I have found another example, and actually a quite interesting one, from the cryptography subdomain at stack exchange:

What is a “witness” in zero knowledge proof? A witness for an NP statement is a piece of information that allows you to efficiently verify that the statement is true. For example, if the statement is that there exists a Hamiltonian cycle in some graph, a witness would be such cycle. Given a cycle, one can efficiently check whether it is a valid Hamiltonian cycle, but finding such cycle is difficult. Knowledge extractors are used in the definition of proofs of knowledge. There, you don't just prove that some statement is true, but that you know a witness for this statement.

In upstream pure mathematics, computation in its entirely abstract, Platonic worlds is deemed effortless. Downstream cryptography cannot assume that, and must also take into account issues of computation effort. Hence, the requirement that the witness must be efficiently verifiable. Still, this twist is obviously not needed in upstream pure mathematics. So, it is a matter of correctly switching between both context-dependent views on the concept of witness.

Buddhism appeals to the rational aspect — TheMadFool

There is a rational element and a transcendental element. Quite a few people cannot assess the soundness of the rational element. So, they mostly ignore it. Use of the rational element only starts at a particular level of education, but everybody, educated and uneducated, will manage to assess the transcendental element, using their unknown mental faculty.

That said, what if we were to purge scripture of miraculous material and instead emphasize the reasonable parts? — TheMadFool

The Quran rejects that option. I don't know why, actually. It just does. The Quran just acknowledges it in globo without much detail. It refuses to purge the older scriptures from their miraculous material. It is not my choice, but hey, I instinctively trust that this decision is the better one.

Would there be anything left to instil or maintain faith? — TheMadFool

Yes, in my opinion, the miracles are not essential.

Now that I brought it up, what about "faith"? Isn't that belief despite lack of evidence? — TheMadFool

I have no clue as to how that mental faculty works. It just seems to be there.

I'm afraid the "unknown mental faculty" is NOT rationality. — TheMadFool

Yes, it is not rationality, but unknown mental faculties show up in so many different circumstances, that we cannot understand humanity without them. Another example. Can you explain why people like watching football? There is no rational explanation why looking at a bunch of people running after a ball would be so exhilarating. Still, it is.

I conclude that rationality is a tool amongst other mental tools. These other mental tools cannot be explained, because they are not rationality. If it were possible to explain them, then they would just be rationality again, which they aren't.

Do logical limits point to the limits of what is possible or to limits of our thinking? — Fooloso4

Logic is a formal language.

There is a mismatch in power between what we can say (formal language) and what we can solve (system). The solution in the development of set theory was to add constraints to restrict formal language as such to prevents particular questions from being asked. ZFC was extended with three "hacked" axioms for that. They have no other function than to restrict what can be asked. Still, the strategy ultimately failed because you can still do it (Gödel's incompleteness).

We should also clarify that you weren't saying that politicians can't invent laws period, but that there are particular laws they'd have a problem either getting approved, recognized or at least that they'd maybe not bother to enforce. — Terrapin Station

The simplest solution is to forbid the political invention of new laws. That also automatically solves the problem of new, foreign-import laws that these countries get shoved down their throats. Still, if they believe that their politicians are allowed to invent new laws, then as far as I am concerned, just let them. These new import laws will punish the population, but since they are unbelievers, the Quran says that we must not intervene in that process. In other words, it is not considered a problem whatsoever that very bad laws apply to unbelievers, because that is actually the way it should be. The more the problem is self-inflicted, the more we should encourage the process as well as its inevitable consequences.

Even if that were the case, it wouldn't be a matter of not being allowed to make a law. You could argue that it's not being allowed to enforce a law that was made. — Terrapin Station

In quite a few Islamic-majority countries, they do not even make such new foreign-import law, simply, because it is against Islamic law to do that, and they can also afford to refuse to do that. Countries with lots of business with China are very much like that; such as half of Africa nowadays. They no longer create new foreign-import laws. Other countries do it anyway, but with a view on never enforcing them. It boils down to pretty much the same outcome.

The economic clout of China is changing the ballgame quite a bit. Almost no country gives as flying fart abou the IMF or World Bank anymore, because they'd rather make the deal with China. In that sense, China has become in some ways the long-awaited saviour of the world.

That's not very specific, unfortunately, and it looks like it's saying that politicians are creating laws that politicians aren't caring about, which isn't the same as them not being allowed to make laws. — Terrapin Station

To an important extent, it is.

For example, the legislature in those countries often comes under pressure from the so-called western democracies to adopt a new law. For example, domestic-violence laws sponsored by West and touted by western so-called NGOs. The local legislature grudgingly adopts the new law, but with a view of never, ever applying it. They simply do not want these foreign-import laws, if only, because they would have disastrous consequences. In the example, it would lead to a divorce fiesta, while they simply have no money to subsidize the living expenses of a new and growing demographic of divorced, single mothers. Furthermore, their population does not want these new laws either. If the bureaucracy or law enforcement really tried to enforce such new law, they would probably also have an insurgency on their hands. So, they just don't. In fact, they didn't even intend to from the very start.

So I take it there are no examples of this? — Terrapin Station

I just found an example, but in a different context:

Most Countries Have Environmental Regulations. Very Few Actually Abide by Them.
A new U.N. report finds that, to address climate change, we don't need new laws or regulations, but to get countries to comply with laws that already exist.

I actually like environmental regulations, but they would need to be vetted to ensure that they are also halal. I am wary of new rules that cannot be fitted into, and properly derived from the existing framework of religious law.

You can safely that statement to:

Most Countries Have politically-invented law . Almost none outside the so-called western democracies actually abide by them. A new U.N. report finds that it is virtually impossible to get countries to comply with politically-invented laws that already exist.

So you're basically talking about practical nullification? What would be an example of this--a law is put on the books, but not only the citizenry, but the law enforcement arms of the government in question ignore the law so that it's the same as if it didn't exist? — Terrapin Station

In practical terms, it often depends on the composition of the population.

Politically-invented law always applies to the unbelievers who believe in their legitimacy or behave in a way that suggests that they believe in their legitimacy. Believers do not believe in politically-invented law. Therefore, it does not apply to believers.

A person is tributary to the law that he accepts, only.

If you accept Islamic law, you can be held to it. If you accept politically-invented law, then you can be held to that. Hence, it depends on yourself. The Quran is adamantly clear that Islamic law does not apply to unbelievers.

Therefore, unbelievers cannot restrict their taxes to the taxation rates in the Quran. That is not possible, because they reject the Quran.

Politicians are obviously physically able to create new laws. They do this all the time. — Terrapin Station

Maybe in some places they can. There are a lot of places, though, where that does not work. You need a very gullible population for that to be possible. That does not exist everywhere.

Nothing happens to them in response to creating new laws that would amount to, say, "If you do x, you'll be arrested/imprisoned/etc." — Terrapin Station

We, the believers in the text, do not recognize politically-invented laws. Still, there are quite a few countries filled up with unbelievers. That is where you will find systems of punitive taxation.

But then again, we are also not against that, because unbelievers are simply meant to be punitively taxed. As believers, we are not allowed in any way to reduce the taxes on unbelievers or to alter the systems of punitive taxation that apply to them. The unbelievers are simply meant to pay exorbitant taxes, because that is what they are here for.

Read the Quran, and you will find it all explained there in excruciating detail.

So we'd need to clarify what "allowing" amounts to there. — Terrapin Station

The Quran is a text with directives and guidelines, meant to be implemented by the believers in the text, at their earliest convenience.

You don't believe that politicians are allowed to invent laws? — Terrapin Station

Of course, I do not believe that politicians are allowed to invent new laws. Is it even in my interest to believe a thing like that? We were talking about gullibility ...

This is one thing I don't believe. Speak for yourself. 1/2 of the world's entire population don't believe this. — god must be atheist

Islamic law does not allow for liberally inventing new extensions. Read the page on Sharia. The consensus of religious scholars will never defend the view that politicians would have the authority to extend Islamic law. That is unthinkable.

Taxes, at their most basic, much like laws, are necessary to alleviate the fatal fractures that would be caused and created by social forces. Why, do you think that law courts should be abolished, and let criminals run free? Or that schools be closed to the common people's children? Or that roads ought not to be built? You are a fool if you think taxes are wasted money. — god must be atheist

If you believe that you should pay taxes to the politicians, then feel free to do so. All taxes and mandatory contributions that I am supposed to make are all listed in the Quran, along with the applicable tax rate. For a believer, there are no taxes other than the ones listed in the Quran. For a believer, there are no obligations outside the ones listed in the Quran.

An unbeliever who does not believe that all the taxes he owes, are listed in the Quran, cannot be exempt from taxation on grounds of the Quran. Therefore, the Quran says that the unbelievers must continue to pay the taxes that they have always paid.

I can guarantee to you that Islam is by far the most tax-efficient religion for its believers. All other religions lead to paying much, much larger tax bills. I am not interested in these other religions (or views such as atheism), if only, because they are more costly without providing anything of value in return.

The hitherto unknown mental faculty that miracles in ancient texts seem to appeal I call "gullibility to the max". — god must be atheist

Well, if you look at the alternative, you will detect gullibility that is much worse. What to think of people who believe that politicians are allowed to invent and enforce any new law to their liking? We believe that God has invented all the laws already, and that politicians are not allowed to further restrict our freedom.

For example, is there anything more gullible than paying more taxes, because politicians have increased the tax rate? We do not believe that we should pay, and when we can, we simply do not. So, who exactly is gullible? The ones who pay, or the ones who don't?

You mean to say anyone can be a prophet? — TheMadFool

Not in Islam. Mohammed, may he rest in peace, was the last prophet.

If we remove miracles from the metric what's the difference between a prophet and a very imaginative, resourceful and eloquent story teller? — TheMadFool

No, what a prophet says, needs to appeal to an otherwise unknown mental faculty.

If rationality is about the capacity to use inference in order to produce statements of knowledge, then
It is trivial to argue that there are other mental faculties. A first example are the signals that the brain sends to the heart in order to adjust its rhythm. It is not under control of any conscious mental faculty. Still, it is definitely an important ability of the brain.

A second example is the discovery of knowledge. If access to existing knowledge along with rationality were enough to discover new knowledge, then humanity would either never have discovered any knowledge at all, or else, discovered all possible knowledge already. Hence, another, unknown mental faculty must be involved.

Do you mean to say miracles aren't the pillars that hold up religion? — TheMadFool

In my impression, miracles are not necessary in religion.

If Jesus hadn't done his set of miracles and Moses his would people have believed? — TheMadFool

The ancient texts are deemed to appeal to the otherwise unknown mental faculty. So, in my impression, yes, people would still have believed them.

If Jesus hadn't done his set of miracles and Moses his would people have believed? If you watch TV it won't be long before there's a report on how a statue was weeping blood or a cancer patient is cured by faith alone. Are these small snippets of human thought not evidence for miracles --> God? — TheMadFool

In Islam, there cannot be any new prophets. This is what has been prophecied. So, there will be no new people recognized in that class any more. The ability to transmit transcendental messages will not be awakened again. That was elucidated in the stream of transcendental messages transmitted by the prophet of Islam.

With the second coming of Jesus, however, the historical person is expected to return to earth. That is a firm expectation in Islam. We are generally deemed to be able to recognize who it is, when he will have come back, by using our otherwise unknown mental faculty.

These achievements do not equal those the Great Designer but incomparably more intelligent in terms of use of material resources and time. So, where is Intelligence in the Design? — Jacob-B

I will raise a counter argument of syntactic, formalist nature, by juggling with definitions.

You see, according to the Dunning-Kruger research into ineptitude, the test subjects thought that they knew, but in fact they didn't. So, if that behaviour is a good definition for stupidity, then "knowing when you do not know" should be a suitable definition for the term "intelligence".

According to the offshoots of second-temple Judaism, God has a copy of the Tablet of Wisdom, i.e. the Preserved Tablet, i.e. the Book of Decrees ("al-Lauh al-Mahfuz"), which obviously contains the Theory of Everything (ToE), because it allows God to flawlessly predict the future and the entire trajectory of the universe.

Hence, the divine attribute: All-Knowing.

Someone who is all-knowing obviously does not need to know when he does not know, because that situation does not even occur. Therefore, an attribute such as All-Intelligent does not make sense. Unlike ourselves, God does not need "intelligence". The term is simply inapplicable.

With intelligence defined as the ability to handle one's limitations, does it make sense to be better at that than someone who does not even have these limitations?

However, the religious don't follow these, what I assume are, rational principles. They simply infer God/supernatural from so-called miracles. From a scientific standpoint that's jumping to conclusions. — TheMadFool

Miracles are indeed a bit controversial.

In the Islamic narrative, the prophet was often asked by unbelievers to perform miracles to give them evidence of his contact with God. He always refused to do that. He said that his only "miracle" was the Quran.

On the other hand, the Quran does not reject the miracles described in older scriptures, such as the Torah and especially the Gospels. Denying Jesus' miracles in the Gospels would obviously have discredited the son of Mary, while he is firmly considered to be the Christ, i.e. the Messiah, in Islam.

The Quran rather chooses to confirm these external miracles in globo without elaborating on any details.

I am not necessarily beholden to the testimony in the Gospels about the miracles, but I am also not particularly beholden to questioning that part of the narrative. If the Quran feels that it is suitable to confirm them, then who am I to come up with a different view? What useful result would I achieve by doing that?

So, strictu sensu, there is indeed no pressing need to perform miracles while transmitting messages of transcendental origin. The prophet of Islam certainly did not feel the need to do that.

You can't answer a question with a question. — Bartricks

The first issue is always the decidability of the question. A good, historical example of an undecidable question is Russell's paradox:

Does the set of all sets that do not contain themselves, contain itself?

This question is undecidable. The bug fix was to make it impossible to ask this question in set theory (ZFC), by adding an axiom, i.e. restricted comprehension, that strictly prevents asking this question. That is how it was solved.

I still don't know what your answer is to the question. Can an omnipotent being make a square circle or not? — Bartricks

You are asking a question. On what grounds do you believe that this question is decidable?

I am not entirely sure what you're saying - are you saying that even if an omnipotent being were bound by logic, this would not be much of a bind, or are you saying that an omnipotent being is not bound by logic, or are you saying that logic, as it is, shows evidence of being the creation of an omnipotent being? — Bartricks

No, it is an objection involving the limitations of knowledge itself.

With all knowledge necessarily constrained within the boundaries established by the Church-Turing thesis, on what grounds do you believe that your question would be decidable?

An answer is effectively calculable if its values can be found by some purely mechanical process.

With which purely mechanical process can your question be answered? If you cannot successfully propose such mechanical procedure, then the knowledge question must be declared undecidable.

Epistemology is about the existence of knowledge-justification methods. What method is it about? How do you know that the answer is within reach of the chosen method? Otherwise, the question can simply not be answered.

So, on this view an omnipotent being cannot, for example, create a stone heavier than he (an omnipotent being, that is) can lift, for that involves a contradiction and omnipotence does not involve being able to do the impossible. — Bartricks

TLDR; It is a problem of logic as a tool.

You see, logic is not omnipotent. On the contrary, first-order logic is notoriously full of issues. You can easily say things in first-order logic language that are utmost paradoxical. (It is officially a "language")

For example, Richard's paradox (1905) created a serious problem in number theory. This paradox describes a number that cannot possibly have a decimal or other positional representation. The number is simply ineffable.

An even more famous example is Russell's paradox (1901). Does the set of all sets that do not contain themselves, contain itself? Both the answers "yes" and "no" are contradictory. This problem is known for causing the "foundational crisis" in mathematics.

At the beginning of the 20th century, they addressed the problem by hacking the axioms with several bug fixes that simply prevent you from expression the Russell sentence in set theory (Zermelo-Fränckel-Choice: ZFC). The axiom of restricted comprehension is specifically aimed at Russell's paradox:

This restriction is necessary to avoid Russell's paradox and its variants that accompany naive set theory with unrestricted comprehension.

In general, you can say that the axioms of regularity, pairing, and restricted comprehension are bug fixes to prevent you from asking questions that would throw ZFC into a tail spin.

This was the relatively stable situation in mathematics between 1908 (Zermelo's publication) and 1921 (Fränckel's late bug fixes). Was all of this bug fixing enough to solve all problems of that sort? No, not at all, and far from. The language itself causes problems too.

Gödel's incompleteness theorems (1931) are exactly about that problem. The language in which the typical mathematical theory is expressed, i.e. first-order logic, is full of issues, irrespective of what axioms you express in them.

You can trivially express Gödel sentences in first-order logic. Gödel sentences are yes/no questions that are not decidable from any theory. So, whatever theory you pick to try to solve your question, the theory will not be able to decide whether the answer to the question should be logically true or logically false.

That is how the entire field of computability came in to existence.

Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.

As a matter of fact, most problems have turned out to be undecidable:

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run.

It is a widespread misconception to believe that all problems would be decidable. The decidability of a question is, in fact, always the first question to consider. It is very, very naive and even ignorant to liberally assume decidability.

The point I made is that 2+2 is not the same as 4. So if set theory treats them as the same, it is in violation of the law of identity. — Metaphysician Undercover

Well, first there is the understanding that the "=" symbol pretty much never means "identical". The symbol is much more permissive than that. It usually means something along the lines of "extensional" or "equivalent", depending on the axioms in use, but not necessarily "identical".

In arithmetic, "2+2=4" means that the equality is provable from number theory -- or from the larger, encompassing theory such as set theory -- by using the inference/rewrite rules of arithmetic.

From there the notion that two different, non-identical symbol streams can be "equal" to each other, with "equal" meaning that their extensionality or equivalence is provable from the main theory in which we happen to be operating.

In abstract, Platonic worlds, we almost always assume that computation does not require "effort". This view may very well fall apart in virtual worlds, generated by running computer processes. There will be some calculation effort involved for a computer process to derive that "2+2" resolves to "4". So, the more computing intensive the resolution process, the less the equality will be automatic. In the real, physical world, the problem is further exacerbated by the fact that humans tend to be slow and error prone at carrying out calculations in arithmetic.

The meaning of the "=" symbol is not only very context-sensitive, but I actually do not know of even one context in which it means "identity".

For example, in Javascript, the single "=" symbol is already taken up to express assignment. For example, "a=5" means store value "5" in variable "a". It does not want to express that "a" and 5 would be equal or so. It is rather an instruction that seeks the side effect of changing what value is stored in a.

"a === b" means "a == b" and "typeof(a)==typeof(b)".

So, '3' == 3 resolves to "true" but '3' === 3 does not, because the string '3' and the integer 3 are of a different type.

They are considered equal in the expression " '3' == 3 " because the "==" operator will carry out enough work to convert both types to a permissive common denominator, and if it can then declare a match somewhere, it will return true.

The permissiveness of the "==" operator is generally considered questionable. The practice creates dangerous corner cases. For example, 0 is considered a falsy value while "0" a truthy one. That can go surprisingly wrong in the context of permissive equality.

The following is an interesting article about the difference between === and == in javascript.

What's interesting about Banach-Tarski is that it's a purely syntactic paradox. The free group on two letters has a paradoxical decomposition, and this is purely a matter of meaningless syntax. One then lifts the paradox to Euclidean 3-space since the isometry group of 3-space (that is, the group of rigid transformations) contains a copy of the free group on two letters by virtue of the existence of a pair of independent, non-commuting rotations. — fishfry

I've found a machine-verifiable version of the Banach-Tarski proof for the Coq proof assistant. It looks endless. I first thought that this is because the Coq formalisms are excruciatingly lengthy, but the classical, annotated first-order-logic version is also 30 pages long.

It uses pyramidal vocabulary. For example:

Theorem 22 (Tarski’s Theorem)Let G act on X, and let E ⊆ X. Then there exists a finitely additive, G-invariant measure on X defined for all subsets of X and normalizing E if and only i fE is not G-paradoxical.

So, it requires figuring out what "G-invariant measure" and " normalizing" means. Otherwise, Tarski's theorem 22 will remain inaccessible. It is interesting, though. If the proof were about formal language, I would probably keep drilling down in order to figure it out.

Actually, Tarski does have theorems in the realm of formal languages, e.g. his undefinability theorem. I wonder how he ended up also working on abstract algebraic geometry and topology? Hilbert is also like that. He did his language-oriented Hilbert calculi but also his geometry-oriented Hilbert spaces. I wonder how people manage to not only handle both domains but even be original in both?

There could actually even be a deeper link between geometry and formal language, because the late Voevodsky saw homeomorphisms everywhere in formal language domains, while those are clearly a geometry concept. I still don't understand Voevodsky's univalent foundations. Everybody seems to be raving and hyping that stuff, but I still cannot wrap my head around it.

There is of course nothing more fashionable than being able to come up with a finer point in the Voevodsky stuff. I cannot "show off" because I unfortunately don't get it! ;-)

a view which atomized individual actors — rlclauer

Atomizing individualism is a social disease that is rather unrelated to economic issues.

If you want a functioning kinship structure, you will need some kind of marriage policy that reinforces it. That in turn is not compatible with western ideas that promote so-called romantic-love marriages that seek to couple up people with mostly arbitrary other people.

That kind of marriage practices is exactly what prevents a stronger kinship structure from emerging. Hence, atomized individualism is a self-inflicted problem.

Nobody can save people from their own stupidity, especially not when they so staunchly believe in their wrong ideas, and from there, even double down on them. I do not understand why people keep complaining about their self-inflicted problems. I believe that people should be grateful for receiving exactly what they have asked for.

The rich and higher up in the economic hierarchy are obviously in a better position to "do something about the problem." — rlclauer

Yes, for themselves and their own relatives.

According to Islamic religious law, their mandatory contribution as charity to the wider society is limited to 2.5% of their net capital gains. I do not see why they should pay one more dollar than that. As far as I am concerned, they do not have to.

I am asking, do you think the people in question could and would afford crippling sentience enough, in order to abolish gender? — Shamshir

I have no clue ... (seriously)

The abolition of gender would involve the abolition of psyche.
Do you think these neophiles could pull it off? — Shamshir

Well, I do not speak from personal experience, as I resolutely resigned from the ongoing experiment in the so-called "western democracies" over a decade ago. I just happened to have run into reports that mention the new phenomenon.

Even though my own kids speak English with me, they are also perfectly fluent in their mother's tribal language. They very well know that they firmly belong to, and are supposed to identify with, their mother's clan, and that I become grumpy if they ask too many questions about any so-called western democracy that I would originally have been loosely affiliated with. So, they have learned to avoid the subject.

I applied some kind of matrilinealization twist to the situation, which is some kind of hack to prevent getting my own kids dragged into an experiment that I simply do not want. They have a system of arranged marriages here. So, that should also keep the kids out of the western-style dating cesspool. As I have said before, I could only ever have hoped to solve the problem for myself. Seriously, I am not the Messiah.

Since my own kids clearly match their gender with their biological sex, I have no clue as to what it means to have "nonconforming" offspring at home, i.e. not boy nor girl, nor both, nor homosexual either, i.e. so-called "choice-resisting". I also do not know what any new articles on the subject will be reporting back in the future in terms of the ongoing genderlessness takeover. They are apparently already at 25% now.

I see now you deleted your paragraph on how transpeople are somehow a "problem" because they can't "decide what gender they want to be". Good choice, since many trans and LGBTQ youth are at the forefront of some of the most powerful social movements of this century so far-these minority and oppressed groups have been the backbone for some of the very rights we say we "take for granted". — Grre

↪Grre
Just a tip: pay attention to who you are responding to, especially if you’re going to get angry and abusive. You seem to be confusing the OP with a response by alcontali. — Possibility

What I wrote, was not in relation to the alphabet soup but to a new strand of articles that have appeared such as this example, "27 Percent of California Teens Are Gender Nonconforming. A new study of California youth found that more than one in four teens say their classmates view them as resisting dominant forms of gender expression."

The alphabet soup is about men who prefer to be women, or women who prefer to be men. That phenomenon was mentioned in ancient manuscripts millennia ago already. That is clearly nothing new, and nothing to be fundamentally worried about, since it has always been there. The article mentions something else altogether. It is about the current trend, which seems to be massive and wholesale, towards the complete abolition of gender. That is a whole new level of confusion. I do not believe that society can handle that.

Well, we have been livestock for the rich and powerful since economic hierarchy came into being. — rlclauer

Being rich can be a side effect of being a good manipulator, proficient at producing believable deceptions. Still, not all rich people have gained their wealth through deceptive manipulations. Furthermore, this view exempts the "manipulee" from responsibility, while it obviously takes two to tango.

In religion, it is the believer in false gods who is held responsible, and not the false gods. If you choose to believe the false gods, then it is you who are at fault.

In my opinion, it is preferable to place the responsibility with the party who is in a better position to do something about the problem. It makes more sense to exhort people to stop believing in lies than to get angry with the liars.

If a manipulator can rip off your money by telling you a lie, then he will, quickly, before someone else does, because a fool and his money are easily parted. Given the expectation that your money will soon be gone anyway, he will try to act faster than the other manipulators as to be the one to successfully pocket the loot.

A pod of killer whales will hastily speed in the direction of a mother grey whale with her calf, because according to their sonar signals, the calf is toast anyway. That is just a question of time. Therefore, it is a question of separating the calf from its mother, pushing it under until it drowns and then devouring it before another pod of killer whales beats them to the finish.

It's not arbitrary then, it just looks arbitrary, in appearance, but it really is not. That it is arbitrary is an illusion. Would you see mathematical axioms in the same way? They look arbitrary, but they really are not. What is required to get beyond the illusion of arbitrariness is to get inside of the head of the artist. This does not mean to literally get inside, but to learn how to think in the same way as the artist. Then you will no longer be an outsider who sees mathematical axioms as arbitrary. — Metaphysician Undercover

Agreed, but that is exactly what is not possible. These other, unknown mental faculties are out of reach of any ability to inquire them rationally. Furthermore, their assumed input could still truly be random, because there is no method available to distinguish between the output of unknown mental faculties and sheer randomness.

Yes, I see mathematical axioms in the same way. They look arbitrary but they probably aren't.

There is something uncannily recognizable to Plato's theory of forms, but the purported link between the forms and the real, physical world is unfortunately out of scope for the instrument of rationality. Still, the uncanny sensation of recognition suggests that this link is not necessarily, completely out of scope for other, unknown mental faculties.

However, the issue of the truth of these scriptures is never open for reasonable discussion. No need is seen by its followers for it to justify its "truth" in a reasonable way. Its truth has to be accepted "blindly" - an act of faith is required. My question is why I have to accept scriptures written by fallible human beings as being true? — Daniel C

It is the axiomatic epistemic domain which works like that. The question then becomes: Why do you accept the axioms of an axiomatic theory?

In my opinion, the best starting point for an answer can be found in the page on the Brouwer-Hilbert controversy.

So, Weyl asks, what might guide the choice of these rules? "What impels us to take as a basis precisely the particular axiom system developed by Hilbert?". Weyl offers up "consistency is indeed a necessary but not sufficient condition" but he cannot answer more completely except to note that Hilbert's "construction" is "arbitrary and bold".

The question then becomes: What does the term "arbitrary" mean in this context?

So, that brings us to the nature of random numbers. If you look at the following Mersenne Twister test page, you will see that it produces a sequence of ten random numbers. Are these numbers truly random? For outsiders, yes. For someone who knows the seed, no, because with the seed, he can generate exactly the same sequence again, and flawlessly predict the next random number. Therefore, since we do not know if a true random number generator even exists, the issue of randomness is fundamentally subjective. In general, if we do not understand the source of a particular phenomenon, we will just consider it to be arbitrary.

At the same time, rationality cannot possibly be the only mental faculty.

For example, if the main ingredients for discovering new knowledge were rationality along with existing knowledge then either humanity would have never discovered any knowledge at all, or else, discovered all knowledge already. Hence, there must be mental faculties that are not rationality. Since we do not rationally know them, they will appear to us as arbitrary.

That explains to me the Islamic concept of Fitra.

"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.” 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.

Fitra refers to mental faculties other than rationality that are innate and which predispose us to instinctively accept the basic rules of religion, while from the outside, this choice will appear as arbitrary.

Well, that would depend on how you define "arbitrary". Use of mental faculties in one's decisions negates randomness. If such decisions are arbitrary, then how do you understand "arbitrary"? — Metaphysician Undercover

I see arbitrary in this context as "further unjustified".

For example, I do not trust what a literary critic says about why Charles Dickens wrote a particular passage. I strongly suspect that even Dickens himself did not really "know" it. It just came up to him, sourced from other mental faculties than mere rationality. So, from the outside it looks "arbitrary".

It is the same situation as with a sequence generated by a Mersenne Twister. From the outside, it looks random. From the inside, we can see that you will always get the same sequence depending on the seed that you use. Is the sequence random? For outsiders, yes. For insiders, no.

You can find an online demo for a Mersenne Twister here.

In that sense, if a true random number generator does not exist -- which is an unsettled question -- then randomness is always a subjective perception. Mutatis mutandis, if we have no clue as to how these other mental faculties work, then their output will appear as arbitrary to us.

s it true that life has "a" meaning and that our task is only to discover / find that meaning to have the experience of living meaningfully? — Daniel C

Quran 51:56. I have created the jinn and humankind only for my worship.
Quran 23:115. Did you think that We created you in vain, and that to Us you will not be returned ?

So, according to the ancient scriptures, we are here to show that we can be keepers of God's law.

In that view, the universe is one big filter to separate the worthy elements from the unworthy ones. On the Day of the Last Judgment, we will all be returned to our rightful owner, who will keep for himself the useful specimen of mankind while discarding the useless ones.

People who believe what is written in the ancient manuscripts, obviously have no qualms with the "meaning of life". It is not a question that particularly torments the believers. Well, I have never met one who had issues or struggled with this question. For the believers, the answer is utmost trivial as well as completely satisfying.

I'ts okay. Philosophers use no categorical language; they say, "That's post-modernist regressivism" or something of the like, and they leave it at that. It's us, dilettante, who spell everything out for each other. — god must be atheist

Yeah, but what is a philosopher?

There are obviously the grandees, and then there is everybody else who discusses the grandees. Still, you cannot become a grandee yourself merely by talking about the grandees. There are no grandees about the grandees, or grandees in grandee-hood.

In Nassim Taleb's lingo, success in philosophy has "extremistan" characteristics. It is certainly not a normal, Gaussian distribution. It is the same in music or movies. There are just a few grandees, and everybody else is pretty much a nobody. Now, young people had better be aware of the fact that having a degree in philosophy, or any subject for that matter, will not elevate them from the status of a merely nobody. If all you can bring to the table, is a degree, then you are not needed, and also irrelevant, just like millions of others.

Furthermore, none of the actors we see on a TV screen or singers on music channels have a degree in film or in music. It is the same in philosophy. Not one grandee became one by rehashing from memory what other grandees had said.

Of course, people with a degree in philosophy would want to see an intermediate level in the hierarchy, i.e. of "grandee in discussing grandees", since the whole point of getting that degree was to get some recognition. Well, no. There is no recognition whatsoever. A degree signals nothing meaningful. It does not elevate you above the populace. On the contrary, it is just a worthless piece of paper. Get over it.

On the other hand, slagging off degrees is only fun if you can bring something else to the table, but that was exactly the point I was trying to make.

idiotic people who think nothing of world issues or even issues in our own government. Is this wrong? — Lucielle Randall

You cannot do much about your government. However, since there are 200+ of those, as an individual, you can certainly pick the one that disturbs you the least. Hence, I have abandoned the so-called western democracy in which I used to live in search of better pastures, which I confirm to have found in Southeast Asia.

One of the most powerful tools against intrusive regimes that stick their noses into your private life and otherwise none of their business, is simply: JURISDICTION SHOPPING

Businesses do that all the time. If some government wants too much money in some place, then just put up the activity in another place. It works like a charm, and it certainly, duly reins in the arrogance.

Many people in the past fought for rights and liberties — Lucielle Randall

Do you mean the socialist-style labour conflicts of the erstwhile industrial factory-worker society? They were called the proletarians, because all they had was a wife an kids. So, what is the result of all the strife and agitation for their "rights"? Nowadays, they systematically get divorce-raped by the powers that be, and almost never have wife and kids. So far, so good, for the so-called "progress" that they claim to have made. Seriously, I do not particularly want to live in the soviet, factory-worker paradise of the so-called "western democracies". Even places like China, and certainly Vietnam, offer a more pleasant lifestyle than that.

We are becoming livestock for the rich and powerful to prey upon and we are allowing it! Aren't we awake? — Lucielle Randall

The fact that the population is gullible, is not the fault of the rich. The ones who are easily manipulated, will get manipulated. That is just one of the laws of nature.

Is there any possible way to help those in need, and revive us, the younger generation, to become the leaders our world needs? — Lucielle Randall

In the so-called "western democracies"? No, they are addicted to Ritalin, which they use for their imaginary ADHD problems. Furthermore, a great number of them are gender-confused. They simply do not want to make a choice as to whether they are male or female. I may be mistaken, but I somehow believe that all of that won't fly high.

You see, the dirty, little secret is that society is based on a very simple process. Men have 17 times more testosterone in their blood than women. So, men need sex all the time, while women only see it as possibly nice to have, while they can more easily do without. So, the boys need to offer some compensation to make up for that disparity. So, they need to work, make money, and pay these bribes. That is why men put in an inordinate amount of effort in trying to succeed professionally.

If you throw gender confusion into the equation, the entire scheme falls apart. Why would you have to bring home the bacon, when your gender confusion says that you could be both man and woman, or neither? Hence, the society-building efforts will inevitably come crashing down. You can already notice it from the fact that the labour force is disintegrating already. The society as you know it today, will no longer be possible in the future, because there is nobody who will volunteer to keep it afloat. So far so good for these dead-end, so-called "western democracies".

Functional languages are the big thing now and they have monads — fishfry

When I look at the monad page, it says:

With a monad, a programmer can turn a complicated sequence of functions into a succinct pipeline that abstracts away auxiliary data management, control flow, or side-effects.

Now, when I think of succinct pipelines, I think of method calls that return the object itself, such as in:

var p=new Person("John Doe").age(24).height(160).weight(70);

One problem is that programmers who discuss pipelining rarely use categorical language in their discussions. So, I cannot determine if both things are related (monads versus typical pipelining practices).

I also do not really recognize the examples in the monad page. because they are mostly in Haskell, while Haskell is really a specific niche. Mainstream programming does not (yet) include Haskell.

Haskell is only number 49 in the Tiobe popularity index for 2019 with 0.174% usage. I only know one tool in widespread use that was built in Haskell: the pandoc markup format converter; which I certainly use, because in my experience, pandoc is much, much better at gracefully handle lousy input that is full of errors.

Still, I find Haskell code incomprehensible to read. It requires jumping over an enormous hurdle, without any visible payoff. It would be perfectly possible to write pandoc in a language that is more mainstream.

But then again, of the first 35 languages in the tiobe index, I only like 6:

like (c, javascript, php, sql, assembly, lua)

dislike (java, python, c++, c#, vb.net, objC, ruby, matlab, groovy, delphi, vb, go, swift, perl, R, D, sas, pl/sql, dart, abap, f#, logo, rust, scratch, t/sql, cobol, fortran, lisp)

One of the languages I like the best is Bash, ranked only number 48 (0.187%), which surprises me, because the bash shell comes pre-installed with approximately every linux system. So, I suspect that the Tiobe index drastically underestimates its use.

Well, I really don't agree, and I think you misunderstand creativity. Art is not a product of arbitrariness, there are reasons for what the artist does, purpose, so arbitrariness is not the hallmark of creativity. — Metaphysician Undercover

That would almost amount to saying that an artist's design choices are exclusively rational, and could therefore even be expressed in formal language. My own take is that I do not believe that. I believe that artists make use of other mental faculties, that are not rationality, when making their design choices. I also do not believe that it is possible to express, even in natural language, the output of these other mental faculties.

Banach-Tarski paradox — fishfry

The explanations for the Banach-Tarski paradox in the following video are very intuitive:



It really helps understanding the set-theoretical symbol manipulations in the proof. Of course, the section in Wikipedia is called "sketch of the proof" instead of "proof". It is some kind of disclaimer with which they very often label a proof. Maybe they use the disclaimer because the proof is not expressed in strictly and rigorous first-order logic language only? Not sure ...

As a definition? It sure seems so. But definitions in themselves can satisfy themselves insofar as they can consistently reach. It appears you're looking to test the "granularity" of this one to see if it holds "all the way down." And again, as expressed, it seems it must. You need a counterexample, and in terms of the definition, it would have to be something that at the same time both does and does not exist - or so it seems. — tim wood

Agreed. The issue may actually be elsewhere, though. A witness is sometimes a proof and sometimes it isn't. For example, For S1="Oranges exist", showing an orange is a witness that proves S1. For S2="Oranges are juicy", showing an orange that happens to be juicy is not a witness that proves S2. I wanted to confirm my understanding of "witness as proof" by looking at more examples of witnesses.

In another thread, a claim was made that we are entitled to have children. Are we? This is a commonly believed idea, whether stated in these terms or not. But is it well-justified? — petrichor

A killer whale undoubtedly believes that grey whales have every right to have children, because that is what they count on for their lunch: grey whale baby calves.

Nowadays, there is unfortunately no species counting on snatching human babies from their mothers, and who can vouch for the dire need to produce them in as large quantities as possible.

Therefore, what we lack, is the Devil's advocate, i.e. some biological, baby-snatching predator who declares that he sees a real need for our sexual reproduction work. We may solve the problem by letting some lions loose?

I am concerned with the principles of the system, not any installed base, or legacy, these are irrelevant to the acceptability of the principles. I know that you believe axioms are completely arbitrary, making such things very relevant, so join the mob, if you like the "mob rules" philosophy. — Metaphysician Undercover

There is the perennial requirement of consistency, but beyond that, anything flies, really. I am certainly very open-minded in mathematics. The more applications and users for such arbitrary concoction, the more likely that I will end up having a look at it. Arbitrary axioms are the hallmark of creativity! ;-)

No! In very simple terms either your child will hurt or get hurt. You don't want your child to hurt someone. You don't want your child to suffer. Ergo it's unethical to have children. — TheMadFool

From within the perimeter of lowered violence of human society, it is sometimes difficult to imagine how other realities can be so different.

For example, I have recently been watching youtube videos in which killer whales hunt the calves of grey whales. It is fascinating. You can even book a cruise in the gulf of Monterey to watch them doing that. The killer whales start by switching off their sonars, because grey whales can hear sonars from at least a dozen miles away. So, the killer whales start swimming in silent combat formation, until they are very close to a grey whale mother and her calf, who then hears them and will frantically start swimming in the direction of shallow waters to escape the attack, but it may be too late.

For hours, the killer whales will try to separate the mother from her calf, by swimming in between them, or by ramming either of both, until they can start jumping on the calf to push it under and in that way drown it, after which they rip it to pieces. Here is some nice footage of a successful confiscation of a grey whale's calf:



Hence, the congratulatory applause from the bystanders on the boat. Hey, they did it!

Here some other footage, where the killer whales manage to devour another grey whale baby while the mother is taking off. Hence, the remarks, "The mum got away, but the baby they ate. Baby orcas got to eat too! The baby is dead now. They are eating it. Do you see the blood there?"



There are actually quite a few species that specifically hunt the babies of other species. For example, chimpanzees hunt the babies of Colubus monkeys. So, yes, babies of one species are a delicacy for other species. They attack, kill, and eat them with great satisfaction. So, if you have free time, go and watch killer whales eating babies. It may bring you back to the "real world"! ;-)