Yet he has not, by all his experience, acquired any idea or knowledge of the secret power by which the one object produces the other; nor is it, by any process of reasoning, he is engaged to draw this inference. (Hume) — Purple Pond

So, we readily assume causality when "one object produces the other" ...

For wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of Custom. (Hume) — Purple Pond

... but only when it habitually does so.

In other words, when you regularly see two kinds of events following each other, you will start assuming that the first event causes the second.

By employing that word, we pretend not to have given the ultimate reason of such a propensity. — Purple Pond

In fact, we may not know why the cause causes the consequence, but since it does, we (used to) call it "Custom".

If you systematize this empirical approach, you get experimental testing, which is indeed the core knowledge-justification method of science.

What warrant gives Hume the right generalize that all humans and animals possess this induction instinct, past, present, and future? — Purple Pond

(later on) Pavlov's dog:

Classical conditioning (also known as Pavlovian or respondent conditioning) refers to a learning procedure in which a biologically potent stimulus (e.g. food) is paired with a previously neutral stimulus (e.g. a bell). It also refers to the learning process that results from this pairing, through which the neutral stimulus comes to elicit a response (e.g. salivation) that is usually similar to the one elicited by the potent stimulus.

If you repeatedly show to people experiment tests in which a dog will associate ringing a bell, with food (the dog will start salivating), you will condition these people into believing that repeated occurrence of such two events will lead to a learning process in which these two events will be understood/misunderstood to be cause and consequence, i.e. causality.

In the context of Karl Popper's falsificationism, the generalization from a mere sample is permitted. It will not be proof but merely evidence for the causal pairing, until a counterexample is produced somewhere.

We have long ago abandoned verificationism:

Logical positivists within the Vienna Circle recognized quickly that the verifiability criterion was too stringent. Notably, all universal generalizations are empirically unverifiable, such that, under verificationism, vast domains of science and reason, such as scientific hypothesis, would be rendered meaningless.

Pavlov's dog is very reasonable, and the dog's approach is epistemically absolutely sound. Pavlov's dog is a Popperian falsificationist who rejects verificationism, which he undoubtedly dismisses for being an unrealistic requirement, which would prevent him as a dog from learning anything at all.

So I ask: do philosophers agree that Hume is inconsistent in his Enquiry? if not, how do you explain away Hume's supposed inconsistency? — Purple Pond

Hume is not inconsistent. The laws of nature can only be learned by using the laws of learning in nature. Pavlov's dog is not a verificationist who first wants to verify all possible cases. Pavlov's dog is a falsificationist, just like science is.

It's always struck me that there is only one place for those mathematical entities to exist - the mind of God. A belief in Platonic ideals and a belief in God are equivalent. — T Clark

There may be a danger in thinking like that. The core claim in religion, the belief in God, is about the origin of the real, physical world. Religion is not about the origin of the abstract, Platonic world of mathematics. It is about the origin of our true reality.

In my opinion, natural predisposition is the reason why the belief in God, as the creator of the real, physical world, is so prevalent.

A first reason is that we instinctively sense that the universe cannot have existed forever. The mathematical intuition for this is that, since time progresses, it cannot be infinite, because infinite plus a finite amount, is still infinite. Hence, if time were infinite, it would stand still, which it doesn't. Therefore, instinct says that there must be a beginning of times. Furthermore, since everything that exists has a lifecycle, i.e. a beginning and an end, the universe will also come to an end. Hence, our intuition about a Last Day, i.e. the Day of Last Judgement.

You will also find this theory of instinctive acceptance of a Beginning and an End, Alpha and Omega in the religious scriptures, i.e. the Bible and the Quran:

"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.”

It has also been suggested that the religious meaning can be translated into the logical equivalence in philosophy, as Kant's concept of 'ought'. In a mystical context, it can connote intuition or insight and is similar to the Calvinist term "Sensus divinitatis".

The danger in excess Platonicity inside the core of religion, is that we would be repeating views from the notorious Mutazila heresy ( 8th to the 10th centuries).

Excessive rationalization of "fitrah" can lead to far-reaching trouble:

This paradigm is known in Islamic theology as wujub al-nazar, i.e., the obligation to use one's speculative reasoning to attain ontological truths.

A purely Platonic view on God was widespread and known as the "Greek heresy" in the Golden age of Islam:

Harun Nasution in the Muʿtazila and Rational Philosophy, translated in Martin (1997), commented on Muʿtazili extensive use of rationality in the development of their religious views saying: "It is not surprising that opponents of the Muʿtazila often charge the Muʿtazila with the view that humanity does not need revelation, that everything can be known through reason, that there is a conflict between reason and revelation, that they cling to reason and put revelation aside, and even that the Muʿtazila do not believe in revelation. But is it true that the Muʿtazila are of the opinion that everything can be known through reason and therefore that revelation is unnecessary? The writings of the Muʿtazila give exactly the opposite portrait. In their opinion, human reason is not sufficiently powerful to know everything and for this reason humans need revelation in order to reach conclusions concerning what is good and what is bad for them."

The Greek heresy will always end up denying the axiomatic base for religion, i.e. in Kant's lingo, the unexplained (="revealed") categorical imperatives that serve as a starting point for religious law, i.e. morality. As Aristotle nicely said (probably in Metaphysics, Book Gamma), "If nothing is assumed, then nothing can be concluded". Without axiomatic starting point, reason alone becomes an exercise in infinite regress.

Hence, I am against the excessive Platonic rationalization of "fithrah" ("Sensus divinitatis"), i.e. the natural predisposition ("instinct") to believe in God and the Last Day. Rationality is merely a tool and does not encompass every possible mental faculty.

As I said, statistics is not just an empty structure we fill in, it has it's own meanings. — T Clark

Well, my own staunch resistance against incorporating any premature semantics into mathematics, especially en provenance from physics -- which is undoubtedly the greatest culprit in that respect -- is because it could easily make mathematics unusable for application in other disciplines.

Take, for example, a look at Kleene's closure:

In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics it is more commonly known as the free monoid construction.

Kleene's star is the basis of Kleene algebra:

In mathematics, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions.

Like every abstraction in mathematics which is either without value, or else with very high value, this construct is meaningless/nonsensical (=no real-world semantics), useless (=no direct use), lazy (doesn't do much; even as little as possible), and therefore, ultimately ridiculous.

Of course, most such abstractions will turn out to be worthless, but most high-value abstractions are also like that. The formalist philosophy in mathematics warns for that:

According to formalism, mathematical truths are not about numbers and sets and triangles and the like—in fact, they are not "about" anything at all.

The governing rules in mathematics demand that the domain for each variable is properly declared. For example:

∀x∈A={x|x ∈N∧x<10}

When introducing x, you must declare what domain it belongs to. This domain is never the real, physical world. The following is forbidden:

∀ x ∈ real_world

So, if the variable does not belong to the real, physical world, where does it exist? Well, in an abstract, Platonic world that is not the real, physical world.

In other words, the metarules in mathematics staunchly enforce Platonism, even though mathematics is in essence a bureaucracy of formalisms that are not "about" anything at all.

Stephen Kleene originally started writing about his algebra in 1951, in his technical report for the US Airforce, "Representation of Events in Nerve Nets and Finite Automata". It took decades for his work to snowball into the incredible hype that it is today:

Welcome to Regular-Expressions.info.
The Premier website about Regular Expressions.

If you just want to get your feet wet with regular expressions, take a look at the one-page regular expressions quick start.

Do not worry if the above example or the quick start make little sense to you. Any non-trivial regex looks daunting to anybody not familiar with them. But with just a bit of experience, you will soon be able to craft your own regular expressions like you have never done anything else. The free Regular-Expressions.info Tutorial explains everything bit by bit.

If you're hungry for more information on regular expressions after reading this website, there are a variety of books on the subject.

His work has become bigger than life now. There are an incredible number of addicted afficionados who are gurus in the field that Stephen Kleene created. Kleene is truly a grandee.

Note that after practical implementation of Kleene algebra inside a regex engine, it is still not "about" anything at all. Kleene's work would not have taken off, if its purity had been badly tainted from the get-go with real-world semantics en provenance from physics.

Physics is statistics. — T Clark

Other disciplines, unrelated to physics, also successfully use statistics. Hence, physics uses statistics.

It is not that math is useless in and of itself, It is that that there is no such thing as math in and of itself.To think of calculation is to automatically imply a substrate. That is what counting means. To count is always a counting OF something. — Joshs

That is quite an anti-Platonist view. Mathematics deals with counting of not anything in particular. In the abstract, Platonic world of number theory, which is obviously not the real, physical world, there is no need for something to count. Mathematics explores that non-real world.

The "OF something" is simply abstracted away:

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected.

If the "OF something" is still present, then the statement is not part of mathematics but of something else (physics, engineering, and so on ...).

Multiplication, addition ,subtraction, simple counting, these are all specific procedures ,and as such they represent specific semantic meanings, developed through pragmatic interaction with the world at some point in human history. — Joshs

These specific procedures obviously originate from pragmatic interaction with the world. However, the goal of mathematics is to abstract away the real world. Otherwise, without abstracting the real world away, it is not mathematics, but something else. Mathematics adopted its current nature in the first half of the 20th century. Mathematics prior to that, was not exclusively abstract, axiomatic, and algebraic.

The turning point is generally considered to be the year 1905, with the publication of ZFC set theory:

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.

Still, attempts to move to pure abstraction already began earlier, e.g. with Cantor's work on the various infinities. It triggered quite a bit of resistance:

Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive – even shocking – that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections.

Nowadays, Cantor's work is considered uncontroversial. Mathematics is pure abstraction anyway. Mathematics has nothing to do with the real, physical world anyway. Therefore, extensive symbol manipulation (algebra) of infinities, with associated rules, has become a non-issue.

What is math about then, if not quantities? — creativesoul

On the one side, I do subscribe to formalism:

Formalism holds that mathematical statements may be thought of as statements about the consequences of certain string manipulation rules. For example, in the "game" of Euclidean geometry (which is seen as consisting of some strings called "axioms", and some "rules of inference" to generate new strings from given ones), one can prove that the Pythagorean theorem holds (that is, one can generate the string corresponding to the Pythagorean theorem). According to formalism, mathematical truths are not about numbers and sets and triangles and the like—in fact, they are not "about" anything at all.

but I am intuitively also attracted to Platonism:

A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.

The true nature of mathematics is still up in the air:

It is a profound puzzle that on the one hand mathematical truths seem to have a compelling inevitability, but on the other hand the source of their "truthfulness" remains elusive. Investigations into this issue are known as the foundations of mathematics program.

Philosophy of mathematics today proceeds along several different lines of inquiry, by philosophers of mathematics, logicians, and mathematicians, and there are many schools of thought on the subject.

I tend to view mathematics with a mix of both formalism and Platonism.

Math is an attempt to contain meaning within value. — Possibility

Math is not about quantities, or numbers, and in that sense, not about values. Only number theory is.

Furthermore, number theory is, in and of itself, a relatively weak axiomatization which is certainly not Turing complete. Numbers do naturally reappear inside any axiomatization that actually is effectively Turing complete, such as set theory (zfc), lambda calculus, combinator calculus, and so on.

So, if "value" means "quantity" or "number", then no, because it is not an essential building brick in math.

It declares itself ‘meaningless’ in order to maintain the illusion that there is no meaning outside of value — Possibility

Math is "meaningless", i.e. devoid of semantics, because it only seeks to deal with syntax, i.e. the bureaucracy of formalisms that govern the abstract, Platonic world of mathematics.

Furthermore, math only supports knowledge, i.e. justified beliefs, while knowledge is just one limited mental tool. Knowledge cannot possible be an essential or the primary ingredient in the discovery of new knowledge, because otherwise humanity would either have no knowledge at all, or else, have discovered all possible knowledge already.

What's more, not all knowledge can be expressed in language and objectively shared. Michael Polanyi already pointed out the existence of tacit knowledge.

Furthermore, we have no guarantee that our existing list of standard academic knowledge-justification methods is complete: axiomatic, scientific, historical, and epistemic. There could be other epistemic domains generated by their own associated method. Who says that we are successfully operating in all possible epistemic domains?

What's more, not all epistemic domains apply mathematics as a tool. For example, the historical method does not rest on numbers. In fact, it does not seem to involve any mathematics at all.

Yes, in order to make use of meaning in the universe we value, we must eventually position it in relation to value - but it doesn’t follow that there is no meaning outside of value. — Possibility

In fact, mathematics does not tell any of the applied, real-world disciplines that happen to use it, how exactly they should define semantics. To that effect, math would actually have to deal with semantics, i.e. meaning, which it obviously doesn't. These applied disciplines can only use mathematics to maintain consistency in their own semantics-heavy statements. They cannot use mathematics as a source of semantics/meaning, because mathematics refuses to supply that ingredient.

Neither does it follow that we cannot make use of that meaning. — Possibility

You can use real-world oriented disciplines for the purpose of dealing with meaning, but even these disciplines are not the exclusive source of meaning.

I was just pointing out that not all knowledge is meant to provide meaning. In Immanuel Kant's lingo, synthetic statements a priori, such as mathematics, are not providers of meaning, and even actively avoid providing meaning.

It's true that mathematics abstracts away meaningful content but it does does so in order to arrive at meaningfully useful tools. — Joshs

The application of math in the real world is itself not math but always something else, such as physics, engineering, and so on.

Math supplies a bureaucracy of formalisms that will help maintaining consistency in these other fields. It is these other fields that are (possibly) real-world meaningful and useful.

For math, being meaningful, i.e. semantically rich, would only detract from that goal. Being directly useful would also detract from that goal.

In other words, the applicability of math would be badly impaired if it sought to be directly meaningful or useful. Math is necessarily, in and of itself, meaningless and useless, in order to maximally relegate these characteristics to its real-world application.

Your unnamed authority agrees that math is a science. Games are not sciences. Being a science (an organized body of knowledge) means that math is an understanding of reality. — Dfpolis

This unnamed authority was David Hilbert:

It has been claimed that formalists, such as David Hilbert (1862–1943), hold that mathematics is only a language and a series of games. Indeed, he used the words "formula game" in his 1927 response to L. E. J. Brouwer's criticisms: "And to what extent has the formula game thus made possible been successful? This formula game enables us to express the entire thought-content of the science of mathematics in a uniform manner and develop it..."

This letter predates Karl Popper's "Science as Falsification" by almost half a century. The dust hadn't settled yet on the impossibility of verificationism. Certainly the Circle of Vienna still happily amalgamated mathematics and science.

The other objections to David Hilbert's view came from Hermann Weyl: What "truth" or objectivity can be ascribed to this theoretic construction of the world ...

This view makes the applicability of math to nature entirely accidental. If you think about it, you'll see that you can't construct such an isomorphism unless the relevant mathematical relations are already instantiated in nature -- and we can understand that they are. But, if they are already instantiated and intelligible, both Platonism and formalism are wrong. — Dfpolis

Consistency is indeed assumed to be already instantiated in nature. The existence of consistency makes particular things impossible. These impossibilities give inescapable structure to nature. That is in my impression the core of the esoteric link between nature and mathematics. The structure visible in the Platonic world of math will therefore tend to be also visible in the real, physical world.

I personally refute neither Platonism nor formalism (Hilbert). They are a dual view on the abstract, Platonic objects versus the structures that constrain them in math.

Most computer programmers have degrees from universities — Hanover

Do Developers Need College Degrees?

Our 2016 Developer Survey found that 56% of developers in fact do not have a college degree in computer science or related fields. The most popular way for developers to learn is by “self-teaching” in some way (69% of respondents told us they were at least partially self-taught; 13% said they were entirely self-taught).

Of the 4,499 jobs currently listed at Stack Overflow Jobs (across all regions), a Boolean search for “degree OR bachelor OR BS OR BA OR B.S. OR B.A.” yielded 1,760 matches. So we can extrapolate that 2,739 listings, or 61%, do not specify a “degree” or a “bachelor’s” as one of the requirements, and 39% list a degree somewhere in the job posting, either as a requirement or as a preference.

Does this mean you have over 50% more opportunities to get a job as a developer if you have a college degree? Not necessarily. Nick stresses that the ability to demonstrate what you can do and what you have done will always be more important than whether or not you have a degree, even in cases where the company has listed a degree as a requirement.

Smart recruiters know that the people who love programming wrote a database for their dentist in 8th grade, and taught at computer camp for three summers before college, and built the content management system for the campus newspaper, and had summer internships at software companies. That’s what they’re looking for on your resume.

A programmer does not need a degree for the same reason a welder doesn't.

there are also schools that teach music. — Hanover

Take the top 100 grossing artists in music. Check how many have studied at a music school.

Zero?

That has always been like that. Vivaldi, "il prete rosso", was a priest, moonlighting as a music composer.

The longer the software field will exist, the fewer programmers will bother getting a degree.

That you find it easier to self teach says something about you, not about the world generally. — Hanover

I still seem to have a Stackoverflow Developer Survey backing me up. I am quite confident that Github would come up with similar results, if they haven't already.

It also sounds like you struggled in school, although maybe you didn't, but that's what it sounds like. — Hanover

Well, probably not enough. Look at where everybody is going, and then, seriously, go elsewhere.

You see, when you ask a teenage girl why she is wearing her choice of clothes, she will most likely answer: "Because all my friends are wearing them too." If all these teenage girls give the same answer, we would end up in a situation of circularity or of infinite regress. So, that is not possible. Hence, there are original sources of manipulation, talking these teenage girls into wearing what they are wearing.

The general populace is not better than teenage girls.

The schools try to manipulate their students into a particular direction, and that has only gotten worse since I graduated.

For example, why do young women prefer "bad boys"? In my impression, they prefer school drop outs because these "bad boys" have escaped the rampant feminization of boys in schools and are still much more naturally male.

If you look at men in their twenties nowadays, a lot of them tend to be "involuntary celibate", i.e. their female peers do not wish to deal with these over-feminized and effeminate individuals, apparently over 80% of the lot. This problem did not exist when I was in my twenties.

In the meanwhile, the school system is gradually destroying the sexual reproduction process in the West.

The uncritical belief in the schools will destroy the false believers and their offspring in the 7th generation. The ancient scriptures already warned for that problem. Their false gods will gradually turn on them, and then devour them, by eating their flesh and drinking their blood.

"Verify" is no more common or uncommon than "falsify". :chin: :chin: :chin: — Pattern-chaser

Ok. Point conceded. The verificationists, i.e. the Logical positivists within the Vienna Circle, have managed to taint the term so badly that it now carries too much baggage:

It was unified by the aim of making philosophy scientific with the help of modern logic.

They were obviously deeply mired in the heresy of scientism and clearly beyond salvation ...

I'm guessing some useless graduate programs those computers. — Hanover

When I was 14 years old, somewhere in the 80ies, my father came home with a second-hand Apple IIe computer, which had two floppy drives but no hard disk, along with a photocopy of a Borland Turbo Pascal manual, in a language that I could barely read, i.e. English.

So, a few months later, I wrote my first, utmost useless program in Pascal, which is one of the worst languages to program in, but that is something I did not know back then.

The teachers at my high school could not use a computer, because none of them had one, let alone, write programs. That last bit is still the case today. High-school teachers still cannot write programs.

Programming is not knowledge. It revolves around the discovery of new knowledge.

If existing knowledge were the sole or most important ingredient in the process of discovering new knowledge, then first of all, humanity would never have discovered any knowledge at all, and secondly, we would by now have discovered all possible knowledge already.

Hence, programming is an aptitude similar to composing music. It is not possible to "teach" it. Either you manage to figure it out by yourself, or else, you will never be able to do it. That is why most programmers cannot program.

I was incredulous when I read this observation from Reginald Braithwaite: Like me, the author is having trouble with the fact that 199 out of 200 applicants for every programming job can't write code at all. I repeat: they can't write any code whatsoever.

Being good at memorizing useless information or at carrying out tedious procedures does not attract people who like discovering new knowledge. Therefore, talented individuals will tend to score badly at high-school and university tests. I was personally only good at mathematics. I was horrible at probably every other subject. Since the system grudgingly allowed me to filter pretty much everything else away, I still did quite well.

Good programmers, just like good welders, tend to come from outside the education system. Being good at any real-world skill is not particularly so compatible with being good at school; and the reverse also tends to be true.

How were you able to transcend your useless education and gain such wisdom? — Hanover

I find the term "wisdom" quite impredicative. What exactly does it mean? Not a "justified (true) belief", I hope, because we use that elsewhere already! ;-)

Did I gain something ineffable? Well, the answer to that question is obviously also ineffable!

I learned much more from drilling down in Wikipedia over the last 15 years than I ever did at university, which never contributed anything, actually.

In Wikipedia, you can always find the original publications mentioned in the foot notes. Still, I only click on what I am interested in. So, there are always topics that I just totally skipped, because at that point they were of no importance to me.

At the moment, I am completely stuck in the proof for the Curry-Howard correspondence, which I would like to fully grasp, but I am too lazy to first figure out Hilbert Calculi.

It is not the first time that Hilbert's work in logic is a blocking factor. Every time I try to figure out the late Voevodsky's univalence axiomatization (homotopy type theory, aka HoTT), I get stuck again in Hilbert Calculi.

David Hilbert was undoubtedly a genius, but his work is simply unreadable ...

I'm btw happy with pragmatism: usefulness is far more important than we typically think. — ssu

The term "usefulness" is quite controversial in mathematics. I tend to agree with Hardy on the matter:

I have never done anything "useful". No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.

We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not.

As I see it, and in line with what Hardy said, while the low-hanging fruit is almost immediately useful, but only moderately so, the real game changers may take even centuries to find their way into applications. That is why it is necessary to abstract away "usefulness" when exploring the abstract, Platonic world of mathematics for new discoveries.

That doesn't describe my educational experience. If you were educated in Europe, how do you know what my experience was in the US? — Hanover

I can perfectly see how you were tested for your academic attainment. I just need to take a look at the multiple-choice questions you were supposed to answer. That says it all.

No they're not. — Hanover

They were trained on memorizing useless information. We have photocopiers for that job. Cheaper and better. They were trained on executing tedious procedures. We have computers for that job. Cheaper and better. So, what do we need them for, huh?

What sorts of things are meaningful? How do these things become meaningful? To whom are these things meaningful? These are all reasonable important questions to ask. We can look towards actual everyday events and find plenty of good answers. — creativesoul

Meaning, i.e. semantics, are not always a useful goal.

The best part of advanced mathematics and metamathematics is about removing all possible meaning from an abstraction while only leaving structure, i.e. a bureaucracy of formalisms to apply to a preferably meaningless symbol stream.

The flagship of mathematics is general abstract nonsense.

In mathematics, abstract nonsense, general abstract nonsense, generalized abstract nonsense, and general nonsense are terms used by mathematicians to describe abstract methods related to category theory and homological algebra. More generally, “abstract nonsense” may refer to a proof that relies on category-theoretic methods, or even to the study of category theory itself.

In other words, the presence of meaning, i.e. any possible reference to real-world semantics, is considered to be a bug, an error, and a serious defect in higher mathematics. It needs to be corrected by applying additional operations of further abstraction:

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. Two of the most highly abstract areas of modern mathematics are category theory and model theory.

Every time I see an attempt to attach meaning, i.e. semantics, I shiver, because we should be doing exactly the opposite of that. Full abstraction can only be reached when the expressions in language have become completely meaningless. If they still mean something, then there is something wrong, which then needs to be corrected.

I’m curious to hear what members perceive as differences in our educational systems. — halo

I was educated in Europe. The short answer: there is probably no difference worthwhile mentioning.

The core of an education system revolves around how it tests student achievement. Everything always follows from there: curriculum design, teaching and learning, infrastructure support, staffing, and so on. Hence, you only need to look at how the system examines student achievement to understand its fundamental nature.

Both systems test the student on their ability to memorize useless information and moderately also on their capacity to execute tedious procedures. Hence, it favours those personalities that have acquired the strongest resistance against boredom and which have the strongest inclination to slavish orthodoxy.

An education system is never, ever more useful than the behaviour that its evaluation procedures encourage.

The reason why graduates from both systems are increasingly considered by future employers to be utterly useless and utmost inept individuals, is because they were specifically trained to excel in uselessness and ineptitude. That is why they successfully graduate with such good grades in the first place.

A secondary source is not a citation from Aristotle. — Dfpolis

Well, if Aristotle said this -- I guess he did, and there are other links who say that he did -- he will most likely have done that somewhere in 'Metaphysics', probably, book gamma; but it could also be in 'Posterior Analytics'. So, if someone feels like scanning the text ...

While he says we cannot deduce everything, he is convinced that we can justify axioms non-deductively and does so in a number of instances. — Dfpolis

Can you give an example of where Aristotle does that?

Yet that world view is taught in schools as if it was fact, as if it was more certain than other world views. Science has become the religion of the modern age. — leo

It may be your kids, but that does not mean that you have a say in what the ruling elite's indoctrination machine will teach them. The populace gave up that right when they implicitly agreed to compulsory schooling schemes in State-run indoctrination factories, to be paid by extracting the money upfront out of the parents' wallets.

The current type of government naturally emerges out of the population's take on what government is supposed to be. If the population believes that the government should have wide-ranging power to coerce other people, that is exactly what will emerge out of the fray.

By catering to the populace's false belief in scientism, the ruling elite successfully manages to transfer even more authority from the family to themselves.

In my opinion, the population in the West consists of the dumbest idiots that have ever walked the face of the earth.

I think that that is wrong. Not all belief has propositional content. — creativesoul

Not all belief has propositional content, but all knowledge does.

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

In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules. A central idea of formalism "is that mathematics is not a body of propositions representing an abstract sector of reality, but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess." According to formalism, the truths expressed in logic and mathematics are not about numbers, sets, or triangles or any other contensive subject matter — in fact, they aren't "about" anything at all. Rather, mathematical statements are syntactic forms whose shapes and locations have no meaning unless they are given an interpretation (or semantics).

There may be an esoteric link between the abstract, Platonic world of mathematics and the real, physical world, but this hypothetical link cannot be used for any practical purpose.

It has been claimed that formalists, such as David Hilbert (1862–1943), hold that mathematics is only a language and a series of games. Indeed, he used the words "formula game" in his 1927 response to L. E. J. Brouwer's criticisms:

And to what extent has the formula game thus made possible been successful? This formula game enables us to express the entire thought-content of the science of mathematics in a uniform manner and develop it in such a way that, at the same time, the interconnections between the individual propositions and facts become clear ... The formula game that Brouwer so deprecates has, besides its mathematical value, an important general philosophical significance. For this formula game is carried out according to certain definite rules, in which the technique of our thinking is expressed. These rules form a closed system that can be discovered and definitively stated.

We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules. Rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise.

Hermann Weyl to David Hilbert:

What "truth" or objectivity can be ascribed to this theoretic construction of the world, which presses far beyond the given, is a profound philosophical problem. It is closely connected with the further question: what impels us to take as a basis precisely the particular axiom system developed by Hilbert? Consistency is indeed a necessary but not a sufficient condition. For the time being we probably cannot answer this question ...

My own opinion is that mathematics is a bureaucracy of formalisms that seeks to maintain consistency in its own symbol streams.

Mathematics is consistent by design while the real, physical world is consistent by assumption. Therefore, it is sometimes possible to construct consistency isomorphisms between both, that will be uncannily effective in mirroring some sector of reality inside an abstract, Platonic model. Physics is a heavy user of that principle.

they're talking about identifying dark matter through particle physics — leo

They are trying to do that, but this approach has not succeeded until now.

Wikipedia articles are not neutral reports of original research written by researchers. — leo

There is the Wikipedia no original research and neutral point of view policies and then there are the practical results visible in their pages.

If you detect a violation of these policies, you can report them to the editors in the "talk" metapage for the page.

By that they mean the existence of matter, not the mere existence of a "calculated excess amount of gravitation". — leo

The research paper clearly underlines that they have not been able to identify what kind of particle it would consist of. If it is matter, then there is a requirement to disclose that. This has not been possible at this point. Therefore, the phenomenon is only matter-like; assuming the standard model in which it is matter that causes gravitation. Note that this is yet another hypothesis that cannot be tested experimentally.

Popper introduced the criterion of falsification because he believed that theories cannot be verified in any way (neither in the 'strong' nor 'weak' sense), because of the problem of induction. — leo

The term "verify" is common language, and therefore, highly ambiguous. In my opinion, it is not suitable as a technical term.

Outside the very narrow context of verificationism, it means probabilistic sampling for counterexamples, with no pretension that it would constitute full or fail-safe proof. Therefore, "experimentally testing" is a suitable synonym for "verifying" in the context of falsificationism.

As an example, again, observations that didn't fit the predictions of the theory of general relativity didn't falsify that theory, because an invisible matter was invoked to make up for the difference, and it's always possible to do that. If an observation doesn't match the theory, invoke some invisible phenomenon, and the theory is not falsified. Which makes the criterion of falsification flawed just like the others. — leo

Yes, but "invisible matter" is still a cutting-edge research topic in search for more concrete results.

Citation? — Dfpolis

I have found a reference here:

Aristotle also popularized the use of axioms (self-evident principles requiring no proof), claiming that nothing can be deduced if nothing is assumed.

Unfortunately, it does not say in which one of Aristotle's books he writes this. I suspect that it must be 'Metaphysics', but I am not sure about that.

Predictive modelling is what science is about, making accurate predictions from past observations. If you exclude predictive modelling from science you remove pretty much everything from science. — leo

In my opinion, mere predictive modelling without establishing causality should not be counted as science. Only observations en provenance from controlled experimental testing may be used in science:

A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable. This increases the reliability of the results, often through a comparison between control measurements and the other measurements. Scientific controls are a part of the scientific method.

if all controls work as expected, it is possible to conclude that the experiment works as intended, and that results are due to the effect of the tested variable.

He said that theories cannot be verified. — leo

Karl Popper said that theories cannot be verified under Carnap's thesis. That means 'strong' verification, i.e. full inclusive proof, and not 'weak' verification, i.e. probabilistic experimental testing, which is obviously possible. You are digging up an old debate in which Karl Popper participated and that is no longer active. Verificationism and its vocabulary are dead now, and completely replaced by falsificationism.

What you call "demonstrating causality" is predictive modelling just as well, it is assuming that the apparent causality will keep being valid in the future. — leo

It is about the requirement for scientific controls:

Scientific controls are a part of the scientific method. Ideally, all variables in an experiment are controlled (accounted for by the control measurements) and none are uncontrolled. In such an experiment, if all controls work as expected, it is possible to conclude that the experiment works as intended, and that results are due to the effect of the tested variable.

Without these controls, you will get snake oil vendors phishing for naturally occurring but meaningless correlations in "big data". So, it is about putting a stop to the practice of calling this type of activity "data science", because in absence of there being some causality between variables, it is in my opinion not science.

They should rename "data science" to "correlation phishing".

Saying that some models are not "science" just because you don't like them is what scientists do already, calling 'scientific' the models they like and 'unscientific' the ones they don't. — leo

It is not about any personal preference ("because you don't like them"), but about what Nassim Taleb also complained about:

big data means anyone can find fake statistical relationships, since the spurious rises to the surface.

Clearly, many mathematicians are concerned the justifying their axioms. I am also concerned about this issue. You seem not to be. So, we do not share a common interest. — Dfpolis

If you justify the axioms, then the justifications will become the new axioms. Your strategy simply leads to infinite regress. That is why the axiomatic method does not allow this. As Aristotle wrote: If nothing is assumed, nothing can be concluded.

You are attacking Platonism, which I do not hold. — Dfpolis

I subscribe to mathematical Platonism. However, for practical reasons, I do not make use of the possible link between the real, physical world and the abstract, Platonic world of mathematics. I rather leave this link unspecified. In fact, so does everybody else.

So there is no point in our continuing to dialogue on this topic. — Dfpolis

Well, in that case, don't.

https://arxiv.org/abs/1201.3942 : From astronomical observations, we know that dark matter exists — leo

From astronomical observations, we know that dark matter exists, makes up 23% of the mass budget of the Universe, clusters strongly to form the load-bearing frame of structure for galaxy formation, and hardly interacts with ordinary matter except gravitationally. However, this information is not enough to identify the particle specie(s) that make up dark matter. As such, the problem of determining the identity of dark matter has largely shifted to the fields of astroparticle and particle physics. In this talk, I will review the current status of the search for the nature of dark matter.

Given the absence of detections in those experiments, I will advocate a return of the problem of dark-matter identification to astronomy,

"Dark Matter" means "calculated excess amount of gravitation in current model of universe". This calculated excess "exists" in a sense that you can observe total gravitation and calculate the excess part.

Go tell them that Wikipedia is a more reputable source. — leo

Wikipedia does not contain original research. It is supposed to only refer to externally-published research. Do you have any reason to believe that they are guilty of original research concerning dark matter?

What reputable source do you have to show that if the 'input' of the test cannot be chosen freely then it isn't an experiment? — leo

A controlled science experiment is setup to test whether a variable has a direct causal relationship on another.

Identify your independent and dependent variables. The independent variable is commonly known as the cause, while the dependent variable is the effect. For example, in the statement A causes B, A is the independent variable and B is the dependent. A controlled scientific experiment can only measure one variable at a time. If more than one variable is manipulated, it is impossible to say for certain which caused the end result and the experiment is invalidated.

And I argued extensively how the criterion of reproducibility is not applied consistently by scientists, but you're just ignoring that. — leo

It is a well-known problem that quite a bit of published research is in fact not reproducible. Well, quite a bit of that research is undoubtedly deemed so uninteresting by others that nobody even tries.

What you are doing is applying your own definition and own criteria of what science is and what it isn't, — leo

I think I actually made it clear what my possibly original idea is: to only consider theories backed by controlled experiments only, and no longer consider mere predictive modelling, to be science.

and scientists mostly disagree with your criteria — leo

Up till now, it is only you who seems to disagree. I do not believe that anybody else has ever looked into the matter.

https://en.wikipedia.org/wiki/Verificationism
Popper regarded scientific hypotheses to be unverifiable — leo

The full quote is:

Popper regarded scientific hypotheses to be unverifiable, as well as not "confirmable" under Carnap's thesis.

Types of verification
Ayer distinguishes between ‘strong’ and ‘weak’ verification, noting that there is a limit to how conclusively a proposition can be verified. ‘Strong’ (fully conclusive) verification is not possible for any empirical proposition, because the validity of any proposition always depends upon further experience. ‘Weak’ (probable) verification, on the other hand, is possible for any empirical proposition.

To verify under Carnap's thesis means 'strong' verification, which means 'proof' in proof theory, while 'weak' verification means experimental testing. By the way, Carnap later on abandoned verificationism and the requirement of 'strong' verification:

In 1936, Carnap sought a switch from verification to confirmation. Carnap's confirmability criterion (confirmationism) would not require conclusive verification (thus accommodating for universal generalizations) but allow for partial testability to establish "degrees of confirmation" on a probabilistic basis. Carnap never succeeded in formalizing his thesis despite employing abundant logical and mathematical tools for this purpose. In all of Carnap's formulations, a universal law's degree of confirmation is zero.

In the context of verificationism, it is needed to clarify if "to verify" is meant as "strong" or "weak". Furthermore, I do not believe that the verificationist vocabulary is still in use.

Verificationism has been replaced a long time ago by falsificationism:

Karl Popper's The Logic of Scientific Discovery proposed falsificationism as a criterion under which scientific hypothesis would be tenable. Falsificationism would allow hypotheses expressed as universal generalizations, such as "all swans are white", to be provisionally true until falsified by evidence, in contrast to verificationism under which they would be disqualified immediately as meaningless.

Deductions are only sound if the premises are true and the logic valid. According to you, no mathematical proposition is true. — Dfpolis

If you are only going to repeat you faith claims, and not try to justify them there is no point in posting on a philosophy forum. — Dfpolis

The page in Britannica is good starting point to answer your objections:

Axiomatic method, in logic, a procedure by which an entire system (e.g., a science) is generated in accordance with specified rules by logical deduction from certain basic propositions (axioms or postulates), which in turn are constructed from a few terms taken as primitive. These terms and axioms may either be arbitrarily defined and constructed or else be conceived according to a model in which some intuitive warrant for their truth is felt to exist.

In my opinion, the premises in mathematics should be thought of as arbitrarily defined. Axioms are indeed not correspondence-theory "true":

In epistemology, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.

The possibility that these premises would be conceived according to a model in which some intuitive warrant for their truth is felt to exist harks back to the core philosophy of mathematics, which is Platonism.

In Plato's Theory of Forms, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations.

Just like in Plato's Allegory of the Cave, there may indeed be some further unspecified link between both the real, physical worlds and the abstract, Platonic world of mathematics.

I am not necessarily opposed to this view, but I think that it is, for all practical purposes, unusable.

This unspecified link is certainly not correspondence-theory "true". Therefore, for all practical purposes, it is safer to consider mathematical axioms to be arbitrarily defined, rather than somehow esoterically linked to the real, physical world.

So, yes, I maintain my position that axioms are not correspondence-theory "true".

The dominant philosophy in mathematics is Platonism, and most mathematicians subscribe to it:

A major question considered in mathematical Platonism is: Precisely where and how do the mathematical entities exist, and how do we know about them? Is there a world, completely separate from our physical one, that is occupied by the mathematical entities? How can we gain access to this separate world and discover truths about the entities? One proposed answer is the Ultimate Ensemble, a theory that postulates that all structures that exist mathematically also exist physically in their own universe.

The reason why you criticize this view is because you are not a mathematician while you insist that mathematicians should think about mathematics like you do, i.e. as some kind of theory that is isomorphic with the real, physical world. Your views are completely rejected in mainstream mathematics. It is not me who would be "repeating faith claims", but it is you who are deeply mired in your false, pagan beliefs and other heresies.

... but that ought to be self-correcting. — T Clark

These people have already invaded the academia.

Examples from the link:

University of California, Berkeley
University of Denver
Syracuse University
Southern Methodist University
University of Dayton
American University
Pepperdine University
...

They are happily busy invading the corporations and the government bureaucracies, while in the meanwhile they have a vested interest in making sure that their expensive diplomas in concocting snake oil are not being criticized.

So, they will need to invade the mainstream media too, who are spectacularly proficient at black mouthing every opinion that does not suit them. They will seek to grab co-control over the social media too. That also seems to have become much easier than it used to be.

There are already way too many "forbidden" opinions.

Sooner or later, criticism on "data science" and similar practices, is simply going to become one more thing that you are no longer allowed to say.

That gang of pseudo-scientists, one of the so many, is gradually going to become one more guild of liars, manipulators, and deceivers that are above all the rules. They badly need protection against criticism, and read my lips, they will make sure to get it.

But you go ahead and act like it is knowledge that science will never be able to take a position on God. — Coben

The (Abrahamic) theological argument is that God does not have a physical incarnation.

Therefore, anything that has a physical incarnation cannot be the creator of the heavens and the earth.

Hence, yes, I maintain my position that the epistemic domain of science, which requires physical observation, cannot take a position on the matter.

But since your defense of your deduction here is mere repetition of your opinion without addressing my points, consider the possibility you are just speculating wildly. — Coben

Which point did I not address? In my opinion, we should simply agree to disagree.

I would say that, if I can generate predictions of the behavior of complex systems on a consistent basis, i.e. significantly better than chance, I have applied a method that models the actual real-world conditions that lead to that behavior. — T Clark

In "Beware the Big Errors of 'Big Data'", Nassim Taleb creates a beautiful visual representation of the problem:

We’re more fooled by noise than ever before, and it’s because of a nasty phenomenon called “big data.” With big data, researchers have brought cherry-picking to an industrial level. Modernity provides too many variables, but too little data per variable. So the spurious relationships grow much, much faster than real information. In other words: Big data may mean more information, but it also means more false information.

big data means anyone can find fake statistical relationships, since the spurious rises to the surface. This is because in large data sets, large deviations are vastly more attributable to variance (or noise) than to information (or signal). It’s a property of sampling: In real life there is no cherry-picking, but on the researcher’s computer, there is. Large deviations are likely to be bogus.

We used to have protections in place for this kind of thing, but big data makes spurious claims even more tempting. And fewer and fewer papers today have results that replicate.

"F = ma" is a model. — T Clark

Yes, but in "F = ma" there is at least an attempt at establishing causality. Newton was not merely "phishing".

No. The theory that you feed your input into is a model just as much as the technical analysis of stock markets you decry. — T Clark

Well, Nassim Taleb also concludes that only data en provenance from experimental testing should be taken seriously:

In observational studies, statistical relationships are examined on the researcher’s computer. In double-blind cohort experiments, however, information is extracted in a way that mimics real life. The former produces all manner of results that tend to be spurious (as last computed by John Ioannidis) more than eight times out of 10.

Although no one has mentioned it, I keep waiting for the other shoe to drop - using your argument to undermine the credibility of climate science. — T Clark

No, no. Climate science is way too political for me. Seriously, I don't want to talk about that debate and I refuse to take a position.

If it works, they're not charlatans. — T Clark

The amount of cherry picking in spurious correlations has now turned into a problem bigger than life. I don't think that we can keep denying the problem. Seriously, it is now absolutely running out of control. We cannot keep going on like this. The correlations are there. So, it seemingly works, but it is also totally fake.

I doubt they care whether you are willing to designate what they do as science. — T Clark

But the charlatans certainly care. There is a reason why they have renamed "big data" to "data science". They want the credibility associated to the "science" part. They are hell bent on further fooling a demographic already badly afflicted with rampant scientism.

Seriously, predictive power by using spurious correlations cannot be considered enough to give their concoctions any kind of serious status. What they are doing, is just alchemy!

I think the comparison with stock market pricing is completely unjustified. The predictive capacities of physics are an essential part of the science. — Wayfarer

Agreed, but charlatans, such as the ones in the stock market, must not be able to repurpose that capacity to claim scientific status. Most physics is obviously beyond reproach.

At the very small scale, there are epistemic problems in physics, but that was inevitable. The very concept of light, observation, quantum nature of energy differences, and so on, will simply start interfering with practices that we otherwise take for granted at a larger scale.

Paul Dirac predicted the discovery of anti-matter on the basis of mathematical symmetries. I can’t see any justification for declaring his work non-scientific. And how else are you to validate the accuracy of physical theory but testing it against observation? ‘Oh, that looks like it ought to be right.’ — Wayfarer

Since his original hypothesis was successfully, experimentally tested, there are clearly no objections to his theory. It is not physics that generally requires scrutiny.

Those opposing dismiss these criticisms by describing their proponents as ‘the Popperazi’, saying that their conservatism is stifling progress. — Wayfarer

There is a whole world outside physics that will happily make use of any relaxation of epistemic constraints in science to claim scientific status for their snake oil. Outside physics, there is an entire reservoir of claims of a very deceptive nature waiting exactly for that.

So I think your definition of scientific method is far too restrictive. — Wayfarer

Have you had a look of what is out there, claiming scientific status? Take as an example the monstrosity of "data science":

Data science is a multi-disciplinary field that uses scientific methods, processes, algorithms and systems to extract knowledge and insights from structured and unstructured data. Data science is the same concept as data mining and big data.

If you unleash something like the ordinary least squares method on approximately any collection of (x,y) tuples, you will almost always find some correlation that will give the resulting prediction function some or more predictive power. These people can then trivially defend their concoction by occasionally, correctly predicting a future (x,y) tuple. Even a broken clock gives the time correctly twice a day. So, moderate predictive power does not mean anything. Still, these people increasingly boast about their "data science" craft.

Their alchemy is widespread now. Just take a look at the articles "4 Reasons Not To Get That Masters In Data Science" or "Best 23 Schools with Data Science Master’s Programs".

Isn't it obvious that the barbarians really are at the gates by calling themselves "data scientists"?

They obviously want to repurpose the populace's false pagan belief in scientism -- which gives the term "science" excessive credibility anyway -- for their own nefarious and self-serving ambitions. With an overly permissive definition for the epistemic domain of science, we are giving these people the ammunition to wholesale manipulate and deceive.

Therefore, there is an urgent need to further restrict the epistemic domain of science by expelling any approach, and also any theory, that merely has predictive power, and which cannot be tested experimentally, by freely varying the input variables of the experiment.

https://www.scientificamerican.com/article/is-dark-matter-theory-or/ — Coben

Yes, but just the title sounds already impossibly inept: "Is dark matter theory or fact?" I am not even going to read it. Furthermore, this article is not an experimental test report. Hence, it engages in "original research" without backing every word they say with experimental test reports. These people are simply not serious.

I do not deny (or confirm) that there is unexplained, excess gravitation that can be observed through its effects on observable matter. I do not deny that it could be interesting to design experiments that would further shed light on the problem. In the meanwhile, however, we must considered any explanation for this "calculated excess gravity" to be hypothetical.

Further research could even discover that there is actually something wrong with existing calculation rules. Why not?

I can't see how we can rule out that this would never be the case with a deity. — Coben

According to Abrahamic religious rules, God has no physical incarnation. Therefore, God cannot be tracked down by conducting a search for his physical presence. Hence, the scientific method cannot possibly apply. Furthermore, I personally see no value in furthering that kind of heresies.

But they have interventionist gods, with interventions with physical effects. They also have communicative gods. Both these phenomena, should they be real, could potentially be tracked by scientific research. — Coben

This would only be possible if God deterministically responded to a particular input with the same output. In that case, it would be a function. If you feed input I to God, the effect will be output O, i.e. O=f(I).

In that case, God would be a deterministic device.

Scientists, not just journalists, take as real things that have not been directly confirmed — Coben

A scientist is the author of an experimental test report in which he fed input I and received output O. If he did not receive output O, then his experiment has failed. If this person then still considers the hypothesis to be scientifically justified, then he is simply not a scientist.

The scientific method simply does not allow for claiming that a theory is justified in absence of successful experimental testing.

They draw conclusions about what happens inside Black Holes due to relativity, since this holds in other places. — Coben

Black-hole conjectures have never been tested experimentally. At best, they belong to the epistemic domain of predictive modelling and not to science.

Most astrophysicists believe in dark matter and energy because the effects have been observed. — Coben

Astrophysics is also just predictive modelling and not science. It is simply not possible to back their hypotheses by experimental testing.

We don't observe quarks or particles in superposition. We observe effects, sometimes effects of effects or machine interpretations of effects. — Coben

I am not familiar enough with very low-scale research to pinpoint what exactly in contemporary research is merely hypothesis and what has been properly confirmed by experimental testing.

Some researcher may deliberately confuse things, but in principle the concept of scientific status is easy: If you can confirm it by reproducible experimental testing, then the theory is scientifically justified. Otherwise, it is just a hypothesis, possibly awaiting successful experimental testing.

Not all scientific hypotheses will successfully be tested experimentally. Popularity of the hypothesis really does not matter in that regard. It really does not matter to the status of the hypothesis how many people believe that the hypothesis will be successfully tested in the future. Such imaginary experimental test results should not be taken into account.

1) it depends on the deity, some versions do interacti with or even encompass the physical. — Coben

Well, other religions may have physical gods, but the Abrahamic ones, i.e. Rabbinic Judaism, Christianity, and Islam, clearly don't.

Nearly all have effects on the physical. — Coben

The creator of heavens and earth, in his capacity of first cause, is deemed to be the ultimate reason for every physical and non-physical effect in the universe. Therefore, extracting one such effect out of the many does not produce any interesting or useful information.

since the physical now covers fields, massless particals, things in superpostion and potentially the rest of the multiverse, as some examples, theologians might say, oh, well, if you expand the physical to such things ... — Coben

These things, no matter how small, are still physically observable in one way or another.

it seems to me science sometimes deduces the presence of things that cannot be detected (now). The — Coben

All long as their existence is treated as a hypothesis awaiting the production of a successful experiment that confirms it, there is nothing wrong with such hypothetical research subjects.

The journalists -- sycophants really -- who report on scientific research activity seem to be exceedingly inept at distinguishing between hypotheses and confirmed theories.

I gave examples where scientists say that dark matter exists, you keep saying that they treat it as a hypothesis — leo

The journalist whom you referred to is not a scientist.

He is just some kind of sycophant.

Furthermore, only when authoring experimental test reports, in which he reports on the experiments he has done, a person actually operates as scientist. There are no scientists outside the strict confines of experimental test reports.

That problem rarely occurs in Wikipedia, because they actively enforce their "no original research policy":

Wikipedia articles must not contain original research. The phrase "original research" (OR) is used on Wikipedia to refer to material—such as facts, allegations, and ideas—for which no reliable, published sources exist.[a] This includes any analysis or synthesis of published material that serves to reach or imply a conclusion not stated by the sources. To demonstrate that you are not adding OR, you must be able to cite reliable, published sources that are directly related to the topic of the article, and directly support the material being presented. The prohibition against OR means that all material added to articles must be attributable to a reliable, published source, even if not actually attributed.

The persons you mentioned were not authoring an original experimental test report nor sticking to the requirements of a "no original research" policy. Therefore, the source was simply not reputable.

Furthermore, there was no reason to believe that these people had ever authored any original experimental test report. Therefore, on what grounds do you call them scientists?

I explained why we can test predictive models — leo

Of course, you can.

Still, that does not make any difference because you cannot freely choose the input to feed into the test. Without that ability, the test is not "experimental". Other people will not be able to reproduce the test either.

I explained why experiments won't prove the existence of dark matter, even if they detect what they're trying to detect, you keep saying that they would. — leo

I cannot guarantee that their scientific research efforts will yield a successful experiment. I never did. In fact, I do not even care, because I am personally not involved in these efforts.

I explained that some people see evidence of God in life or in the universe, that they see evidence of divine creation in what they see, just like some other people see evidence of invisible matter in the motion of stars, you keep ignoring it. — leo

The scientific method can possibly handle the issue of invisible matter -- not sure -- but it cannot handle evidence of God, simply because God has no physical incarnation. That is an epistemic issue that you keep ignoring.

I explained that theories cannot be verified, even Popper said that, you keep implying that the "scientific method" can verify theories. — leo

Yes, the scientific method can verify scientific theories by experimentally testing them. Popper never said that scientific theories cannot be verified. It is not possible to prove scientific theories, but that is not even required in the scientific method. A scientific theory only needs to withstand repeated experimental testing.

You're not replying to what I said, you're replying to your own mistaken idea of what I said. — leo

I reply from an epistemic point of view on what you said. The answer may not be what you expect, but that is again caused by a difference in epistemic views.

Honestly I don't think this is a valid distinction. Here you are basically saying that fundamental physics isn't science. — leo

Fundamental physics can be tested experimentally. If a hypothesis cannot at this point, then it is a topic of scientific research, in which they will make attempts to finally test it experimentally.

Topics in scientific research are not yet science. They are merely scientific hypotheses. Dark matter is such hypothesis with merely pending scientific status, awaiting the successful conclusion of the experiment that they need to justify the hypothesis as a fully-fledged theory.

A theoretical function is a predictive model, and your example with sodium acetate is a predictive model too — leo

It is more than just a predictive model, because unlike the weather, you can also experimentally test it.

If the theory doesn't match observations, it's not that the theory is falsified, it's that there is invisible matter everywhere! — leo

Well no, you refuse to give them enough time to finally, successfully set up the experiment that will justify the hypothesis of black matter. The hypothesis is still in research, and does not have full scientific status, in absence of a successful experimental test.

If we can't find that matter after dozens of experiments and billions spent then we need to make more experiments! By their own criterion their theory is unscientific, yet they treat it as scientific. — leo

They have spent billions on trying to set up a successful experiment, but all attempts have failed up till now. The hypothesis is not unscientific. If an experimental test really exists that will justify it as a theory -- still to be discovered -- then it will have acquired full scientific status.

It does not make sense to reject scientific research trying to develop an experimental test, on grounds that it has not yet managed to develop such test. This should rather be a reason to look harder and not to stop looking. Seriously, what makes you believe that they should give up the search already?

My problem then again, is when scientists say there is evidence of dark matter but not of God. — leo

Scientist say that there is a calculation issue in their models. The total amount of visible matter and the total amount of gravitation are out of sync. There is too much gravitation, according to their models.

Maybe they should not call it "dark matter" but rather "calculated excess gravitation".

The claim that God has no physical incarnation is not a decision made by scientists, but simply part of religious doctrine. In absence of a physical incarnation, there cannot be physical evidence; which is a requirement for the scientific method. Hence, verifying the existence of God is not within reach of the scientific method.

The scientific method cannot determine if "1+1=2" because, as abstract language objects, numbers do not have any physical incarnation either. The proposition is provable, however, from number theory, by using the axiomatic method.

Again, demanding application of the scientific method where it does not apply, is called scientism:

Scientism is an ideology that promotes science as the only objective means by which society should determine normative and epistemological values. The term scientism is generally used critically, pointing to the cosmetic application of science in unwarranted situations not amenable to application of the scientific method or similar scientific standards.

With the scientific method not even applicable to numbers, why would it be applicable to every possible question? Why would anybody try to determine the existence of God using something like the scientific method?

If your only tool is a hammer, the whole world will soon start looking like a nail.

How do you differentiate predictive modelling from experimental testing? — leo

In experimental testing, you must be able to strictly control the inputs:

outputs = theoretical_function ( inputs )

When you feed the inputs into the experiment, it will act like a function that maps it on the outputs. Good examples can be found in chemistry experiments:

Hot Ice is a name given to sodium acetate, a chemical you can make by reacting vinegar and baking soda. A solution of sodium acetate can be supercooled​ so that it will crystallize on command. Heat is evolved when the crystals form, so although it resembles water ice, it's hot.

sodium acetate = f ( vinegar, baking soda)

You strictly control the inputs, i.e. vinegar and baking soda, and then the experimental function will map them onto sodium acetate. Chemistry, with its formula system, allows for rigorously calculating input and output quantities along with energy absorbed or produced.

Without complete input control, you do not have a legitimate experiment, and therefore, you would not be doing science.

And how do you differentiate it from comparing observations with what some theory predicts? — leo

Predictive modelling does not require input control. We do not control the forces that generate the weather, but the weather forecast will still model and predict future weather reports. This is not science, because they are not in control of the inputs that go into the weather process in order to output any particular weather. It is merely predictive modelling. No matter how accurate the predictions may be, I do not wish to include it in the scientific method. If it is allowed in, the stock-market charlatans will call their predictions also science.

Yea I didn't say it was a good article, but it shows that scientists believe dark matter exists, they mostly don't treat it as a hypothesis. — leo

They don't treat it as a hypothesis but as something that exists. — leo

They have never detected it and still they say that it exists, that's the thing. — leo

They observe more gravitation in the universe than can be accounted for by the existing total quantity of matter (that they can observe). A lot of things could go wrong in this hypothesis, if only, the accounting of total quantity of matter.

So, now they are looking for something that they believe should cause the excess amount of gravitation that they observe, code-named "dark matter", which is something matter-like, because it causes gravity -- as the standard model believes that matter causes gravity -- but not matter itself, because that would be visible, which it isn't.

What is your problem with these people conducting experiments to figure out where the catch is? Let them try to figure it out, no?

They could equally assume that God exists and that he has such and such properties which would manifest in such and such ways. — leo

Abrahamic religions are adamant that God, creator of the universe, has no physical incarnation, and without which, observations are obviously pointless. Hence, whatever physical phenomenon anybody discovers anywhere, Abrahamic religion is adamant that it will not be a physical incarnation of God, because God is not a physical object or a physical being.

Scientific experiments are exclusively about physical inputs that produce physical outputs. How do you reconcile that with the rule that God does not have a physical incarnation? How could the scientific method ever be able to reach the answer to this question?

They are choosing to assume the existence of dark matter, not the existence of God, which to me is a sign that they believe in a material universe without God. — leo

They assume the existence of a problem, i.e. the mismatch between total matter and total gravitation. These things have a physical incarnation. God does not have a physical incarnation and cannot be reached by experimentally testing anything in a laboratory. Seriously, you will not find a physical God by using a telescope or any other device for observation. All of that is contrary to religion itself. Looking for God in a physical way with devices that measure physical things would just be some kind of heresy.

I don't agree with that, life is a continuous experiment, people didn't need to write reproducible experimental test reports to come up with tools that allowed them to hunt more easily or to start agriculture, they didn't need test reports to make experiments and create technology. — leo

This is one of Nassim Taleb's pet peeves:

Theory is born from (convex) practice more often than the reverse (the nonteleological property)

Science is much more about systematizing existing discoveries inside a framework that guards consistency than about making new discoveries.

Scientific research most often just documents what is going on already. In that respect, Taleb writes:

This makes us live in the contradiction that we largely got here to where we are thanks to undirected chance, but we build research programs going forward based on direction and narratives. And, what is worse, we are fully conscious of the inconsistency.

Still, in my opinion, this rigorous systematization and documentation practice is useful in itself.

in many cases the experiment doesn't get repeated and scientists assume that they would get the same result if they repeated it. — leo

Yes, that is the scandal that plagues modern scientific research. Most experimental test reports are not reproducible when someone attempts to. That is one reason why a lot of modern scientific research needs to be taken with a grain of salt. I suspect that the majority of published scientific research is simply not serious.

Scientists are totally inconsistent in the way they label theories as 'scientific' or 'unscientific', they apply the rules they want when it suits them and not when it doesn't, they call 'scientific' the theories they want to keep and 'unscientific' the ones they want to eliminate. — leo

The less the audience understands about the epistemology of science, the easier it is to mislead them. Therefore, the propensity to deceive is not a property innate to scientists but to their audience. If you see a herd of sheep, the wolves cannot be far away. If you see a gang of manipulable people, you will see the manipulators automatically materialize in their neighbourhood, out of the fricking blue.

Scientists model the influence of the Moon and Sun on the tides here on Earth, in what way are they moving the Moon and the Sun? — leo

That amounts to predictive modelling.

In some cases, I will accept it as serious, but in many cases, I will not. Again, the problem is that you can also do that kind of predictive modelling with the stock market. It is obvious that not all predictive modelling is unserious, but the safe approach is to refuse to grant it scientific status; a status which should be limited to experimental testing only.

Why would a theory that models the influence of celestial bodies on Earth tides be scientific, and not a theory that models the influence of celestial bodies on people's lives? — leo

The one is serious predictive modelling with a real risk associated -- in terms of Karl Popper's article -- while the other is not. In my opinion, neither is science. I consider Karl Popper's definition for science, which includes predictive modelling, to be simply too permissive.

Example from Scientific American https://www.scientificamerican.com/article/is-dark-matter-theory-or/ — leo

I was going to read the article, until I saw its title: "Is dark matter theory or fact?"
Sorry. I am not reading that. Opposing "theory" (bad) to "fact" (good) can only be an exercise in stupidity.

But they don't say the theory is falsified, no no, they say it does exist and they need to make some other experiment to detect it. They could keep going like this forever, and still say it exists, and never falsify it, and still call it science. See the hypocrisy? — leo

Give them time to design an experiment for their conjecture. In the meanwhile, their hypothesis should be considered to be merely an interesting research topic.

But precisely they have designed experiments and performed them, look how many there are! https://en.wikipedia.org/wiki/Category:Experiments_for_dark_matter_search — leo

I have had a look at the Axion Dark Matter Experiment.

The experiment (written as "eXperiment" in the project's documentation) is designed to detect the very weak conversion of dark matter axions into microwave photons in the presence of a strong magnetic field. If the hypothesis is correct, an apparatus consisting of an 8 tesla magnet and a cryogenically cooled high-Q tunable microwave cavity should stimulate the conversion of axions into photons.

The hypothesis is certainly interesting, and most likely an ambitious research topic, undoubtedly worth exploring, but none of the wording suggests that the experiment would be conclusive at this point.

And again they could do the very same thing with God: say what we should observe in such or such experiment if God exists, and carry out the experiment. But they don't, because double standard, they want to believe in a material universe without God, so they frame their research and theories and reasonings in that way, and that way they're sure to always find matter and never God. — leo

Would you want them to use something like an axion haloscope to that effect? The fact that they do not believe that searching for God with an axion haloscope is a suitable approach, does not necessarily mean that "they want to believe in a material universe without God".

It is also not because someone is not interested in searching for God by looking for him with a telescope, that he would be an atheist. I think that such view on science, scientists, and scientific research is flawed.

Secular law is teaching us better morals and ethics than religions. — Gnostic Christian Bishop

Are you shilling again for the ruling elite? How much are they paying you this time?

the subatomic structure of electrons, and atom nucleus in terms of protons and neutrons — alcontali

Electrons have no subatomic structure in chemistry, they are already subatomic. — leo

Well, I meant to say the subatomic structure [consisting] of ...
Sorry, I did not realize that it sounded so ambiguous.

Why do you keep talking about a laboratory, the whole universe is a laboratory, astrophysicists and cosmologists don't physically put planets and stars into a box here on Earth to study them, geologists do not put mountains into a laboratory to observe them, observations happen everywhere, they are an essential part of the so-called scientific method. — leo

You actually pointed out a real problem. In his seminal publication, Science as Falsification, Karl Popper explicitly allows for predictive models in science:

We all—the small circle of students to which I belong—were thrilled with the result of Eddington's eclipse observations which in 1919 brought the first important confirmation of Einstein's theory of gravitation.

Now the impressive thing about this case is the risk involved in a prediction of this kind. If observation shows that the predicted effect is definitely absent, then the theory is simply refuted. The theory is incompatible with certain possible results of observation—in fact with results which everybody before Einstein would have expected.

I think that this view may be too liberal. Even a broken clock gives the time correctly twice a day.

If predictive power were enough and experimental control of input variables unnecessary, then even so-called technical analysis of stock exchange data would be science. Stock-market technical analysis judiciously enrols previous, historical data to minimize future prediction errors.

I think that predictive modelling may be useful, but it must not be confused with experimental testing. Predictive modelling does not establish causality by strictly controlling inputs. Therefore, it must be considered another epistemic method. Predictive modelling is not science.

Still, I agree with Karl Popper that there was risk involved in Eddington's observation. They did put skin in the game. So, it is not mere cheap conjecturing either.

people associate what is labeled 'unscientific' with fantasies — leo

Agreed. A large number of people, undoubtedly the vast majority, believes in the existence of one single epistemic method, the scientific one. That view is utter nonsense, but nonetheless widespread, especially in the West. The more shoddy the scientific training of a western person, the more likely he will glorify scientism:

Scientism is an ideology that promotes science as the only objective means by which society should determine normative and epistemological values. The term scientism is generally used critically, pointing to the cosmetic application of science in unwarranted situations not amenable to application of the scientific method or similar scientific standards.

The absolutely most stupid people on the globe live in the West. The populace in the West may be moderately more knowledgeable than in third-world countries, but is also much more beholden to patently false beliefs. Combine that with rampant arrogance and the practice of claiming credit for other people's work, who were real intellectuals while they are not, and then you probably understand one of the many reasons why these people are hated by the rest of the planet.

Any act is an experiment, if you jump and you observe that you fall back to the ground that's an experiment. — leo

You still need to write your experimental test report in such a way that another person can repeat your experiment and verify that he obtains the same results. Seriously, there is no experiment if you do not produce a reproducible experimental test report.

How would you figure out what year the battle of Waterloo took place if not through observations and hypotheses? — leo

Claims that historical events really took place are not justified by the scientific method, but by the historical method, which revolves around corroborating witness depositions. There is absolutely no expectation that a third party should be able to reproduce the same event/observation (like in the scientific method):

Gilbert J Garraghan and Jean Delanglez divide source criticism into six inquiries:
When was the source, written or unwritten, produced (date)?
Where was it produced (localization)?
By whom was it produced (authorship)?
From what pre-existing material was it produced (analysis)?
In what original form was it produced (integrity)?
What is the evidential value of its contents (credibility)?

The justification and validation of historical witness reports are dealt with using a very specific, epistemic method: the historical method. I do not see how anybody could confuse this method with the scientific method, which is applied in other circumstances and has other requirements.

You can have the theory that the position of planets in the sky has a specific influence on your life that depends on when you were born. You can test experimentally whether what you observe matches what the theory predicts. Is that theory considered science? — leo

No, because you must put the planets by yourself in a particular position and measure the quantified impact on your life. Next, someone else must put the planets by himself in a particular position and see if he gets another impact.

You first need to find a way to painstakingly move the planets in any arbitrary position of your choice, before scientific theories could be feasible.

Again, scientists decide what they should observe if dark matter exists, and then they carry out experiments to decide about the existence of dark matter. — leo

At this stage, dark matter is merely a conjecture. It is not a theory backed by experimental testing.

Then when they say that dark matter exists, that it really is out there — leo

No, it is just a hypothesis. It is something that they would like to test experimentally, but they haven't figured out how yet.

To say that the existence of dark matter is a scientific question but not the existence of God is hypocritical. — leo

What both questions have in common, is that you would need to design an experimental test setup in order to turn them into scientific theories. Since there is nothing to test, nor any test to repeat by someone else, in order to validate that they get the same results as in your test, there is no legitimate scientific activity possible in either realm.

A scientist is a glorified tester, who carries out his work in a laboratory. If you refuse to say what exactly he should test and how he should test it, there will be nothing to test, and therefore no work to do for a scientist.

I'm saying that by the same criteria the existence of subatomic particles is not a scientific question, — leo

It depends what subatomic particles it is about.

Chemistry makes extensive use of the subatomic structure of electrons, and atom nucleus in terms of protons and neutrons. It is ancient stuff that dates back to the 19th century. It is considered solid stuff at the chemical scale.

The closer you get to the Planck scale, the less solid the theories, which are often merely conjectures. However, that does not mean that all subatomic theories are just fantasies that have never been tested experimentally.

Great, a copy-paste from Wikipedia where some dude has written a definition for "the scientific method". — leo

It is equivalent to the definition in Encyclopaedia Britannica and elsewhere. There is certainly a consensus that the scientific method requires experimental testing.

Science is the collection of all statements that can be tested experimentally. Science is an epistemic domain.

With this definition of "the scientific method", you can very well consider the existence of God as a scientific question — leo

Propose an experiment that you will carry out and that other people will be able to repeat. If it is possible to do that, then the question is within reach of the scientific method. Otherwise, it isn't. For example, you cannot propose an experiment to figure out in a laboratory in what year Napoleon's Battle of Waterloo took place. That question is simply not within reach of the scientific method.

I say there is no such thing as "the scientific method" in the sense that it doesn't characterize what we call science, because it also characterizes some of what we call non-science. — leo

If it can be tested experimentally, then it is science. Can you give an example of a theory that can be tested experimentally and that is not considered science?

You're saying we can't observe God — leo

I did not say that. I just don't see what laboratory-based, experimental test would say anything worthwhile on the matter. Science is not the only epistemic domain. If your only tool is a hammer, then the whole world will soon start looking like a nail.