So are you now saying that beliefs aren't literally a part of expressed language? — Terrapin Station

I think that language can express beliefs. However, the precise details of the correspondence is probably a question mark. We do not necessarily know anything about someone beliefs if he does not communicate them.

What do you mean? Have you seen anything defy gravity? Is there anything that breaks the laws of thermodynamics? — TheMadFool

These scientific patterns have an uncanny resistance to falsification in our part of the universe. Still, they are not the true laws of nature, because that would be the theory of everything (ToE):

A theory of everything (TOE[1] or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe.[2]:6 Finding a TOE is one of the major unsolved problems in physics. Over the past few centuries, two theoretical frameworks have been developed that, together, most closely resemble a TOE. These two theories upon which all modern physics rests are general relativity (GR) and quantum field theory (QFT). GR is a theoretical framework that only focuses on gravity for understanding the universe in regions of both large scale and high mass: stars, galaxies, clusters of galaxies, etc. On the other hand, QFT is a theoretical framework that only focuses on three non-gravitational forces for understanding the universe in regions of both small scale and low mass: sub-atomic particles, atoms, molecules, etc.

The Theory of Everything would be the real construction logic of the universe, and not just some patterns that somehow resist falsification (for the time being).

This holds for only a finite set of axioms and axiom schemata, an important condition; as new unprovable truths or straightup undecidable propositions can always just then be added as a new axiom to then be provable. — boethius

If a pattern emerges inside a world constructed by a particular set of axioms, and this pattern stubbornly resists falsification, i.e. counterexamples are not forthcoming, but also resists being proven from the axioms, then adding this pattern to the axioms would be redundant. The pattern already emerges from the existing axioms without explicitly adding the pattern as an axiom. So, what do you gain by adding it?

For example, the Riemann hypothesis has resisted falsification for 160 years, i.e. counterexamples are not forthcoming. At the same time, this pattern has also resisted being proven from the axioms of number theory. Imagine that you add the Riemann hypothesis to the axioms and suddenly someone unexpectedly finds a counterexample. Now your system is inconsistent, because the axiom says that the counterexample does not exist, while someone just produced such counterexample.

Therefore, I really do not see what you would gain by adding the Riemann hypothesis to the axioms of number theory.

No, those aren't beliefs. You can call them beliefs, but that won't make them beliefs. — Bartricks

Language expressions that correspond to beliefs are meant to communicate beliefs. In the definition of knowledge as a Justified (true) Belief (JtB), no distinction is made between both. Still, that distinction only becomes relevant when there is noticeable problem with the correspondence between belief and language expression. As soon as a belief is expressed in language, it can be shared and can acquire some measure of objectivity.

The impression I get from science, what I know of it, is that the so-called laws of nature are universal. — TheMadFool

They are not the true laws of nature, which are unknown, and they are not universal either. These laws only exhibit an uncanny resistance to falsification in our part of the universe.

Yet, that's just a waste of time if anything because as we all agree the conclusion is contained within the axioms/premises. — TheMadFool

Yes, but it can still be amazingly hard to discover the path between conclusion (=theorem) and axioms/premises. Such path is the sequence of rewrite operations (the "proof") that bring back the conclusion back to its axioms/premises.

It has taken 350 years of trying by a large number of people to bring back Fermat's Last Theorem to the axioms/premises of number theory. The conclusion/theorem was known for centuries. The axioms/premises were known (at least implicitly) for centuries. The sequence of rewrite operations (the "proof") was impossible to find for centuries, until Andrew Wiles recently found it anyway. The corrected proof was published in 1995.

There are still outstanding conclusions/theorems that stubbornly resist both falsification and proof. A good example is the Riemann hypothesis. No counterexample has been found for 160 years but also no path/proof that brings it back to the axioms.

Hence, it is not because the axioms/premises and the theorem/conclusion are known that the path/proof is known too. It can be fiendishly hard (or even impossible) to discover that path/proof.

If you construct an abstract, Platonic world using axioms/premises expressed in first-order logic, then there will be perceivable patterns in that world that can neither be falsified nor be proven from its construction axioms. That is exactly what Gödel's first incompleteness theorem proves.

Sure, but that's a different thing though. I haven't claimed that there is a rational explanation for that; I am claiming that Einstein's discoveries involved abductive reasoning, that is involved thinking of new possibilities, theories, that he conjectured might turn out to be explanatory of what is observed.

For example a newly conjectured hypothesis or theory might be explanatory of anomalies that Newtonian physics could not explain, such as the observed procession of the perihelion of Mercury. — Janus

Yes, agreed. Knowledge is rational, even though the mental discovery process of which knowledge is the output, is itself not rational.

I have defined 'subjective' as meaning 'made of a subject's mental states'. All beliefs are going to be subjective according to this definition, because beliefs are always the beliefs of some subject or other. — Bartricks

A belief expressed as language may not depend on any subject's mental state. If you represent a belief as a language expression and feed such expression to a machine, e.g. "a=5; b=7; print(a+b)", the output will not depend on any subject's mental state. The language expression still represents a belief. I can happily believe or not believe that "a=5 and b=7".

Furthermore, what exactly can be known about beliefs that are never expressed in language?

There are beliefs that can be expressed in language and can be shared even with a machine, who can then even manipulate these beliefs. Of course, this is not possible for all beliefs even if they can be expressed in language.

Language expressions can represent moral rules and rulings derived thereof. A machine can then verify if the ruling necessarily follows from the moral rules. Such ruling will be a new shared belief, shared by people who accept these moral rules. Hence, a measure of objectivity is possible in morality. I have never said that it would be universally shared. But then again, objectivity does not need to be universal. It is usually context-dependent.

But you're not challenging anything I've argued. — Bartricks

I think moral values are demonstrably subjective. — Bartricks

I do not think that moral values are necessarily subjective.

A group of people can objectively share a moral system, by accepting the language expressions that represent the basic moral rules and by accepting the rulings -- also language expressions -- that necessarily follow from these basic moral rules.

It is the use of language and communication between these people that allows for some objectivity. Language is itself a common understanding meant to facilitate some measure of objective understanding, i.e. objective belief.

I agree with you that new theories cannot come about via rationality; if by rationality you simply mean deductive reasoning. Charles Sanders Peirce, the founder of pragmati(ci)sm, drew distinctions between deductive, inductive and abductive reasoning. If I remember correctly, Popper denies there is any inductive reasoning (as it is merely expectation that the future will be as the past), but Peirce's abductive reasoning is what Popper would call conjecture. — Janus

I think that all three types of reasoning do not explain why new knowledge is discovered in the first place. They only kick in when we verify if a justification makes sense somehow and supports the conclusion.

For example, there is no rational explanation why Einstein felt like publishing his 1905 paper and how he discovered its content. In fact, the main ingredient could not possibly have been mere reasoning. There is no mechanical procedure known that will lead to that kind of results, and according to Gödel's incompleteness theorems, such mechanical procedure cannot even exist. Reasoning is just about verifying that Einstein's conclusions follow from the evidence he presented. In that sense, reason plays just a minor role in the entire mental effort and activity surrounding his 1905 paper.

You're confusing the expression of a belief with the belief itself. If I write on a piece of paper that "I believe it is Sunday" I have not created a belief made of paper. — Bartricks

The language expression is an abstraction that seeks to represents the belief. It is the language expression that we communicate. It is processed in lieu of the belief. The map is obviously not the territory.

That kind of mappings obviously have their flaws and abstraction leaks, but they are part of what we experience as objectivity.

Don't you deal with your own beliefs? — Terrapin Station

I was referring to the beliefs of others, which are only known to us when they somehow communicate them.

Which is not to mention that what was at dispute isn't whether a linguistic expression can be correlated with a belief, but whether linguistic expressions literally are beliefs. — Terrapin Station

That is exactly what "isomorphic" refers to. It does not mean that two things are identical.

It just means that the mapping is structure preserving with regards to particular operations on both sides. For example, a Google map is isomorphic with the territory that it depicts, with regards to connecting points on both sides and measuring distances. If a one-inch line on the map corresponds to one mile in the territory, then a two-inch line will correspond to two miles.

So, a language expression is meant to be isomorphic with a belief with regards to logical operations that you could perform on both sides.

How do you think that sound waves or ink on a page or whatever can literally be a belief? — Terrapin Station

It is a language expression that is at best "isomorphic" with the corresponding belief, meaning that operations on the language expressions will still correspond to operations on the belief. For example, if you negate the language expression, it will somehow correspond to the negated belief.

We never really know what the belief is, because we only ever deal with the corresponding language expression.

In the justified (true) belief (JtB) doctrine, the term "belief" requires a corresponding language expression, without which it is not possible to communicate it, or from there, to verify its justification.

That does not mean that all beliefs can be expressed in language. It just means that formal knowledge only deals with beliefs that are expressed in language.

If we use "subjective" to refer to mental phenomena, then beliefs would be subjective unless we're claiming that beliefs can obtain outside of minds somehow. — Terrapin Station

Re language, I'd say that you're conflating things like sounds, pixels on computer screens, ink marks on paper--however language is expressed, with beliefs. The sounds, etc. are correlated to beliefs, but they're not literally beliefs. — Terrapin Station

I am convinced that some beliefs can be expressed in language -- and copied outside the mind -- and communicated to others. I have not said that I believe that about all beliefs; but that is not necessary anyway.

Yeah, they're fucked. But not for the reasons you give. — Banno

I believe that every centralized system will become corrupt and will turn on its users. Now, I agree that this belief is quite ideological. Decentralization is a core belief in the cryptocurrency world:

The Danger of Centralization
The internet should be decentralized. The credit industry should be decentralized. P2P markets should be decentralized. Identity should be decentralized. Loans should be decentralized. Anything that has a trusted 3rd party act a middle man without adding value should be replaced with a decentralized system.

Therefore, for ideological reasons, I am also firmly opposed to any centralized education system. I am convinced that centralization in education will go badly wrong. It will go wronger and wronger until it destroys the very society itself that feeds it with students and money, just like the centralized banking is doing by destroying its customers and even society at large.

There are lots of idiosyncratic choices that are made by a school, for which various alternatives are actually viable. It is utterly wrong to get all the schools to give the same idiosyncratic answer. This only happens because the choice itself has been centralized. It is dangerous to do that. There should be alternatives, and with a state-controlled system monopoly, there are no alternatives.

In the end, I do not even care about what the symptoms will be of destruction caused by a centralized education system. I believe that it will always end up destroying itself, regardless of how exactly it does that, simply, because of the centralization itself.

er, what? — Bartricks

Not all beliefs are subjective, because some beliefs are deemed objectively justified. Furthermore, once a belief is expressed in language it is no longer a state of mind, and does no longer require that a person be involved. Machines can also manipulate language expressions.

That hypothesis is that social acceptance of homosexuality is positively impacted by a broad perception of reaching population equilibrium. — JosephS

That would be about one particular element or rule in a system of morality, and not about the entire class of morality systems, which is what the article is about.

If you want to talk about one element across morality systems, for example, category theory tries to handle that, using functors between systems. Theories can be modelled as categories. Since theories are (axiomatic) rule-based systems, a morality is a theory. A functor is then a mapping between two such (morality) systems.

Still, I am absolutely not an expert on functors. I always hope that I am going to read something surprisingly effective when perusing that type of literature, but up till now, I haven't found anything that I can really use out of the box. Besides that functor approach -- which is not necessarily easy to use -- I don't know of any other attempt at juxtaposing (morality) systems.

The actual article does not support your interpretation. McHugh is not himself without controversy. You talkin' shite. — Banno

He does not literally say it, but it is obvious what he means. It is incredible how "critical thinking" is supposedly encouraged in state-controlled schools, but not "critical thinking" about the schools themselves. Centralization leads to corruption, and 150+ years of centralization of the schools has clearly led to an astonishing level of corruption, which is even going to destroy society as a whole.

Here is an article by someone who can actually support their argument. Thoughts? — JosephS

The article, "Darwinian Morality" is yet another exercise in infinite regress, as well as a complete misunderstanding as to what "reason" is. Seriously, the author utterly misunderstands formal knowledge.

If morality is a set of rules embodied by language expressions, then there is no way in which "reason" can discover what these basic rules should be. Mere "reason" can also not discover which derived rule (=theorem) can be proven from these basic rules. Pure "reason" is strictly limited to the ability to verify the proof that a particular theorem necessarily follows from the aforementioned basic rules.

The 1936 Church-Turing thesis insists that there must be a purely mechanical procedure to verify a knowledge solution. Otherwise, it is not knowledge; and if it is not knowledge, then the appropriate tool for the problem is not "reason".

The tool of "reason" cannot discover new knowledge. The tool of "reason" can only verify the justification of knowledge. Hence, the entire exercise in "reasoning" in the article will never lead to any new insights, simply, because that is the prerogative of other, unknown mental faculties.

As normal, I don't really understand what you're saying or see its relevance. I have not denied that justified true beliefs exist, for instance, or that knowledge is made from them (although I think I might deny that, but I haven't done so here). — Bartricks

The idea that all beliefs are subjective, is not compatible with the idea that there exist objectively justified (true) beliefs. Therefore, objectivity in beliefs is assumed to be possible.

Beliefs are subjective (what they are 'about' will often not be). — Bartricks

As soon as beliefs are expressed in language, they are language expressions, which could possibly represent an uncanny correspondence with the real, physical world, or be provable from the construction logic of an abstract, Platonic world.

The existence of objectively justified (true) beliefs (JtB) is a widely-accepted assumption, axiomatized by epistemology, and without which epistemology would not even make sense as a discipline.

Sure, but it is nonetheless humans who program the machines, no? — Janus

Yes, agreed.

According to Gödel's incompleteness theorems, there is no mechanical procedure that can generally discover new theorems along with their proofs. The reason why I mention this, is the Curry-Howard correspondence, according to which:

CHC: a program is a proof and a proof is a program

So, strange but true, the discovery of new theorems (or new programs) is not an exercise in rationality. It somehow uses other, unknown mental faculties.

However, proof verification is a purely mechanical procedure.

So, a human discovers a new theorem with its proof, and then a machine can verify that the proof establishes a path (=a proof) between the construction logic of the theory and the theorem which is being proven.

It is therefore a warning shot in the direction of the practice of memorizing knowledge or merely doing exercises in verifying their evidence. Machines can do that too. The real value is not there. The real value is in discovering these theorems and their proofs.

So, for you reason is a human faculty ... — Janus

That is wrong, because "reason" is merely a mechanical faculty, that can be executed by machines. Humans can do it too, but are way less efficient at it; and much more error-prone.

does the expression "2 + 2" denotes two objects or one object? — Zuhair

It is a language expression. In principle, it has nothing to do with real-world "objects".

There are rewrite rules that allow for carefully reducing this language expression, "2 + 2" to other language expressions e.g. "1 + 1 + 2". The complete sequence of permissible rewrite operations that demonstrates that the symbol stream "2 + 2" is extensional with "1 + 1 + 2" is called a "proof".

The expression "2 + 2 = 1 + 1 + 2" does not necessarily mean anything outside the system of basic rules that define that system. Seriously, it is completely self-contained with no reference to the real, physical world.

mean, I agree - if you don't ruthlessly follow Reason, you probably won't arrive at my conclusion. But that's to my conclusion's credit, I think. — Bartricks

Your way of reasoning is one of infinite regress.

You see, knowledge is either about correspondence with the real, physical world, when the knowledge is empirical, or else, it is about the consistency of language expressions that satisfy particular basic rules, when the knowledge is axiomatic or at least logic-based.

Rejecting a particular choice of basic rules for governing language expressions is not "reason". That view is a complete misconception.

For example, reason in mathematics is about demonstrating that a particular theorem necessarily follows from a particular -- even arbitrary -- set of basic rules. It is never about questioning the basic rules themselves.

Seriously, "reason" is absolutely not what you think it is.

Reasoning is something that a machine can perfectly do too. Feed the basic rules into the device, feed the theorem into it, along with its purported proof, and the machine will perfectly be able to verify if the proof is correct. All of this is purely mechanical; and it has to be. Otherwise, it is not knowledge.

Relevance? — Bartricks

Morality is "subjective" to the context of the basic rules that you accept. The term "subjective" is not really appropriate here, though. The proper term is rather "context-sensitive". Within a system of morality, however, moral rulings are perfectly objective. You could criticize theorems in any axiomatic system for being context-sensitive. It still works perfectly fine, though. Critical infinite-regress considerations about the axioms is not the solution.

that you have got to use some sort of quantification. — tim wood

Yes, Alan Turing's version uses quantification, but not a witness such as S = "S is not provable" as in Gödel's original proof.

I also believe that the problem is somehow fundamentally caused by extending propositional logic into first-order logic by adding universal quantifiers, but there is not necessarily a direct relationship in Alan Turing's proof, which merely states that it would ex absurdo solve the Halting Problem. The Halting Problem itself also uses universal quantification. So, some kind of relationship could already occur there.

LIke I say, you're confusing descriptions with prescriptions. Moral rules, if there are any, are prescriptions. Now, can a machine issue a prescription? No, not literally. Someone can programme a machine to issue prescriptions, but then those prescriptions qualify as prescriptions only because we can trace them to a subject whose attitudes they express. — Bartricks

Well, yes, you can trace the rulings to a set of basic rules.

Whose attitudes these basic rules express is another matter. The setup would still work with pretty much arbitrary ones. I am not arguing here in favour of a particular set of basic rules, but once you accept any such set, then a mechanical device can verify rulings against the basic rules as the result of computational effort.

So, if you feed basic rules into the mechanical device, it will be able to verify a ruling for each case that you present to it. These rulings will only be accepted by people who subscribe to the basic rules.

Other people can feed other basic rules into the device and accept other rulings. As far as I concerned, you can select the basic rules that you prefer. I think that it would be unfair to ask people to accept rulings derived from basic rules that they do not subscribe to.

Tacit (implicit empirical) knowledge is difficult to communicate because it is only partially codifiable, or uncodifiable. It is processed in an automatic, or intuitive (as opposed to a controlled, or cogitative), manner. Types include motor sequences (e.g., driving a car), skills (e.g., hammering a nail), and schemata (e.g., primary social interactions).

So tacit knowledge (which is ineffable) is not actually knowledge, or better: is illegitimate knowledge? — Galuchat

Well, it is obviously legitimate. I should have said that they are not part of "formal knowledge".

Moral norms are prescriptions. That's just what a norm is. Well, it's more of a rag bag than that. Moral philosophers often characterise them as 'favourings'. Doesn't matter. Favourings require a favourer. — Bartricks

No, in principle, rulings are produced, or at least verified, entirely mechanically by a rule-based system, i.e. a machine, from a set of basic rules.

So, again, two no-nothings say the same thing and suddenly we have verification and knowledge, yes? Only, no, no, no. — Bartricks

Verification only occurs when the second no-nothing uses a sound procedure to double check the first no-nothing's justification. We do not ask the verifier to produce a new claim. We also do not ask him if he likes the results of the original claim. We only ask the verifier to verify if the original conclusion necessarily follows from the original evidence.

So, basically, long story short, a big bunch of no-nothings can create knowledge by writing a Wikipedia page, yes? — Bartricks

They do not create knowledge. Read Wikipedia's No original research page.

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.

Your remark suggest that you are not even properly familiar with the core of the epistemic method that governs Wikipedia.

Plus, I thought you didn't value what experts think - why are you suddenly into consensuses? — Bartricks

Epistemology is not mathematics nor science. It has its own requirements and procedures. Consensus does not matter in mathematics. In principle, it also does not matter in science. It does matter, however, in epistemology.

You realize there's a consensus that verificationism is false? — Bartricks

It is not about verificationism. It is about verifying that all formalisms and procedures were followed. Furthermore, verificationism is not accepted in science because impossible. So, science revolves around falsificationism. Mathematics, however, is staunchly verificationist. Unlike the scientific method, the axiomatic method does not allow for mere sampling of random cases. So, verificationism is only rejected in the scientific method.

Does the random non-expert's cancer diagnosis verify the other random non-expert's cancer diagnosis? If not, why not? — Bartricks

Verification in this context means that the method was correctly applied. It does not mean that the results are correct.

Since a diagnosis does not seek to refer to another diagnosis, I do not see how that would work. In what way does one diagnosis verify if the method was correctly applied in another diagnosis?

In the end, knowledge is subject to a bureaucracy of consistency-maintaining formalisms. We just verify if the procedures were properly followed. The result could still be wrong, but that does not matter. In the end, nobody cares about that. If a doctor follows all procedures required, the professional-liability insurance company will not cancel his cover. That is the same principle.

Well, that's nice for you - but your random and unjustified assertions do not determine what's true in this area. Not unless you're an expert, that is (joke). — Bartricks

There is pretty much a good consensus on the three core, formal knowledge-justification methods:
axiomatic, scientific, and historical.

Furthermore, these methods do not guarantee that any claim would be correspondence-theory "true".

The reason why we need to agree on the existence and suitability of these three epistemic methods, is that we need somewhere a starting point. Otherwise, it becomes an exercise in infinite regress.

You're confusing verifiability with truth and justification. — Bartricks

No, not at all. I did not say that the justification had to be some kind of extensive verification. I only said that I wanted to verify the justification, which could perfectly well rest on falsifiability, or on witness depositions, depending on what it is about.

There needs to be a document that contains the justification, and I will verify, i.e. read or peruse, that justification. It is not that I would subscribe to verificationism. I am perfectly happy to accept justification in the form of a falsifiable test report.

And I am justified in thinking I just drank a beer because I seem to remember doing so, even if I cannot travel back in time and verify it. And so on. — Bartricks

Yes, but this is not formal knowledge.

If a random stranger with no expertise in medicine says that my mole is cancerous, and then another random strange with no expertise in medicine says that my mole is cancerous, have they verified each other? And do you think that, because they have both said the same thing, I now have good reason to think the mole is cancerous? — Bartricks

It does not work like that.

Document 1. "Your mole is cancerous".

Document 2. Evidence for document 1.

So, where is document 2?

I only work with documents. I do not work with strangers babbling about arbitrary subjects. I want document 1 and document 2. They must first commit to paper what it is about. Otherwise, the proposition is not even receivable.

You don't have to verify that a belief is knowledge before it qualifies as knowledge. After all, if you did you'd get a regress. — Bartricks

You have the knowledge claim and then you have evidence/justification that supports it. We are talking about two different documents. For example, document 1 claims that water boils at 100C. Document 2 is test report in which they made water boil a few times and consistently measured its temperature.

It is necessary to verify that document 2 at least exists. Otherwise, you can seriously question what is written in document 1. On what grounds do they even write it?

No, a normative rule is a prescription. It tells you to do something. Only a subject can tell you to do something. — Bartricks

Not true at all.

The answer to a jurisprudential question (such as a fatwa) will declare a particular behaviour to be morally permissible or impermissible. These rulings do not tell you what to do, because you do what you want. Still, if you claim to accept the basic rules of the underlying morality then you may want to remain consistent by accepting all its consequences.

Example ruling: "He worked as a programmer for a company but they did not give him his dues; can he sell some of their programs to get his money?"

Whatever the answer may be, there is nobody who will force the person asking the question to act in accordance with the answer. There is, however, a real influence that goes out of the answer, because the person asking the question is likely to want to remain consistent with his basic beliefs. Otherwise, he would obviously not even ask this question.

Morality is much, much more about consistency than about enforcement. In fact, in certain ways, morality has a real and noticeable propensity of enforcing itself ...