In the context of social relations I would describe power as "the ability to impose one's will upon another". I consider that immoral, thus any government that utilizes such a principle I consider illegitimate. — Tzeentch

I used to think like that, but in the meanwhile, I have corrected my point of view. As far as I am concerned, you are allowed to "impose your will upon another" on the condition that you are willing to risk your life and die for what you believe in.

Hence, the person in power can choose the time and the place to do that, but he should never complain if "his target" chooses the next time and place to take revenge on him, because in that case, this person in power is just a bad loser.

In that sense, the problem of power abuse is mostly caused by people who refuse to take revenge, and in that way encourage the power abuse. That is why I utterly despise people who fail to ambush back. Even if you don't do it for yourself, i.e. to carry out vengeful reprisals, you should at least have the conscience to do it for others and for society at large.

Is modern psychology flawed? — Qwex

In the SE Asian country where I live (or the countries where I tend to live), there is just a very small "psycho industry" that revolves around dealing with substance abuse, i.e. rehab facilities. They try to get the patient off the product that they abuse, and then, release them back into the wild, until they undoubtedly reappear again at the rehab facility, for a new round of hopeless work; assuming that their family keeps paying for that kind of help. Only wealthy families spend money on that kind of services. Everybody else will rather quickly end up repudiating the addicted individual because that is the cheaper solution.

We do not have the time or the data required to carry out the verification procedure. — Isaac

This is rarely the case. It is certainly not the norm. We do not often have to make decisions in emergency situations. I cannot remember when I last had to make a truly urgent decision.

None of the solutions on offer can be verified and yet we need to act. — Isaac

If a solution can fundamentally not be verified then there simply are no experts for that type of problems; only fake experts. It means that the trade in that kind of solutions is not even possible. Why would you do business with people who cannot possibly be held accountable? You are asking for trouble if you do that anyway.

Seriously, I instinctively distrust anybody who asks me to trust them.

For example, if a doctor told me that I have the coronavirus, I would naturally expect him to show me the lab result. That would allow me to ask any other lab for new test results, if I felt that the results are in doubt. If he asked me to just trust him, without backing what he says with anything at all, my knee-jerk reaction would be to not trust him.

Buy a gun. — Lif3r

Humanity has never fought as lone individuals.

From the dawn of times, it has always been group against group. Individual fights ("random violence") are even considered unlawful in our fundamentally social species. If you want to fight with legitimacy, your fight will need to be "organized violence", i.e. "war".

In conflict, you will not face other, lone individuals. You will face entire groups. Therefore, you will be forced to join your own group. What will, however, be the principle of cohesion in your fighting group? Traditionally, humanity has always used extended-family ties for that purpose, i.e. clans or tribes.

A common religion may actually also be a sufficiently functional system of cohesion.

If you are not already member of such (virtual) clan/tribe, then by the time the shit hits the fan, it will be too late to develop the mutual trust required. In that case, you do not stand a snowball's chance in hell to survive violent conflict. Hence, I can only conclude that you are toast already.

For example, when discussing technological change in energy production in chapter "Technology and the limits to growth", the authors see only one and only one alternate candidate in energy production to replace fossil fuel based energy production, and that is nuclear fission power. — ssu

Was the report originally sponsored by Westinghouse?

As a result of its participation in the US government's military program for nuclear energy applications (e.g. The Nuclear Navy) Westinghouse was instrumental in the development and commercialization of nuclear energy systems for electric power generation. This business currently operates as the Westinghouse Electric Company, and is owned by Toshiba of Japan. — Westinghouse is now owned by Japanese interests

Quite a few of that kind of alarming reports are sponsored by corporate interests. "For the sake of your health, drink more milk! (The milk lobby). "One banana a day will save your way!" (Chiquita multinational), and so on.

The corporate oligarchy makes an astonishing amount of money by "educating" the consumer into adopting deceptive views that further their corporate interests. That is also why the oligarchy is so keen on controlling what the public-school indoctrination camps teach to the children.

You have given absolutely no support for your assumption that solutions are either verifiable or not. — Isaac

There are questions for which it may not be possible to verify that the solution proposed is indeed the solution. In that case, why would anybody feel the need to accept such solution?

We draw evidence, based on our experience, to judge the liklihood that a solution will work. — Isaac

Everybody and their little sister can say that they believe that their solution will work if we remove any obligation to provide a procedure to verify that their solution is indeed the solution.

What prevents these people from recommending a course of action that is certainly a solution for them but not for us?

Seriously, why on earth would we believe them?

Furthermore, what is the use in believing in that kind of solutions?

doing the right thing requires the political work of a "doctor," as Socrates put it, as opposed to a "candy store clerk." — Michael Lee

Believing someone else only makes sense if it is possible to verify that his solution is indeed the solution. If it is not possible to verify that it is, then this person could tell you whatever, regardless of whether he is a doctor or a candy store clerk.

If it is possible to verify that his solution is indeed the solution, then why would it even matter if the person is a doctor or a candy store clerk?

The doctor would never be voted into office because most people do not behave the way they do in accordance with reason — Michael Lee

There is no point in trusting that person, because we should only trust his solution. That means that we can verify that his solution is indeed the solution.

How can we do that?

If this person does not provide us with an objective procedure that allows us to verify his solution, then it is completely in accordance with reason that we do not trust his solution.

Ok. you can 'declare particular sentences to be 'true'. But what then? What logical process are you going to use to find those sentences that 'necessarily follow from those basic sentences'? — A Seagull

You can use provability to verify how the truth of new theorems in a theory depends on the assumed truth of the theory's basic sentences.

Even if you do have such a logical process, those sentences that follow and are declared 'true' are only true within that particular system; ie they rely on the truth of the original basic sentences for their truth. — A Seagull

Yes, agreed.

The truth of the original basic sentences must necessarily be supplied from outside such system. Such atomic sentences are assigned truth values disquotationally. When reasoning from first principles, the truth of such first principles is always assumed. From within the system, its basic truths are deemed to be of arbitrary nature.

You cannot have a scam without there being legitimacy. One cannot be deceived unless there is a truth of the matter. — unenlightened

I still agree with George Orwell. The term "democracy" is a meaningless word primarily used to fuel an entire agenda of dishonesty. There is indeed a reason why it has no precise definition. It needs to be flexible enough to be continuously re-purposed for evermore nefarious ends.

#1 How can one know what truth is, without knowing what truth is in the first place? — Monist

One way in which it can work, is to (arbitrarily) declare particular basic sentences to be true. Next, all sentences that necessarily follow from these basic sentences are also true, in accordance with the rules of logic that you consider to apply. Therefore, a sentence is logically "true" when it has the same truth status as the basic sentences of the theory created by the basic sentences.

So, yes, agreed. Logical truth is injected from outside the universe-world-model in which it applies.

So no answer to the actual question then? — Isaac

A good school for democratic leaders would be a democratic school. — unenlightened

If words like black and white were involved, instead of the jargon words dead and living, he would see at once that language was being used in an improper way. Many political words are similarly abused. The word Fascism has now no meaning except in so far as it signifies ‘something not desirable’. The words democracy, socialism, freedom, patriotic, realistic, justice have each of them several different meanings which cannot be reconciled with one another. In the case of a word like democracy, not only is there no agreed definition, but the attempt to make one is resisted from all sides. It is almost universally felt that when we call a country democratic we are praising it: consequently the defenders of every kind of regime claim that it is a democracy, and fear that they might have to stop using that word if it were tied down to any one meaning. Words of this kind are often used in a consciously dishonest way. That is, the person who uses them has his own private definition, but allows his hearer to think he means something quite different. Statements like Marshal Petain was a true patriot, The Soviet press is the freest in the world, The Catholic Church is opposed to persecution, are almost always made with intent to deceive. Other words used in variable meanings, in most cases more or less dishonestly, are: class, totalitarian, science, progressive, reactionary, bourgeois, equality. — George Orwell in Politics and the English language

Democracy is a scam. The true nature of the word alone, says it all. So, they want a better school to better train professional scammers, as if there aren't enough of those already. Well, yeah, go for it. Why not?

But what if you needed, nonetheless, to make a decision in a field who's paperwork cannot be verified mechanically? Let's say economics. — Isaac

I consider economics to be an ideology. We already knew that because the Soviet Union had their own completely different brand of economics. If it is possible to have two completely different takes on the same subject, without ending up in glaring contradictions, then the subject is ideological.

Stiglitz and Krugman, both Nobel prize laureates for economics got completely slagged off by the bitcoin community for their incompetent views on bitcoin. Nassim Taleb has also wrecked a Nobel prize laureate for economics:

Taleb and Nobel laureate Myron Scholes have traded personal attacks, particularly after Taleb's paper with Espen Haug on why nobody used the Black–Scholes–Merton formula. Taleb said that Scholes was responsible for the financial crises of 2008, and suggested that "this guy should be in a retirement home doing Sudoku. His funds have blown up twice. He shouldn't be allowed in Washington to lecture anyone on risk."[4] — Wikipedia, Taleb on Myron Scholes

I do not consider Stiglitz, Krugman, or Scholes to be experts. I have already dismissed and disregarded their advice, and done much better because of it. The following is what Nassim Taleb says on the matter:

If I had to relive my life I would be even more stubborn and uncompromising than I have been. One should never do anything without skin in the game. If you give advice, you need to be exposed to losses from it. — Nassim Taleb on being stubborn and disagreeable

Taleb explains this idea at length in The most intolerant wins. The dictatorship of the small minority. Ultimately, society is shaped by naysayers, i.e. people who do not listen. Hence, the message is clear: don't listen. Disbelieve it for the sheer sake of disbelieving it. Why? Because in God I trust and in nothing else.

Often 'experts' are just a shortcut to knowledge which you yourself could verify but not in the space of time you have by which you need to make an informed decision. — Isaac

Yeah, but a large number of messages in a commercial or even societal setting are meant to mislead you, especially, if they already know that you will not be verifying anything. It is by trusting these messages that you make it more profitable for the liars to lie even harder. You are simply turning your own environment into a living hell by doing that.

1. In order to learn this stuff about Big Pharma, about which we both agree, you had to trust someone on the basis of their purported expertise. You did not personally find all this out, you listened to experts - whether they we investigative journalists, drug database system administrators, certification authorities, testing labs - you had to decide that these people were likely to be telling you the truth. You say you used corroboration, but that is exactly the method used to assess all experts at a base level. — Isaac

I guess that this a point on which we may disagree somehow.

We (quite) often need other people to discover knowledge for us -- e.g. to what medical condition do my symptoms likely correspond? -- but we do not necessarily need other people to verify the paperwork for such newly-discovered knowledge. Since the paperwork for formal knowledge is mechanically verifiable, there is no need for an expert to verify it. A machine can do that too; better and cheaper. Hence, my outspoken preference for formal knowledge.

I do not recognize "experts" in disciplines for which the paperwork cannot (conceivably) be verified mechanically. At best, their bet is as good as everyone else's. On average, it is much worse, because they tend to get paid to lie to you.

Empty suit problem ( or “expert problem” ): some members of professions have no differential abilities from the rest of the population, but, for some reason, and against their empirical record, are believed to be experts: clinical psychologists, academic economists, risk experts, statisticians, political analysts, financial experts, military analysts, CEOs. etc. They dress up their expertise in beautiful language, jargon, mathematics, and often wear expensive suits. — Nassim Nicholas Taleb, Black Swan, Impact of the highly improbable

We have discussed an example from the pharma industry. Large areas in medical knowledge are epistemically part of science, and therefore, their paperwork can (conceivably) be verified mechanically. In that respect, it is a relatively safe subject in which I do recognize the existence of experts, even though for a plethora of different reasons, a substantial and noticeable proportion of the medical practitioners will end up being rather dangerous than helpful.

So, I occasionally use experts to discover new knowledge but only if the paperwork for such new knowledge can (conceivably) be verified mechanically. Otherwise, I do not trust these people.

2. In trusting the Asian alternative companies you are presuming, without warrant, that simply because they are not engaged in the deceitful activities of the Big Pharma, they are not engaged in any unsavoury activities at all. Again, this is either an act of trust, or it is monumentally naive. There are all sorts of ways in which these companies might make money at someone's expense, even if the actual molecule they supply is the same one Big Pharma do. That is not the only effect a company has in conducting it's affairs. — Isaac

I did not extend any form of blanket "trust" to Sun Pharma from Uttar Pradesh. I only said, after a short preliminary investigation into the matter, that I do not see any reason to distrust their Methimez (generic) product any more than the Tapazole or Northyx (Big pharma) alternatives.

You cannot personally verify any of these things. To do so you must decide to trust experts. — Isaac

Well, no, I can always verify the paperwork for expert claims, because I do not recognize experts in disciplines of which the paperwork cannot (conceivably) be verified mechanically. I share Nassim Taleb's opinion that that kind of people are just "empty suits". Their claims are simply not knowledge, in an epistemic understanding, i.e. what they proclaim are not objectively justified beliefs. If the beliefs in a professional field are objectively justified, then their paperwork can also (conceivably) be verified mechanically. If that is not the case, then there simply are no experts in that particular field.

Hence, I never trust experts to verify the claims' paperwork. I only trust mechanical procedures for that purpose. I only use experts to discover candidate claims, i.e. hypotheses, and to produce the paperwork, which later on, will need to be verified mechanically (well, ideally).

If they're offering the thing cheaper it's because they're not paying for something the more expensive companies are paying for. To conclude that they're worth going for, you need to know what that something is and be sure you can do without it. — Isaac

Whatever that may be, it is not the manufacturing cost of the chemical molecule that we are talking about, because in the greater light of things, that cost is considered to be peanuts.

To know that you have to trust somebody who is an expert in the field telling you what that thing is. — Isaac

What is needed, is some kind of assurance that Sun Pharma is indeed shipping methimazole in their Methimez product. According to my preliminary investigation, there is absolutely no reason to believe that the problem, "Does Methimez contain methimazole?" is worse or better than when you buy Tapazole or Northyx.

Furthermore, I really do not need the opinion on that matter from an expert liar paid by Big Pharma.

Again, why would these expert liars even consider telling you the truth when their income depends on diligently lying to you?

Unless you convincingly show me otherwise, as far as I am concerned, I would conclude that Methimez is a legitimate substitute for Tapazole and Northyx, and proceed accordingly.

I wouldn't trust some random Internet sale with my health. That would be borderline lunacy. — Isaac

If you do not trust internet sales, then you should not use them. A can of beans ordered online from Amazon could indeed contain rat poison. How do you know it doesn't? Huh? Huh?

Furthermore, unlike your neighbourhood chemist chain, foreign internet platforms are way less likely to collude with Big Pharma. Again, you insist on putting your trust in people known and documented to make a living from lying to you, while distrusting other people who obviously have less of an incentive and less of an opportunity to manipulate you.

How do I even know the pill contains anything but sugar? — Isaac

How do you even know that Tapazole or Northyx contains anything but sugar? You have not given any evidence why this problem would be better or worse for Methimez.

How do I know adverse reactions will be properly accounted? — Isaac

The side effects of the methimazole molecule are the same for all brands under which name it is being shipped. You are mixing problems here. You are just black mouthing products like Methimez for no good reason at all. I would buy Methimez and not Tapazole or Northyx, because I do not see any benefit for me to subsidize the scheming liars and manipulators of the Big Pharma oligarchy.

Yes, but to advocate them, you need to trust that they are at least not worse, ie that no corners have been cut in order to secure that lower price. How can you possibly know that? Lowering the price by using lower quality materials, quality and safety checks, and worse manufacturing techniques is also a known process, so I don't see where this gets you so far as choosing between the two is concerned. — Isaac

The cost of producing drugs is not in manufacturing:

'Profiteering'. With some drugs costing upwards of $100,000 for a full course, and with the cost of manufacturing just a tiny fraction of this, it's not hard to see why. — BBC News on cost of manufacturing in pharma

The manufacturing cost per unit produced in pharma is very much like for software, books, music, and movies: very low to nonexistent.

Therefore, it is not even worth saving money on the production process. The prices do not reflect manufacturing cost but other things:

Drug companies justify the high prices they charge by arguing that their research and development (R&D) costs are huge. ... But as the table below shows, drug companies spend far more on marketing drugs - in some cases twice as much - than on developing them. ... Big pharma companies also say they only have a limited time in which to make profits. — BBC News on pharma manufacturing cost

And, of course, there is also another notorious expense in "Big Pharma":

But drug companies have been accused of, and admitted to, far worse. Until recently, paying bribes to doctors to prescribe their drugs was commonplace at big pharmas, although the practice is now generally frowned upon and illegal in many places. GSK was fined $490m in China in September for bribery and has been accused of similar practices in Poland and the Middle East. Indeed a recent study found that doctors in the US receiving payments from pharma companies were twice as likely to prescribe their drugs. Drug companies have also been accused of colluding with chemists to overcharge for their medicines. They have also been found guilty of mis-branding and wrongly promoting various drugs. — BBC News on Big Pharma bribery

As I have said previously, it is absolutely not sound to trust the advice of doctors and chemists on big-ticket pharmaceutical drugs without pushing their advice through a thorough verification procedure. Seriously, your doctor simply gets paid by the pharma oligarchy to lie to you. Why would anybody tell the truth if his very livelihood depends on furthering lies?

I'm talking about where the problem with any alternative might lie. Companies producing cheap knock-offs are motivated by exactly the same greed as the big companies. — Isaac

If the alternative vendor produces exactly the same molecule/product as Big Pharma, i.e. a "generic", but a lot cheaper, and unless you have an excellent reason to believe that there are manufacturing quality problems -- rather unlikely -- then it always makes sense to buy the generic alternative.

The problem of fitness for purpose is in fact the same in both cases. So, that should not factor into the decision to pick the one product or the other.

They have exactly the same ability to extort and manipulate laws (albeit more likely with bribes than lobbying). — Isaac

No, they don't.

For example, Sun Pharma in Uttar Pradesh does not have the same stronghold on the American FDA as e.g. Merck or Johnson & Johnson. It simply does not work like that.

It's not your assessment of the problem I take issue with, it's your assessment of the solution. — Isaac

The solution that I would apply is to investigate related paperwork and then to proceed by purchasing online an Asian generic version of the drug, typically from the Indian subcontinent (India, Pakistan, Bangladesh) which seem to specialize in keeping afloat an alternative production of generics.

I do not have the nitty-gritty details of the verification procedure for their related paperwork because I have never had to carry out such replacement. Doctors in SE Asia always tend to prescribe the generic version anyway.

What's more, in SE Asia, even the branded pharma costs substantially less anyway. I guess that this is Big Pharma's way of adjusting to competition in a market where they do not have a stronghold on the regulator and where they cannot restrict market access to the generic competition. So, whenever I buy branded pharma, I typically pay less than a 10th of the price in North America anyway. I am quite sure that Big Pharma still makes lots of profit on that much reduced price.

It's a tool for mathematical theorms. Hence it is pseudo-technical to suggest it could apply outside of mathematics. Unless someone in a technical field has made that connection. — Isaac

I was talking about tools to verify the paperwork of a claim. The ideal is something like Coq, but it only works for mathematical paperwork. Furthermore, you need to follow a particular procedure to make it work. First and foremost, you must encode the mathematical claim in the tool's language.

Concerning pharmaceutical claims, you also end up with all kinds of paperwork, and therefore, with a procedure to verify that paperwork. No matter how good the tool for verifying such paperwork, it will never attain the level of accuracy of something like Coq. One reason already, is that the paperwork will be about experiment test reports. These test reports, if conducted correctly, can only be held against other test reports, assuming that they even exist; unless you want to do the tests again. The data will be of falsificationist nature. That is not as solid as data about reasoning from first principles. That alone will be already a problem.

We were discussing how to verify and/or compare information. As I have mentioned already, it will not be that simple to do, and we will have to discover the details of a workable procedure for that purpose.

Whom you'd have to trust to be providing you with the correct information. — Isaac

drugs.com is a database with mostly definitions (well, the part that I have used). Definitions can be corroborated with definitions from other databases. For example: "Tapazole, Northyx, and Methimez are said to contain Methimazole." That is some kind of master metadata that is not really in doubt.

Another piece of information is what Methimazole is used for:

What is methimazole? Methimazole prevents the thyroid gland from producing too much thyroid hormone. Methimazole is used to treat hyperthyroidism (overactive thyroid). It is also used before thyroid surgery or radioactive iodine treatment. — drugs.com on methimazole

That is a witness deposition. There will be other knowledge databases asserting this information. It may be possible to maybe even get hold of databases with the clinical-trial information that backs this claim. It depends on whether you believe that this information is in doubt. It certainly could be. That wouldn't be the first time anyway.

Where you'd have to trust the certification system. ... Whose processes and integrity you'd have to take on trust. — Isaac

All of that is still backed by experimental test reports. I do not need to trust the certification. I corroborate their reports with the reports from other certification parties.

What I objected to is your demented anti-western bias making out that Indian companies are going to be any better than the Western ones. — Isaac

I have never said that they would be "better". In my experience, however, they certainly tend to be cheaper.

If Western companies are bumping up prices by some illicit means, then the Indian company is probably cutting prices by some equally illicit means. — Isaac

Bumping up the price in the North American market is a known process. The pharma oligarchy simply manages to dramatically restrict competition and hence gauge prices. The oligarchy is tremendously being helped by the FDA through regulatory capture.

Regulatory capture (also client politics) is a corruption of authority that occurs when a political entity, policymaker, or regulatory agency is co-opted to serve the commercial, ideological, or political interests of a minor constituency, such as a particular geographic area, industry, profession, or ideological group[1].[2] When regulatory capture occurs, a special interest is prioritized over the general interests of the public, leading to a net loss for society. — Wikipedia on regulatory capture

FDA Depends on Industry Funding; Money Comes with 'Strings Attached'. The system at the FDA is 'unique in the degree to which industry sets the terms of the agenda,' said Daniel Carpenter, a Harvard professor of government who has published work on the FDA and on 'regulatory capture,' a process by which special interests gain influence over their regulators. — Project On Government Oversight on Regulatory Capture of FDA

The reason why the North American pharma oligarchy can strip their customers clean is because it is them who make the rules. The Indian generics vendors cannot do that. Therefore, they cannot extort a regulatory-capture premium from their customers.

We cannot do that without trust. You're acting as if we can eliminate empirical data somehow and somehow derive knowledge without it. Somewhere along the line we'd have to include empirical data the gathering of which we were not personally involved in. — Isaac

Yes, possibly, depending on the procedure that you wish to implement. Redoing the experiment testing may be prohibitively expensive. But then again, there is no way to know without looking at existing test reports. As I have said before, we would have to discover the details of the procedure to follow, "as we are going". Furthermore, there could be other parties interested in a report on redoing the experimental testing. Maybe they would help paying for it. Maybe crowdfunding amongst patients would be possible. It is not possible to know what to do without first getting your feet wet.

I for one would rather trust what an experienced lab technician said happened than what I think I saw. — Isaac

The problem is not the experienced lab technician. That kind of fraud is rarely perpetrated at such a low level. It is more about C-level executives doctoring the reports by cooking their conclusions. That is, for example, what happened at Purdue Pharma, when they cooked the results of the clinical-trial testing and triggered the opioid crisis in the USA:

In 2007, it paid out one of the largest fines ever levied against a pharmaceutical firm for mislabeling its product OxyContin, and three executives were found guilty of criminal charges.[3][4] — Wikipedia on Purdue Pharma

Opioid Crisis. The Nation is in the midst of an unprecedented opioid epidemic. More than 130 people a day die from opioid-related drug overdoses. — USA/HRSA administration on opioid crisis

The problem is really not about the small guy or about lab technicians. The problem is about how the pharma oligarchy manages to write the laws and then contort their application, while killing an increasingly large number of their customers in the process.

pseudo-technical garbage — Isaac

What would there be wrong with e.g. Coq?

Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs. Typical applications include the certification of properties of programming languages (e.g. the CompCert compiler certification project, the Verified Software Toolchain for verification of C programs, or the Iris framework for concurrent separation logic), the formalization of mathematics (e.g. the full formalization of the Feit-Thompson theorem, or homotopy type theory), and teaching. — Mission statement of the Coq proof assistant

It is an excellent tool to verify mathematical theorems with their proof. It is clearly the benchmark for mechanical verifiability of claims. Other tools or procedures can merely aspire to attain that level of fitness for purpose. As I have mentioned before, you cannot expect tools for verifying pharmaceutical paperwork to be at that level.

its not possible to personally verify either of the rival claims (which is what I'd already said) — Isaac

As I have said already, it depends on what exactly it is about. Let's pick an arbitrary example from the drugs.com database: Methimazole.

Generic Name: methimazole (me THIM a zole)
Brand Name: Tapazole, Northyx

Let's pick an arbitrary Indian generic alternative: "Methimez from Sun contains Methimazole."

Next step: Figure out prices for Tapazole and/or Northyx in North America.
Next step: Check what Methimez costs in India and other countries with a relatively free market in pharmaceuticals.

Sun Pharmaceuticals is the largest pharmaceutical company from India and the fifth largest specialty generic company in the world. It has capabilities across dosage forms like injectables, sprays, ointments, creams, liquids, tablets and capsules. Its businesses include producing generics, branded generics, speciality, over the counter (OTC) products, anti-retrovirals (ARVs), Active Pharmaceutical Ingredients (APIs) and intermediates in the full range of dosage forms. It also produces specialty APIs. US formulations contributed the most to company’s US$ 4 billion sales in FY18 with a contribution of 34 per cent, followed by India branded formulations at 31 per cent. — IBEF record for Sun Pharmaceuticals in Uttar Pradesh, India

Now, that is already quite a reasonable starting point for the Indian generic, Methimez, and its manufacturer, Sun Pharmaceuticals in Uttar Pradesh.

One cheap and easy procedure would be to double check in how many different countries their Methimez product has been certified for local distribution. Each of these certifications will have a laboratory reports available. Many countries put their reports online. Some countries do not test by themselves but just reuse the test reports produced by other countries. Then, you have independent laboratories doing their own tests. And so on.

What makes you believe that the paperwork for Tapazole and/or Northyx would indicate that these branded alternatives would be safer to use than Methimez (the Indian generic)? As I have said already, we would need to dig up all the paperwork, scrutinize it thoroughly, and discover the proper procedure to verify it, while doing that. It is a lot of work.

Furthermore, I am much more interested in dealing with mathematical theorems than with this kind of stuff. I would only investigate all that paperwork, if I really needed to use the product. I don't. I do not intend to use this otherwise arbitrarily-chosen product, "Methimez", because I do not need it.

If western pharmaceutical companies are just out to make money by bumping up prices, then why aren't the Indian ones just out to make money by cutting corners on quality? If the medical journals can't be trusted to print the truth becasue of their biases and their sponsors, then why can those sources you just cited who have biases and revenue streams to consider too? — Isaac

Where is the paperwork for the first product and where is it for the second product? What products exactly are you comparing? If you think there is something wrong with the paperwork for either product, then staple a clarifying note to the document that is in doubt.

As I have said before, there may not even be a standardized tool to compare pharmaceutical products. Therefore, there may not exist software that properly embodies the proper procedure to verify the products' paperwork. Hence, an adequate procedure will have to be discovered on a case-by-case basis.

For mathematical theorems and proofs, there exists a standardized procedure. Encode the theorem and its proof in the formal language of Coq, Isabelle, or Lean, and then run the verification function. Unlike for mathematics, not all types of paperwork can be mechanically verified. Furthermore, there may not even be a complete tool for that purpose.

And you trust the medical websites and search engines to provide you with a statistically viable sample? Why? You've tested them personally have you? Your own lab facitilies and access to controlled trials, remarkable. Assuming they're lying doesn't get you anywhere because it doesn't provide you with the alternative. Presuming everyone is lying just tells you anything you haven't directly tested yourself might be false. Great. Now what? You don't have the facilities to test everything yourself, so what are you going to do now? — Isaac

Don’t Trust Your Doctor. I’m a doctor, so I can say this with a straight face: Don’t trust your doctor. There’s no question in my mind that today most doctors are businessmen first and doctors second. — Dr. Peter Rost

Trust in doctors has plummeted by 75%. What can be done?

A doctor tells you why you can't trust your doctor again. Your doctor is merely a pawn in a multi-billion dollar industry - while your health and well-being are a poor, distant second. — Doctors are becoming pawns of a system

Never ask the doctor what you should do. Ask him what he would do if he were in your place. You would be surprised at the difference. — Nassim Nicholas Taleb, Antifragile: Things That Gain From Disorder

As far as I am concerned, it is obvious that there are very good reasons for a healthy distrust of doctors, the pharma oligarchy, and the entire medical industry. Furthermore, what information I trust, is my own choice, and is something that I decide on a case-by-case basis.

Who do you go to when you get sick? — TheMadFool

I go to a doctor.

However, depending on what is at stake, I do not just blindly trust him. Here in SE Asia, their services are affordable enough to ask for a second opinion. Furthermore, you can search online for people with similar medical conditions and double-check their experience. I certainly trust the narrative by other patients a lot better than what one, arbitrary doctor says. This is just a simplistic description of how you could start building a verification procedure for what medical doctors tell you (when it really matters ...). The problem is obviously harder than that.

The medical industry is badly afflicted with corruption and misplaced trust. The ongoing opioids crisis is just one example of things that can go wrong.

Trust that the expert is concerned about your welfare — TheMadFool

You can reasonably assume that the expert is first and foremost concerned about his own welfare.

That is not necessarily a problem as long as you are aware of that. I do not believe in their hypocritical "oath" either. The more a service provider talks about ethics, the more likely his industry is fraught with moral issues.

I mean if an expert has no interest in your welfare then his knowledge/expertise is of no value to you for it can be withheld or misused. — TheMadFool

Exactly.

His expertise may also be ideologically tainted.

For example, some doctors will refuse to prescribe Indian generics, even though they are equivalent and ten times cheaper, because they do not want to miss out on the incentives offered by the pharmaceutical oligarchy. His own interests obviously come before yours:

Pharma chief defends 400% drug price rise as a ‘moral requirement’. Nostrum Laboratories’ Nirmal Mulye says he is right to charge as much as possible and slams FDA. A pharma executive has defended his decision to raise the price of an antibiotic mixture to more than $2,000 a bottle, arguing there was a “moral requirement to sell the product at the highest price”. — Financial Times on the morality of the pharma oligarchy

The next step is to convince doctors to make their patients believe that any alternative to that antibiotic mixture is "highly unsuitable" for the patient. I just safely assume that these people are lying all the time.

for instance we consult not just any doctor but the best among them and the same applies to other areas of knowledge. — TheMadFool

What is "the best" in this context?

Other industries are not necessarily better.

For example, universities just want to saddle you and/or your children with exorbitant student loans in exchange for a worthless degree that will guarantee a successful coffee-slinging career at Starbucks.

I do not believe that there is a simple solution, especially when the incentives are stacked against you. The entire system is purposely built like that, with a view on sucking you dry. It is a minefield. Lots of people knew back then that it was going to run out of control, and now it has.

Much of everything we know about mathematics was developed by that school. — Michael Lee

There is this widespread view of a long mathematical winter between Greek antiquity and the 12th century AD, i.e. a millennium-long standstill:

By the middle of the 1st Century BCE, the Roman had tightened their grip on the old Greek and Hellenistic empires, and the mathematical revolution of the Greeks ground to halt. Despite all their advances in other respects, no mathematical innovations occurred under the Roman Empire and Republic, and there were no mathematicians of note. The Romans had no use for pure mathematics, only for its practical applications, and the Christian regime that followed it (after Christianity became the official religion of the Roman empire) even less so. — storyofmathematics.com on Roman mathematics

Is that view a bit of an exaggeration or is it real?

I shudder to think of what would happen here if the posters on this and other threads with minimal mathematical knowledge apart from set theory and logic were to launch investigations into subjects like functional integration or even metric spaces or advanced calculus. — jgill

Stephen Wolfram wrote something very relevant in that regard:

Curating the math corpus. So how big is the historical corpus of mathematics? There’ve probably been about 3 million mathematical papers published altogether—or about 100 million pages, growing at a rate of about 2 million pages per year. And in all of these papers, perhaps 5 million distinct theorems have been formally stated. — Stephen Wolfram on 'Curating the math corpus'

Being knowledgeable of say 1% of these 5 million theorems, i.e. of 50,000 theorems, is probably already overly ambitious.

Hence, that cannot possibly be what it is about.

Furthermore, it does not make sense to memorize these theorems along with their proofs, because it would turn such person into an incomplete and rather useless sub-database machine of the (curated) math corpus. Either you use the machine, or else you build the machine, because in all other cases you are just a slow, failed, useless, and sorry excuse for a machine.

People investigate what they are interested in.

There is no reason why that would necessarily include functional integration, metric spaces, or advanced calculus, none of which would give that person any understanding in other math sub-disciplines such as for example elliptic-curve cryptography or in zero-knowledge succinct arguments of knowledge.

Vitalik Buterin is a good example of what I mean:

He attended the University of Waterloo but dropped out in 2014, when he received the Thiel Fellowship in the amount of $100,000,[10] and went to work on Ethereum full-time.[10] — Wikipedia on Vitalik Buterin

Vitalik does not just write about top-level mathematics, as in his medium article series:

This is the third part of a series of articles explaining how the technology behind zk-SNARKs works; the previous articles on quadratic arithmetic programs and elliptic curve pairings are required reading, and this article will assume knowledge of both concepts. — Vitalik Buterin's article intro

Vitalik successfully implemented this mind-blowing math in the ethereum source code. As Linus Torvalds famously said:

Talk is cheap. Show me the code. — Linus Torvalds on 'cheap talk'

Why would someone like Vitalik Buterin even be interested in functional integration, metric spaces, or advanced calculus? At the age of 20 he had already become a multimillionaire from his deep understanding of the math subjects that truly mattered to him, while many PhD graduates in math are associate-lecturers living off food stamps:



These people are not just on food stamps, many of them are also widely despised for their runaway arrogance. They should take an example to Vitalik, in order to improve their lives, known to suck. Vitalik, on the other hand, is a very humble person. He is friendly and pleasant. He does not try to "prove" that other people "know nothing". He is just a good human being, albeit stinking rich too. ;-)

Cogito ergo sum. But I can only prove that with any 100% certainty to myself, not to you. — Artemis

Totally agreed.

While René Descartes is rightfully revered as an indisputable grandee in mathematics, through his highly influential work on coordinate systems and on the analytical geometry built on top of that, his work in self-ontology, cogito ergo sum, is just a silly exercise in futile solipsism.

Now, if one does a survey of higher learning, there's a degree for every conceivable subject the acquisition of which makes a student qualified and, fingers crossed, highly competent in the given subject. This has the benefit of making such qualified people into experts in their respective fields and thus become people we can put our trust in. — TheMadFool

It works exactly the other way around.

According to the Dunning-Kruger study, intelligence is defined as:

Knowing when you do not know.

Intelligence has nothing to do with what people do in college, i.e. memorizing phone books filled with trivia.

What happens when you give someone a certificate which says that he knows, i.e. a degree, while he has merely read some trivia on the matter and has absolutely no experience in the field? That person will think that he knows while in fact, he does not. In that sense, a degree increases that person's arrogance and reduces his intelligence.

While a track record of successfully solving problems is a good reason to believe that people are competent, a college degree is the opposite: it is an excellent reason to distrust their ability to do the job.

trusting people to a degree is more efficient and certainly a lot nicer — Isaac

Not really.

In fact, not at all. Trust is exactly what fuels deception.

When we talk about trustless systems, we mean that our ability to trust it does not depend on the intentions of any particular party, which could be arbitrarily malicious. A trustless system allows you to trust in the system without needing to trust in the parties with which you’re transacting. — Trustless systems

The more there are who people trust, and the more blindly they trust, the more dangerous the environment becomes to all people. It is exactly because they trust it, that it turns on them. If they had not trusted it so much, it would not have.

For example, if people did not trust the mainstream media so much, these media would not be incentivized to lie so much. In that sense, it is the audience of the mainstream media who corrupt them with their trust. In another example, it is by trusting the Federal Reserve that its users corrupt the US Dollar. Trust corrupts the trusted party. More trust means more corruption.

The idea of cryptocurrency technology is to eliminate the corruption caused by trust. In trustless technology, it is because we do not need to trust other parties that we can trust them. Trustless technology is incredibly efficient at achieving this goal. Furthermore, people are happy to use it in order to transact with other people. Hence, it allows people to be nice to each other.

Therefore, a trustless approach is more efficient and nicer than corrupting other people with trust.

And who told you about God? — Isaac

"Fitra" or "fitrah" (Arabic: فطرة‎; ALA-LC: fiṭrah), is the state of purity and innocence Muslims believe all humans to be born with. Fitra is an Arabic word that is usually translated as "original disposition," "natural constitution," or "innate nature."[1] According to Islamic theology, human beings are born with an innate inclination of tawhid (Oneness), which is encapsulated in the fitra along with compassion, intelligence, ihsan and all other attributes that embody the concept of humanity.[citation needed] It is for this reason that some Muslims prefer to refer to those who embrace Islam as reverts rather than converts, as it is believed they are returning to a perceived pure state.[2] — Wikipedia on the concept of Fitrah

In short we have an ingrained, fully justified, belief that to solve a particular problem we need to consult an expert in that field and to produce such experts we need schools and education programs in those fields. — TheMadFool

This belief is deeply ingrained but not at all justified.

In fact, it is even a dangerous belief. As a matter of fact, we must never "trust" service providers.

The reason why we may carefully believe a "ruling", i.e. a conclusion, a "professional opinion", is entirely contained in the fact that the justifying paperwork is verifiable, and that we have carried out the procedures for verification.

In that sense, it does not matter in the least who exactly has produced the justifying paperwork. On the contrary, if it matters who has said it, then what he has said, cannot possibly matter.

It is exactly when we trust these people that they will abuse our trust. It is the trust itself in the deceptive statement, i.e. that a=b, that fuels the growth in the total amount of deception (b-a)².

This approach to trust service providers, fully explains the distinction between the intellectual have-nots and the intellectual haves. The have-nots believe a proposition because of who says it (personal "authority"). The haves believe a proposition because its justification is verifiable, i.e. how it was said.

The belief in personal authority of experts simply turns you into an intellectual have-not. Seriously, in God I trust and in nothing else.

Here's my definition of infinity, and for simplicity I'm only referring to positive infinity: infinity is a number, but it has a characteristic that all real numbers do not possess. — Michael Lee

Good luck reading. MO as you know is a site for professional mathematicians so the best one can hope for is to understand a few of the words on the page. — fishfry

The standard reals are the Goldilocks model of the reals. Not too small and not too big to be Cauchy-complete. They're just right. And are therefore to be taken as the morally correct model of the reals. — fishfry

My current understanding is that there exists indeed a detailed description of the infinite model(s) for real numbers but at this point I am unable to pierce through the dense vocabulary and concepts in order to develop a correct mental picture on the matter.

Concerning the phrase "infinity is a number, but it has a characteristic that all real numbers do not possess", in my impression, it does not adequately reflect the breath and the depth of existing knowledge on real-number model(s). I personally feel that this summary is overly simplistic.

Very little of our initial, formative knowledge is formal. And what do you mean exactly by 'formal'? — Sir Philo Sophia

Formal knowledge are sentences for which "the paperwork" containing their justification can (conceivably) be verified mechanically.

Turing stated it this way: It was stated ... that "a function is effectively calculable if its values can be found by some purely mechanical process". We may take this literally, understanding that by a purely mechanical process one which could be carried out by a machine. The development ... leads to ... an identification of computability† with effective calculability. — Statement of the Church-Turing thesis

Paperwork concerning reasoning from first principles (=mathematics) can be verified mechanically. Paperwork related to experimental testing (=science) can (conceivably) be verified mechanically.

why are you limiting the definition or process of knowledge building to formal knowledge? — Sir Philo Sophia

I limit it to formal knowledge because formal knowledge is by definition understood objectively, since its main requirement is that a machine must be able to perform the verification of its justifying paperwork.

In Computational Knowledge and the Future of Pure Mathematics, Stephen Wolfram writes that he believes that formal knowledge can also be discovered mechanically (and not just verified):

Math by enumeration. The first is to enumerate possible statements, and then to use (implicit or explicit) theorem-proving technology to try to determine which of them are true. And the second is to enumerate possible proofs, in effect treeing out possible ways the axioms can be applied to get theorems. It’s easy to do either of these things for something like Boolean algebra. And the result is that one gets a sequence of true theorems. But when I was working on A New Kind of Science, I did a simple experiment for the case of Boolean algebra. One day I’m sure doing this will be an important part of pure mathematical work. — Stephen Wolfram on 'Math by enumeration'

On the other hand, Stephen Wolfram also admits that there are fundamental problems in mechanically searching for knowledge:

In a sense an axiom system is a way of giving constraints too: it doesn’t say that such-and-such an operator “is Nand”; it just says that the operator must satisfy certain constraints. And even for something like standard Peano arithmetic, we know from Gödel’s Theorem that we can never ultimately resolve the constraints–we can never nail down that the thing we denote by “+” in the axioms is the particular operation of ordinary integer addition. — Stephen Wolfram on the limitations of 'math by enumeration'

By the way, I do not completely understand what Wolfram means by "we can never nail down that the thing we denote by '+' is ... [what we think it is]." He seems to say that the existence of nonstandard models of arithmetic effectively renders the semantics of field arithmetic ambiguous. Of course, this could be the case, but I have never run into anybody else describing the problem in this way.

I personally do not believe that knowledge can successfully be discovered by mechanical enumeration. But then again, I am not against Wolfram trying. ;-)

can you clarify in other terms what you mean here? I don't understand the logic/argument supporting "humanity would either have no knowledge at all, or else, have discovered all possible knowledge already" — Sir Philo Sophia

If you need formal knowledge in order to discover new formal knowledge, how do you get hold of the very first formal knowledge? How do you get the process even started? Conversely, all that is required to discover formal knowledge is formal knowledge, then it would all have unravelled already.

You invoked the extended real numbers and claimed it has something to do with L-S, which of course it does not. Unless I misunderstood your point. — fishfry

If I understood the explanations correctly, Löwenheim-Skolem applies to the theory of real closed fields (=first order theory) but not to to the theory of real numbers (=second order theory). That last bit wasn't immediately clear to me:

The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement. It is not possible to characterize the reals with first-order logic alone: the Löwenheim–Skolem theorem implies that there exists a countable dense subset of the real numbers satisfying exactly the same sentences in first-order logic as the real numbers themselves. The set of hyperreal numbers satisfies the same first order sentences as R. Ordered fields that satisfy the same first-order sentences as R are called nonstandard models of R. This is what makes nonstandard analysis work; by proving a first-order statement in some nonstandard model (which may be easier than proving it in R), we know that the same statement must also be true of R. — Wikipedia on Löwenheim-Skolem in the context of real numbers

I had never read anything on model theory for real numbers. The materials I had run into were all about natural numbers.

since the Ultrafilter Lemma isn't constructively acceptable — sime

Examples of non-trivial ultrafilters are difficult (if not impossible) to give, as the only known proof of their existance relies on the Axiom of Choice. — The 'Art of Solving Problems' on giving examples for the ultrafilter concept

I see. ;-)

America has no mainstream left-wing party, and the left-wing people are avidly anti-corporate and terribly disappointed in the Democrats. — Pfhorrest

Religion, more specifically, Islam is strongly opposed to usury:

Allah has permitted trade and forbidden usury. — Quran: 2:275- 279

I strongly dislike corporations, especially the banksters, because they are usury-infested organizations and because they lobby the legislature to modify the laws to their benefit, and also because their mass-market messages are more often than not manipulative lies. They were supposed to merely trade and be engaged in commerce, instead of corrupting society's laws and culture.

Furthermore, with the school system manipulating their graduates into looking for jobs at these corporations, these corporations unduly make large numbers of people dependent on them for their livelihood.

Still, I cannot identify with left-wing politics, because it is mostly about redistributing income outside the religiously authorized channels of extended family and mandatory/voluntary charity. These left-wing people, in fact, also seek to change the laws in order to force and shoehorn everybody else into their state-run socialist utopia.

Also, it's not so clear-cut that corporations are considered evil by religious people. Consider for example prosperity theology. — Pfhorrest

Christianity is much more flexible in that regard than Islam.

Prosperity theology has been criticized by leaders from various Christian denominations, including within the Pentecostal and Charismatic movements, who maintain that it is irresponsible, promotes idolatry, and is contrary to scripture. Secular as well as some Christian observers have also criticized prosperity theology as exploitative of the poor. — Wikipedia on prosperity theology

Christianity is primarily a clerical religion. Morality is traditionally decided by the (centralized) living magisterium. Even though the Protestants were going to implement a sola-scriptura policy, they actually just kept the practices of the Catholic Church alive:

The magisterium of the Catholic Church is the church's authority or office to give authentic interpretation of the Word of God, "whether in its written form or in the form of Tradition."[1][2][3] According to the 1992 Catechism of the Catholic Church, the task of interpretation is vested uniquely in the Pope and the bishops.

Bishops, teaching in communion with the Roman Pontiff, are to be respected by all as witnesses to divine and Catholic truth. In matters of faith and morals, the bishops speak in the name of Christ and the faithful are to accept their teaching and adhere to it with a religious assent. This religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. — Wikipedia on magisterium principle

Islamic theology does not depend on the authority of particular, centralized clergy but first and foremost on deductive reasoning from first principles. There is no Pope and there are no bishops in Islam. Islamic law is very close to a formal system with mechanical verifiability of its moral rulings:

Ijtihad (Arabic: اجتهاد‎ ijtihād, [idʒ.tihaːd]; lit. physical or mental effort, expended in a particular activity)[1] is an Islamic legal term referring to independent reasoning[2] or the thorough exertion of a jurist's mental faculty in finding a solution to a legal question.[1] — Wikipedia on ijtihad

It is the very concept of the "Church" as a centralized organization and "magisterium" (personal clerical authority) that make aberrations such as the prosperity theology possible. Martin Luther's sola scriptura view has actually never been implemented in Christianity.

It means essentially that CH is equivalent to the fact that all models of the hyperreals are isomorphic. The idea is that the particular model of hyperreals you get depends on which nonprincipal ultrafilter you choose. If CH holds then all the models are isomorphic. — fishfry

This is incredible. I didn't know that this was possible. It is so unlike the models of PA:

The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). — Wikipedia on nonstandard models of arithmetic

Well, yeah, I wasn't aware of the fact they behave so differently ...

There's a Mathoverflow thread about this, let me see if I can find it. Ah here it is. Good luck reading. MO as you know is a site for professional mathematicians so the best one can hope for is to understand a few of the words on the page. — fishfry

In my opinion, it is primarily a question of figuring out the foundational concepts embodied in the specialized vocabulary for the subject, i.e. real-numbers model theory. I had to do that for something a bit simpler, i.e. model theory and nonstandard models for PA. It looks like model theory related to real numbers is an entire subject in itself, even bigger than PA, with even more concepts to digest. It doesn't seem to have famous, celebrated theorems, though; unlike PA with Gödel's incompleteness theorems.

I don't know the answers to all the good questions you raise, but I can't help thinking that you're overthinking things and letting yourself get confused by Lowenheim-Skolem. — fishfry

I wasn't sure if real-number theory is first order or second order. There is a disclaimer in the Löwenheim-Skolem page that it does NOT apply to second-order theories. In fact, I was aware of that disclaimer. Real-number theory turns out to be essentially second order. That was the main source of confusion.

To tell you the truth, this is the first time I have run into documentation about real-number model theory. It is totally new to me. As far as I am concerned, it is a completely new world. Very few concepts of natural-number model theory seem to transfer unchanged ...

The extra points don't participate in the field properties as I'm sure you know from calculus. — fishfry

Calculus was just school exam material for me consisting of endless symbol manipulation. I didn't particularly "care" about it. It is not that I have read anything about calculus ever since. It doesn't appear in computer-science subjects either. So, what am I supposed to do with it?

Field algebraic structures are more interesting to me. They reappear in cryptography. In elliptic-curve cryptography, the algebraic structure is specifically extended to contain $\infty$, which does effectively participate in the field. It is even the identity element for addition (without which the structure is not even a field):

This set together with the group operation of elliptic curves is an abelian group, with the point at infinity as an identity element. — Wikipedia on ECC

That's because religious morality is inherently a right-wing thing. Of course right-wing religious moralists think the existence of liberal left-wing morals is a sign of decadence and depravity. — Pfhorrest

Well, the undue influence on the culture and laws of society by corporations is considered evil by religious people, while both left and right are not only happy with the corporate stronghold on society, they even encourage it.

In fact, the left is completely beholden to having corporations around because they see society as the struggle between evil employers and exploited employees. Someone who is, for example, self-employed is not a worthy, exploited victim, and therefore does not even belong in their take on society.

All in all, the corporations need the left even more than the right in order to maintain their undue power, influence, and even for their continued survival. Since the system allows corporate interests to fabricate new laws to that effect, it is them who are the true beneficiaries of the fake antagonism between left and right. That fake conflict is just one big, manipulative lie.

True religion is a bulwark against corporate takeover of society, because it forbids a key pillar in their strategy: the usury-infested fiat bankstering system. Without usury, corporate interests would not be able to enslave their manipulated serfs.

Consumer debt, credit card debt, student loans, inflated mortgages ... are the tools that the oligarchy uses to enslave the manipulated masses. On the long run, religion will win, simply because paper money, that false god, is programmed to become worthless, making it impossible to collect usury payments with it. Good riddance!

Because of this post, I started reading up on the axiomatization of real numbers, and of course, I have run into issues that I do not properly understand:

The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement. It is not possible to characterize the reals with first-order logic alone: the Löwenheim–Skolem theorem implies that there exists a countable dense subset of the real numbers satisfying exactly the same sentences in first-order logic as the real numbers themselves. — Wikipedia insisting that the reals are a second-order theory

In mathematics, a real closed field is a field F that has the same first-order properties as the field of real numbers. Some examples are the field of real numbers, the field of real algebraic numbers, and the field of hyperreal numbers. — Wikipedia on real closed fields which are a first-order theory

The first-order theory of real closed fields is the first-order theory whose primitive operations are addition and multiplication, primitive predicates are = and ≤, and axioms are those of a real closed field. More precisely, a first-order theory is roughly speaking, a theory where quantifiers apply only to elements (not to sets of elements).

Alfred Tarski proved (c. 1931) that the first-order theory of real closed fields is complete, and decidable. This means that there exists a general procedure that takes as input an assertion expressed in this theory and decides which of the assertion and its negation is true (complete means that either the assertion or its negation is true). — Wikipedia: unlike natural-number logic, real-closed field logic is decidable

Real closed fields seem to be dramatically different from the standard real number system, but what is the actual difference?

Then, they say something very interesting but really complicated about the generalized continuum hypothesis in conjunction with real closed fields. I think that this is the kind of things that could shed light on the true nature of infinite cardinality in real-number theory.

(if only I understood what they are saying ...)

The advantage of using a religious regulatory framework for morality, such as Jewish or Islamic law, is that left-wing versus right-wing does not even exist. There is simply no scope for that. Society is supposed to hang together through strong extended-family ties along with mandatory ("zakaat") and voluntary ("sadaqah") charity. The very fact that something like left-wing versus right-wing even exists, is considered to be a symptom of decadence and depravity.

so how can any of that be used to explain or reproduce what the (philo of) human mind does? They tried decades ago to use things like symbolic, predicate calculus/logic but failed to anything useful beyond creating automatic theorem provers. — Sir Philo Sophia

It only applies to some human thought processes, i.e. the ones related to reasoning within or about a formal system.

Since the human mind does not only reason from first principles but, for example, also deals with sensory input, using empirically-driven thought processes, formal reasoning was never meant to be the complete picture of human thinking. There are also informal and even tacit thought processes that are not covered by formal knowledge disciplines.

Furthermore, even the discovery of formal knowledge cannot be achieved through formal knowledge. Otherwise, we would never have discovered formal knowledge or else we would have discovered all possible formal knowledge already.

For example, it is not possible to enumerate all numbers that represent theorems in a theory and then locate for each such theorem the number that represents its proof. Discovery of theorems and their proofs is entirely governed by informal thought processes ("creativity", "innovation", and so on).

Not all thinking is formal-deductive. That would be a serious misconception. I guess that most thinking is probably even not.

don't often say such-and-such is infinite, rather they say a process tends to infinity — jgill

The affinely extended real number system simply adds infinity as two real numbers in a Cantor-like approach:

Extended real number line. In mathematics, the affinely extended real number system is obtained from the real number system ℝ by adding two elements: + ∞ and − ∞ (read as positive infinity and negative infinity respectively), where the infinities are treated as actual numbers.[1] It is useful in describing the algebra on infinities and the various limiting behaviors in calculus and mathematical analysis, especially in the theory of measure and integration.[2] The affinely extended real number system is denoted R ¯ or [−∞, +∞] or ℝ ∪ {−∞, +∞}. — Wikipedia on the affinely extended real number system

According to the explanations this extension approach is entirely consistent with existing results in mathematical analysis. This extension approach is actually what the Löwenheim–Skolem theorem does for Peano's arithmetic (PA) and other theories with infinite models:

It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism. As a consequence, first-order theories are unable to control the cardinality of their infinite models. — Wikipedia on the Löwenheim–Skolem theorem

If you can extend the real number system with uncountable infinity then you can extend it with any other infinite cardinality (upwards), since the theory is unable to control the cardinality of its infinite model. However, this also depends on whether this real number system is still a first-order theory.

Still, the fact that an affinely extended real number system is possible, suggests that mathematical analysis may have exactly the same interpretation problem as Peano's arithmetic (PA), i.e. if one infinite cardinality satisfies the model, then all other upward infinite cardinalities also do.

Hence, mathematical analysis could suffer from the same fundamental interpretation problem surrounding infinity.

thanks for sharing that. cute, but not very useful in the relm of the mind. That is, my original statement/assessment still stands re " any property has to convey some kind of unique meaning/utility concerning the object it is a property ", except for trivial utility like concatenating, etc.- no meaning is conveyed/preserved to how is that useful to reasoning or the mind? — Sir Philo Sophia

Provability is the property of a number. It is a definable predicate.

Given Gödel's semantic completeness theorem, all provable numbers are also semantically true in their universe. So, even though truth is not a legitimate predicate for all logic sentences in the language of such universe, it is a legitimate one for provable ones.

If provability is not a useful property, then we would have to conclude that mathematics is also not useful to reasoning because provability is what it is all about in mathematics.

"The undefinability theorem shows that this encoding cannot be done for semantic concepts such as truth." — Sir Philo Sophia

Yes, this undefinability drops straight out of Carnap's diagonal lemma. When applied to provability, the diagonal lemma still leaves the door open for a legitimate provability predicate:

"There are provable sentences that are false =OR= there are unprovable sentences that are true."

Carnap's lemma closes the door, however, to a legitimate truth predicate:

"There are true sentences that are false =OR= there are false sentences that are true."

Given the above, the lemma syntactically entails that the truth predicate is undefinable.

So, we assume the truth of the construction logic of a Platonic world and then we can reach derived truths in that world through syntactic entailment. We cannot reach derived truths by using a truth predicate.

your idea on that is unclear to me. any property has to convey some kind of unique meaning/utility concerning the object it is a property of. How does a number, alone, impart/convey any meaning? — Sir Philo Sophia

numbers, alone, have no properties. so, your ideas here seem to be incomplete at best, flawed at worst. — Sir Philo Sophia

Gödel noted that statements within a system can be represented by natural numbers. The significance of this was that properties of statements - such as their truth and falsehood - would be equivalent to determining whether their Gödel numbers had certain properties. — Wikipedia on Gödel numbering

Arithmetization. A method used in mathematical logic for replacing a reasoning on the expressions of some logico-mathematical language by reasonings on natural numbers. For this purpose the replacement is constructed by some sufficiently simple one-to-one mapping of the set of all words (in the alphabet of the language under consideration) into the natural number sequence. The image of a word is called its number. Relations between and operations defined on words are transformed by this mapping into relations between and operations on natural numbers. The requirement of a "sufficiently simple" mapping leads to the fact that some basic relations (such as the relation of imbedding of one word into another, etc.) and some operations (like the operation of concatenation of words, etc.) are transformed into relations and operations having a simple algorithmic nature (e.g. are primitive recursive). — Encyclopedia of Mathematics on Arithmetization

In 1931, Kurt Gödel published the incompleteness theorems, which he proved in part by showing how to represent the syntax of formal logic within first-order arithmetic. Each expression of the formal language of arithmetic is assigned a distinct number. This procedure is known variously as Gödel numbering, coding and, more generally, as arithmetization. In particular, various sets of expressions are coded as sets of numbers. It turns out that for various syntactic properties (such as being a formula, being a sentence, etc.), these sets are computable. Moreover, any computable set of numbers can be defined by some arithmetical formula. For example, there are formulas in the language of arithmetic defining the set of codes for arithmetic sentences, and for provable arithmetic sentences. — Wikipedia on the arithmetization of logic in Gödel's work