to the physical world isn't the logic that glues mathematics into a rigorous system, but logic itself. Above all, something that we have thought to be a mathematical axiom isn't shown to be false from physical reality, but with mathematical logic.

Especially if you use the term 'unscientific' it makes even a more confusing relation:

The remaining hypothetical axioms can't be tested, e.g. the axiom of choice. These are unfalsifiable and unfalsifiable hypotheses are unscientific. As they are unscientific, pursuing their consequences is merely a game, no different in principle than any other game with well-defined rules, such as Dungeons and Dragons. — Dfpolis

Here you seem to have the idea that if the axiom of choice is independent of ZF, it is somehow 'unscientific' as if other axioms would be the 'scientifically' approved. Well, just look here on this site how utterly confused people are about infinity and try to then reason that axiom of infinity is scientific. But there there the axiom is, in ZF. On the other hand, the axiom of choice (AC) has a lot of equivalent findings in mathematics like Zorn's lemma, Tychonoffs theorem, Krull's theorem, Tukey's lemma and the list goes on and on. To say in this case that all of the math in all of those various fields of mathematics are unscientific is, should I say, out of whack.

In fact the independence of AC just shows how huge gaps we still have in our knowledge of the foundations of mathematics. If something is flimsy, it's more likely the whole notion of ZF, because the whole reason for ZF to have been made in the first place is to counter Russell's paradox. Yet when we have these independence results (and undecidability results), for me these seem to show that not all is there yet. It may be that ZF could likely be itself 'unscientific', but that will only be proven by logic, not with a physical test or measurement.

To make my argument short, scientific/unscientific is a poor definition in math, far better would be to speak of logical and illogical. We have had and can indeed still have illogical presumptions (or axioms) of the nature of math, just like some Greeks thought that all numbers had to be rational and were truly disappointed when finding out that there indeed were irrational numbers.

Yet, Godel's work shows more: it shows that there are truths that cannot be deduced from any knowable set of axioms. — Dfpolis

Does the Incompleteness Theorems say really this? Correct me if I'm wrong, but doesn't (the first Gödel Incompleteness Theorem) say that for any 'set of axioms' or consistent formal system there exists specific true but unprovable statements. That's a bit different

I think maybe "unscientific" in this context is wrong usage. In any case, mathematics is not an experimental science. — tim wood

I agree here with tim wood, talking about scientific/unscientific here with foundations mathematics is totally out of whack.

I think Wallows chart (on the first page) shows the truth quite well: those fields that actually have something to do with understanding how economies function have a negative view of socialism. Philosophy as a theoretical field looks at more of the ideological issues at stake, so no wonder that philosophers have typically been socialists (and believers in trendy totalitarian systems of the times).

IMHO Capitalism only works for everyone when the workers have some say about their work. Like in Germany where the boards of companies must have laborer members on them. — Noah Te Stroete

There are many prerequisites for capitalism to function well starting from the rule of law (hence a functioning state) in the society. There being a board member representing the employees maybe not the most important issue here. For example the ability of workers creating labour unions and negotiating salaries collectively with the employer is a far more important issue and totally in line with capitalism.

Trump illustrates two personal characteristics that are relevant: First, as a CEO, he behaves in the presidency as if was a CEO--with lots of prerogatives, and not part of a government. — Bitter Crank

Trump is more of an investor-owner than a CEO. CEO's typically are career professionals that are hired for the job and are responsible for the board, typically other people like himself. An investor that inherited his wealth isn't: it's his money, his wealth. Hence Trump has had the ability of having a multitude of entrepreneurial disasters, thanks to the Russians coming to assist him after American banks wouldn't lend him any more.

What we (I, and TheMadFool if I'm not wrong) are admitting is that usage of many vague labels like heap relates to numbers without difficulty in some cases, e.g. a single grain, and the problem is to describe the fuzzy border further along. — bongo fury

So basically your argument is the vagueness of the language.

Your passion against settling for an arbitrary sharp border, which we applaud, stops you from admitting this, and from appreciating that a vague category usually correlates in this puzzling way with some or other more fine-grained (often continuous) series. — bongo fury

Ok, it's seems you didn't get my point, because I don't find anything close to my reasoning in this.

I think we're approaching some kind of agreement.

you think usage of heap should be kept separate from the naturals. — bongo fury

If people get puzzled with the Sorites paradox, then yes.

I think my point is that the so-called "problem" isn't vagueness of language, but incommensurability, which is a mathematical feature itself. When talking about math, better use logic.

You are so appalled by inappropriate reductions of systems to arithmetic that you won't hear of any such intermingling. — bongo fury

Oh it's not me, it's the logic in mathematics. You see a crude counting system, like "nothing, 1,2,3, many" is logical in it's own way, if one hasn't the need to count things more than up to three. For some animal it can be a splendid counting system: why would they need to count to several thousands? And so is with "heap of x" versus "mountain of x" as a simple scale system.

The challenge of the heap game is to describe the fuzzy/tolerant bounds of this tacitly agreed range. — bongo fury

Tacit agreement is the word.

We typically have some idea of the range. If I say "There were many mosquitoes near the swamp" or say "There were many aircraft carriers in the harbour", you hopefully have some idea of how many mosquitoes can be in a swamp and how many aircraft carriers can be in one place at a time. Hence you can easily understand that "many mosquitoes" can be a number in the hundreds if not in thousands and "many aircraft carriers" is number likely more than three, but very likely less than ten, as there simply aren't many in the World (less than 20 are in service around the World and there surely isn't a get-together-party for aircraft carriers organized in some harbour).

Ah, the Epstein thing!

Wonder when that would pop up to the surface like a ballooned rotting corpse that the gangsters failed to put into cement and which the tides have brought back to the beach from the ocean. This carcass won't go away.

As correctly quoted, the real gem is the New York Magazine article from 2002, which then was totally innocent with Trump eagerly telling the Magazine what a close friend he is to Epstein. I urge anyone that hasn't read it, but is interested in this strange thing to read it: Jeffrey Epstein: International Moneyman of Mystery. It has everything, even Kevin Spacey!

Actually was it VICE NEWS in 2016 that quite correctly forcasted that this was so filthy to both sides it wouldn't be an issue. See The Salacious Ammo Even Donald Trump Won’t Use in a Fight Against Hillary Clinton.

So rape is fine as long as it's not with minors? Or grabbing them by the pussy doesn't count as such? — Benkei

I'm just thinking how terrible the books about Trump will be after some time has gone. I mean if some authors portray the Kennedy's with a shady brush, just how shady will it be with Trump.

None of this is evidence of Trump having sexual contact with underage girls, but then there is the story from 1994 of the 13 year old girl who filed suit against Trump for raping her in Epstein's apartment. From Newsweek, 11/16/17: — Fooloso4

Actually, didn't Trump settle with this rape victim? I remember it happening just before the election.

This was also corroborated by a friend of the 13 year old girl who she told, and also by an associate of Epstein. Will have to look up the details again, but there is evidence that Trump did rape a 13 year old girl. — Maw

I remember something similar. After all, one of the victims was working in Mar-a-Lago

Anyway, this is far more interesting and far less loony than Pizzagate or the Seth Rich conspiracy.

Not sure I understand. — bongo fury

Ok, you said:

correlation 2: an arbitrary individual threshold... a policy with some good PR (e.g. "you have to draw the line somewhere, and that's that"), but which will inevitably deprive the usage of its useful fuzziness / tolerance — bongo fury

"You have to draw the line somewhere" is itself the problem. When you don't have a common measure, just how are you going to draw the line somewhere? You simply need that common measure to draw the line somewhere. This is similar to where just assumes Calculus, but forgets what it means not having a common measure.

In fact, the first correlation too goes also against incommensurability:

) Hooray if, for example, you want to resist this correlation because you have a sense of clarity or absolutism about certain cases of heap and of non-heap, and a sense that the same clarity will transmit from these cases to certain others. — bongo fury

The issue won't transmit so easily, because notice the definition of incommensurability: two or more quantities having no common measure.

If they have no common measure, how do you think the clarity will transmit from one to the other? Think about it this way: try to do the following algorithm in arithmetic:

1) Start from the natural number 57.
2) Add a somewhat large natural number to it.
3) Substract from the sum a small natural number.
4) So in which natural number are you in the end...exactly?

This is what looks like when you mix two incommensurable systems together. The problem is simply to assume that you can do it, and that you get an exact answer. Yet "somewhat large" or "a small number" is quite practical sometimes, assuming there is an universal agreement just what the range is. Not so if you just take as here.

One should really stop are really think about what it means when in mathematics two quantities have no common measure. That in math we have quantities that are unmeasurable. The answer isn't that if it's a quantity, it has to have a measure. The issue is that it isn't measurable to others.

That's the beauty in Calculus. You can describe incredibly complex relationships without using numbers, or many numbers. — god must be atheist

And for this you need arithmetic to apply and there needs to be a number system.

IN this case, the fundamental law of Calculus applies, but it yields a (possibly) different value of number of sand from human to human. — god must be atheist

Actually, it really doesn't genuinely apply.

It's as wrong as to try to put infinity, as a number, or an infinitesimal, as a number, on the number line. You simply cannot do it. And thus people don't regard either as numbers. Yet both are extremely useful in mathematics, so there isn't anything wrong with them.

In fact, the first fundamental law of Calculus only uses 2 to find the midpoint between two values. But it does not go beyond that in any more ways of using numbers. — god must be atheist

This again is a fallacy here, because you simply deny the existence of incommensurability. Think about it: if you have a heap of sand and a mountain of sand, what then is the middle, really? It would be something like "an amount more than a heap and less than a mountain". Is that useful? Likely not, and still you don't have any idea when a heap turns into 'more than a heap and less than a mountain'. The laws you refer to don't really solve the issue at all.

Again, you simply do not get from one system to another, even if you argue that all amounts of sand are made of individual grains of sand.

Well, to insist we must. - . If there are two points on a function... — god must be atheist

You aren't getting the point. The measurement system of heap of x < mountain of x isn't straight forward calculus as you cannot answer exactly how much bigger is a mountain of sand compared to a heap of sand. Hence you cannot add them up together and divide them into two, because you are using the number system. In order to talk about mathematical functions, you do need the number system and arithmetic to calculate functions. With heaps it isn't so!

That's the whole point: 'heaps' or beauty do not have a common measure with an arithmetical system like the natural numbers. That's the whole point of incommensurability.

What other method would you choose to describe how a heap of sand stops being a heap? Isn't it the number of sand grains in a collection that determines the heap-ness? — TheMadFool

When does a beautiful girl stop being beautiful and become 'OK looking' or 'ordinary' or even be outright 'ugly'? If you cannot draw a specific line, then is the notion of being beautiful in peril?

Even if you would very rudely give numbers for attractiveness, it still begs the question of what is the measure. Being beautiful is obviously fundamentally something that you simply CANNOT put into a measurement system of exact numbers, points or decimals. The whole point of being 'beautiful' or there being a 'heap' of sand is that you cannot measure it exactly on an arithmetic scale. It's based quite on a personal judgement and the only comparison that we can agree on is that a heap of sand is smaller than a mountain of sand.

Isn't it the number of sand grains in a collection that determines the heap-ness? — TheMadFool

No.

That's how you just get to the paradox: you are insisting that an exact number of sand grains determines what a heap of sand is. You simply dismiss there being the notion of incommensurability, but falsely think that everything can be measured by exact numbers. (Perhaps because of reductionist thinking that every amount of sand has an exact number of sand grains, which is true but meaningless here.)

If you are against either of these reductions, then hooray. If your talk of "incommensurability" isn't, after all, about trying to separate usage of heap from the naturals, then even better. — bongo fury

Let's first give a definition to incommensurability:

two or more quantities having no common measure.

So your correlation 2 goes totally against the definition and I'm not exactly sure what you mean by correlation 1.

What the important point here is that in mathematics there indeed is this incommensurability: that you simple cannot measure everything to everything else with some common measure. To assume it would be so is simply incorrect. And this is totally logical.

Therefore, to isolate one variable, the number of objects in the collection, may be a mistake. Nonetheless this is an issue for the heap paradox specifically and doesn't detract from the problem of vagueness, the central message of the paradox. — TheMadFool

Yes. As I said, It's basically because "heap" as a measurement system isn't measurable the same way like the number system. You just get smaller and larger comparisons to "heap". With let's say "a mountain of sand" compared to a heap is bigger and a perhaps smaller comparison to a heap is let's say "few grains of sand". If we want to go into measuring specific grains of sand, the scale system "few", "a heap", "a mountain" simply doesn't cut it. It's incommensurable.

When we look at paradoxes, the usual reason for them is that we have the premises wrong. Just as here, where we make the totally incorrect and false presumption that everything could be reduced to being measured by a common measure, notably with natural numbers.

I agree with Harry. To create a controversy is one of the oldest publicity tricks in the book — Metaphysician Undercover

Taking Colin Kaepernick to be the face of Nike was the 'controversial' trick that you refer to. That was indeed intensional: that made Nike look good, progressive and active to the younger crowd they are after.

I did. — Metaphysician Undercover

That's great. At least someone takes a direct position. Not "I don't mind, but someone else..."

The flag represents the political state, and the political state exists as the ideology, which is gone because we do not support it. Why ought we support that flag? — Metaphysician Undercover

Really? I thought the reason was that you simply have more states belonging to the Union. And that it didn't I think become an official flag. And what do you mean that it's not supported? Here's the flag prominently displayed at the Capitol Building during a second inauguration of an US President.



That being President Obama, that is.

So sorry if I'm confused as a foreigner on just when did this flag come to be a symbol of racism.

In this case, we're told the teleprompter stopped working, so he had to rely on his personal knowledge of history. — Relativist

:grin:

Well, bloopers are funny. Just like this one from Older Bush admitting he had sex with President Ronald Reagan.

It seems that Trump gets away with anything.
But it still needs to be called out. — Amity

The only thing would be if he would appease the Democrats and that would create perhaps a backbone for opposition of Trump in the GOP. What is really lacking is any kind of opposition to Trump in the Republican party.

Good that Trump isn't as able and cunning as Putin. The thing is that Trump simply is unable to mold the political system into what he would like it to be. (And of course, I doubt that he has really true ideas or agendas what he would like other than to be praised on Fox.)

An important area of difference between the sorites paradox and objectivity is the former is physical and sand grains have volume and becoming a heap isn't that difficult to imagine. — TheMadFool

I think one of the reasons why the Sorites Paradox is important and comes up so frequently isn't not only that we have a problem with vagueness. It's also that mathematics, as we understand it today, is built upon or founded on the practical need for counting. Hence we start with counting natural numbers. Now math has developed from this practical need, but it's logical foundations might not be good to be chained to counting. Now a heap confuses this thinking that "Let's start with counting" and we tend to just think of it as problem of mixing math with definitions from a spoken language.

I think it isn't just a problem of vagueness as it isn't so even in Mathematics. The problems what we have with infinity and what many mathematicians and philosophers had with what is now termed limits just shows that everything doesn't start from natural numbers and counting. The obvious reasoning what has puzzled people for long is that there cannot be a largest number and there cannot be a smallest number. Yet infinity and the infinitesimal, or limits are very useful. Both they have a different logic to them. And so does a heap.

Basically you have incommensurability between a heap and an exact number of grains. The paradox rises when we don't take into account the incommensurability between the two.

So that's what's wrong. Simply that we think every logical system can be reducted to a simple system of arithmetic. Why the paradox is so persistent is that we don't understand that incommensurability is part of the foundations of mathematics, which is extremely important for the whole system to be logical.

invoking the heroism of an army that defeated the British in the 18th century in part because “it took over the airports”. Lol: behold, the ignoramus president. — Amity

Reading of a teleprompter is so difficult. How could we assume the President of the United States to be able to clearly read out from a teleprompter a prepared speech. :razz:

Anyway, where ever Trump stumbles on any issues or speeches doesn't matter. What gives energy to Trump supporters is a) the condescending way Trump seems to be attacked in the media (or portrayed to be attacked) and b) their utter hatred of the Democrats. The more progressive the Democrat candidates seem to be and the more they play for the woke Twitter crowd, the better for Trump.

A shoe was pulled from the market. It's not an actual "issue". — Maw

Yes, obviously in the category of Maw answers: "I don't care at all about this… but I'll still actively participate in this thread."

When in Rome, do as the Romans do. That's what I think. — frank

I believe that when you are actually in Rome surrounded by Romans. Yet even there it doesn't mean you change totally what you think and become a different person. Being diplomatic doesn't mean you change your beliefs just to appease people you talk to. At least in a democracy you can speak freely. In a totalitarian state you do watch what you say, just not to get your hosts into an awkward situation or in trouble.

Now it's like: Uh, there might be Romans here… better act as if we would be in Rome, even if Rome is very far from here. Above all, better yet not to answer as a Roman might get upset.

Could be. All it takes is a community that sees it that way. — frank

Could be? Seems that all it takes is a hypothetical community for you not to answer what you yourself think about it.

Again, could be. I think women's issues stand apart because a woman's relationship to her oppressors was so intimate: it was her sons, father, brothers, and lovers. — frank

Was so intimate?

So from your I take it that you believe that women's families oppressed them earlier and this oppression has ended. :roll:

FYI; Women not having the ability to vote in national elections wasn't a family issue, it was indeed a political/legal issue.

(Besides, where on Earth comes this idea of sons oppressing their mothers?I think earlier people respected their mothers more than now)