On one hand mathematicians are of the view that truth requires proof and on the other they're claiming, through Godel, that some truths are unprovable. Isn't that a contradiction? — TheMadFool

Can there be proof for the proposition X="There is no proof for X in theory T" in theory T? If there is proof for X in theory T, then theory T is inconsistent. If there is no proof for X in theory T, then X is true. That makes proposition X "true but not provable".

The fact that proposition X is even true, is actually not even the main problem.

The main problem is: Do there exist yes/no questions in T for which T cannot prove a yes or a no answer? The existence of such questions would be the "incompleteness" of T.

Answer: If the language of T does not allow for expressing proposition X, then the problem does not even apply. If it does, however, then there is at least one yes/no question in the language of T, namely proposition X, for which T cannot prove/decide the answer, irrespective of the axioms in T. Furthermore, the problem cannot be fixed by re-engineering the axioms of T either.

Well, that's just false. — Bartricks

In what way will you justify your claim about Helen's attitude?

You have absolutely no certainty about what she really values. Helen may possibly not even know it herself. Neither what you say about what Helen values, nor what Helen herself says about that, can be considered knowledge.

You would need to present two documents:

document 1) What does Helen value? Explain.
document 2) Justification for document 1

There is simply no way in which you can produce a legitimate document 2. Therefore, document 1 will always end up being considered unsubstantiated.

Should Israel give the land back to Palestine? Should Australians give back their land to aborigines? Should Americans give back the land to the natives? — Purple Pond

These are different cases.

The aboriginals in Australia are not being banned from (parts of) Australia. The same holds true for native Americans. A native American can go to New York or San Francisco and live there like he wants.

That is not the same for a large number of Palestinians who fled (or were "helped" to flee) and who are now being denied the right to return to where they originally lived. A Palestinian who ended up in Gaza or Bethlehem will be prevented to travel to Haifa or Tel Aviv if he wanted to live there.

In that sense, it is not even about "giving back the land".

These people were citizens and residents of the complete former British mandate of Palestine. They had free movement all over mandatory Palestine. They could live anywhere they wanted in mandatory Palestine. These rights were taken away by the State of Israel. There is absolutely no reason why they should accept such reduction of their rights.

As ever, I do not know what you are talking about — Bartricks

Whatever you say about Helen's attitude, it is not possibly knowledge, because there is no way in which you could ever justify it.

Eh? No, the judgement is about something featuring as the object of one of Helen's attitudes - a valuing attitude. — Bartricks

Justification means that our view on Helen's attitude necessarily follows from it. What justification could you ever produce? Anything solid? Anything that other people would not be able to trivially reject?

If you cannot produce such justification, then claims about Helen's attitude must be excluded from the domain of knowledge.

a judgement such as "Helen values X" — Bartricks

There are two possibilities. Either the judgment is about the real, physical world, or else it is about an abstract, Platonic world.

In the first case, making assumptions about the real, physical world is not allowed. The judgment is necessarily a conclusion. Therefore, you need an extensive, experimental test report as evidence; which is impossible to provide. Therefore, we need to reject such empirical proposition both as a starting point (=assumption) and as an end point (=conclusion) in knowledge.

In the second case, it is about a hypothetical Helen in an abstract, Platonic world. Since the construction logic of living beings is unknown, they cannot be constructed as part of an abstract, Platonic world, of which we always need to have access to the full construction logic. Therefore, logical propositions about a hypothetical living Helen are not allowed in knowledge either.

There may be other, unknown mental faculties -- that are not reason/rationality -- that can take the proposition "Helen values X" as input or produce it as output, but it can never be part of knowledge.

For example, yes, I agree that morality is not empirically available. — Bartricks

In that case, a serious problem occurs because the meaning of "true" defaults to correspondence-theory truth, which is always empirical.

Therefore, what you wrote in "the truth conditions of those judgements - so, that which would make the judgement true" is dangerously ambiguous. What meaning of "true" is it about?

There is also logically "true", but that is an arbitrary symbol in the construction logic of an abstract, Platonic world that allows for logical inference, or at least for basic boolean-aristotelian algebra. It has in principle nothing to do with correspondence-theory "true".

There is nothing magical about the choice of symbols for the values of Boolean algebra. We could rename 0 and 1 to say α and β, and as long as we did so consistently throughout it would still be Boolean algebra, albeit with some obvious cosmetic differences.

So, in the algebra with values V and operators P, i.e. <V={false,true},P=(and,or,not)> the symbol "true" is just whatever you arbitrarily mention in the second position of the algebraic structure <V={_1_,_2_},P=(_3_,_4_,_5_)>.

It is not because a logical inference -- always in an abstract, Platonic world -- ends in a logically true statement, that this statement says anything at all about the real, physical world.

Claiming some kind of definite connection between logical "true" in an abstract, Platonic world and correspondence-theory "true" (always in the real, physical world) is only permissible on the basis of an extensive, experimental test report. In all other cases, liberally associating logical "true" with correspondence-theory "true" is simply spurious.

One line of reasoning may be used to establish premises for a different line of reasoning. I think you are looking at reason in too linear a fashion; it is more of an infinitely complex web or network. There is no ultimate first point in such a complex. It would be like asking which point is the centre of the universe. — Janus

The conclusions/theorems in an abstract, Platonic world are necessarily ramified. It is a non-optional requirement that conclusions/theorems can be reduced to a base level represented by a finitary set of unexplained basic rules, i.e. axiomata, i.e. "first principles" (which could internally indeed be circular). An "infinitely complex web or network" is not allowed, because logical inference is not allowed in that kind of web. It would automatically degenerate in infinite regress.

My point is that the truth conditions of those judgements - so, that which would make the judgement true - is not our own valuing activity, but the valuing activity of Reason. — Bartricks

Morality is not about empirically observing/testing patterns in the real, physical world and can therefore not possibly be correspondence-theory "true".

Hence, being "true", cannot possibly be a requirement for moral judgments.

All you can require from a moral judgment is that it necessarily follows from the basic rules of your morality. Therefore, a moral judgment would ideally be "provable" from these rules.

Can you have a look at Godel's Incompleteness Theorems vs Justified True Belief — TheMadFool

First of all, there is an enormous problem with knowledge as a Justified (true) Belief. Mathematics is not correspondence-theory "true". In fact, mathematics has not necessarily anything to do with the real, physical world. Mathematics does not "correspond" to the real, physical world.

Mathematics is about patterns in abstract, Platonic worlds constructed from their basic axioms. For some of these patterns it is possible to demonstrate that they necessarily follow from their Platonic world's construction logic. Such demonstration is a "proof".

In more practical terms, the term "provable" means that there exists a sequence of rewrite transformations that will connect a theorem to the construction axioms of its world. It has nothing to do with correspondence-theory "true", which is a real-world, physical concept. Hence, mathematics are justified beliefs, but not justified true beliefs.

Furthermore, logically "true" does not mean correspondence-theory "true".

Using a clever hack, Gödel manages to create a theorem that is algebraically "true" in the abstract, Platonic world of number theory, but which by simply asserting its own unprovability, is not provable from the construction logic of that world. Hence, true but not provable.

The Gödel statement says that it is not provable. So, it isn't. What is says, is therefore true.

Concerning the real, physical world, we cannot prove anything at all, because we do not have access to its unknown construction logic. Therefore, every correspondence-theory "true" statement is always not provable. Therefore, in the real, physical world, "true" always implies "not provable".

Stephen Hawking argued that Gödel's incompleteness theorem has an effect on science -- which seeks to be correspondence-theory "true" -- and will lead to undecidable statements in science too. It would be nice if someone came up with a witness statement for that, though.

Undecidable = neither provable nor disprovable??? — TheMadFool

Yes. ;-)

Empirical observation is not unreasonable. — Banno

Experimental testing is another purely mechanical procedure. If a machine cannot (conceivably) carry out or repeat the tests, then there is something wrong with the empirical theory. In that sense, objectivity means that a machine can do it too, also for empirical knowledge. Otherwise, it is subjective. Formal knowledge is always objective in a sense that there must exist a purely mechanical way to carry out the verification of its justification.

The argument I have presented is about moral values. It establishes - whether you like it or not, and whatever theory you favour - that moral values are the values of a subject, a subject who is not me, or you, but Reason. — Bartricks

Reason is just a verification tool to travel safely from premises to conclusion. Morality rests on ultimate premises about which Reason necessarily says nothing at all.

Furthermore, once these ultimate premises are expressed in language, there is nothing subjective or subject-specific about them. At that point, these ultimate premises operate as the foundations of an absolutely objective theory. People are not needed for handling language-expressed abstractions, because machines can perfectly-well handle them too. Therefore, any reference to such a subjective person is totally unnecessary in axiomatic morality.

That's a pretty limited interpretation. — Banno

What else can it do?

There exists a mechanical procedure to verify the purported path between conclusion and premises. It is the ability to carry out such mechanical inference that is defined as "reason". What else would it be?

In this context, there is no mechanical procedure to discover premises. There isn't one to discover conclusions. And even if you already have premises and conclusion, there is no mechanical procedure available to discover the inferential path that connects them.

It is not possible to discover anything new by using reason. It can only be used to verify what exists already. In that sense, it is a relatively weak capability.

And if my reason prescribes something different than yours? What then? — Janus

It is only "reason" if you can feed the premises along with the derivation path into a device so that it can use a purely-mechanical procedure to verify the derivation path as to arrive at the same conclusion. If this is not possible, then it is not "reason".

Note, however, that "reason" is not capable of discovering what premises to use, nor what conclusion to reach, nor what should be the derivation path between premises and conclusion.

Reason is just inferential execution that makes use of a few rewrite rules. It is just a mechanical thing .

Therefore, all this talk about "my reason(ing)" and "your reason(ing)" is absurd. It is based solely on a serious misunderstanding of what reason is, and/or what it can do. Seriously, the practice of glorifying reason is absurd.

'Universality' simply means that nothing can contravene those laws, not that the laws determine "everything". — StreetlightX

Laws backed by experimental testing -- no matter how extensive the testing -- cannot guarantee that nothing will contravene them.

That is a core characteristic of the falsificationist framework of science. It is the the very epistemology of science that prevents it from being truly universal.

Furthermore, deviations into scientism are often caused by forgetting or even wilfully ignoring the falsificationist nature of science. At that point, science can easily degenerate into the object of a strange kind of religion that seeks to worship its fake certainties, the kind of which has recently been killing tens of thousands of people in the opioids crisis. Scientism is therefore even a murderous delusion.

In some systems, not all. Maybe alcontali can tell us which, and why. — tim wood

An example of a system that is weak enough as such that the incompleteness problem does not occur is the Presburger arithmetic. It only uses "0" and "1" as numbers and only addition "+" as operator.

So, it is only capable of saying things of the following form:

1) 0+0=0
2) 0+1=1 and 1+0=1
3) 1+1=0

Universal quantifiers only run over {0,1}. So, in my impression, they may not even be needed. For example, $\forall x$ can be always be replaced by x=0 or x=1 (This is known as quantifier elimination).

The following remark supports that:

The decidability of Presburger arithmetic can be shown using quantifier elimination, supplemented by reasoning about arithmetical congruence (Enderton 2001, p. 188).

Still, there is also the following remark:

Generally, any number concept leading to multiplication cannot be defined in Presburger arithmetic, since that leads to incompleteness and undecidability.

I am not really sure why that is, though. According to the remark above, axiomatizing the following would cause incompleteness. Not sure why, though:

1) 0*0=0
2) 1*0=0 and 0*1=0
3) 1*1=1

I do not completely understand how adding this simple multiplication scheme would prevent quantifier elimination, but the text seems to claim that it does. It has something to do with "arithmetical congruence". (how!?)

So, my take on the matter is that, if quantifier elimination is not possible, because for example that would lead to infinitely long axioms, then the theory really requires first-order logic, and in that case, it will be incomplete.

For example, normal (=Peano) arithmetic runs over an infinite set n $\in$ { 1, 3, 4, ... }. Quantifier elimination would lead to replacing it by sentences that look like: n=1 or n=2 or n=3 or n=4 ... which is an infinitely long sentence. Hence, the use of first-order logic quantifiers cannot be avoided -- to keep the size of the theory's rules finite -- leading to incompleteness.

"For each natural number the following is true" becomes: it is true for 1. It is true for 2. It is true for 3 ... ad infinitum. "There exists a natural number for which the following is true" becomes: It could be true for 1. It could be true for 2. It could be true for 3 ... ad infinitum.

So, my tentative interpretation is that when a theory gets rephrased in propositional logic (=without universal quantifiers), and it will always consist of infinitely-long construction rules, then the theory will be incomplete.

(but issues with "arithmetical congruence" can apparently also cause incompleteness, but I am not finished trying to figure that out yet ...)

Are you saying that sub atomic particles have no spatiotemporal location, spin, momentum, etc. prior to our measurement? — creativesoul

It is not clear. There are different interpretations possible for the Schrödinger's cat thought experiment, one of which is that pre-measurement values are really confused and indeterminate. Einstein did not like this interpretation a bit. But then again, if this interpretation turns out to be resilient to falsification by experimental testing, then subatomic reality is simply to be considered confused.

If I were to make an educated guess, "unprovable" and "undecidable" mean the same thing. — TheMadFool

Undecidable is actually stronger. It means not only unprovable, but also that the negation is unprovable.

So, what exactly did not exist - in it's entirety - prior to the first report of it? — creativesoul

That what they will measure, does not exist, until they measure it.

All things exist in their entirety prior to the first report of them. — creativesoul

In quantum entanglement, any measurement of a property of a particle performs an irreversible collapse on that particle and will change the original quantum state. In the case of entangled particles, such a measurement will be on the entangled system as a whole.

Apparently, such property has no definite value until you measure it.
It is the act of measuring itself that forces the property to adopt a value ("collapse").

Well, that is what they report back from weird corners in nuclear physics.

Einstein had complained about that. He said that quantum mechanics would lead to weird, paradoxical outcomes, and therefore, that there was something wrong with quantum mechanics. What happened later on, however, is that experiments managed to reproduce the weird outcomes that Einstein had complained about ...

If we look at the six main sub-disciplines in philosophy -- there could be other ones -- i.e. ontology, epistemology, ethics, metaphysics, aesthetics, and logic, then they are not all equally useful to me.

Then there is the distinction between philosophy and philosophyOf(X), with X being mathematics, science, religion, or any other possibly domain-specific choice. The classics are usually philosophyOf(X) with X=philosophy itself. They are not necessarily the most interesting part of philosophy. Domain-specific philosophy often ends up being more interesting than ... meta-philosophy.

Ontology is fascinating and in my impression a naturally-arising question. What is mathematics? What is science? What is X? What is Y? The only problem is that there is rarely a single, generally-accepted answer. The method of ontology may not be that effective. The only sub-discipline in philosophy that is possibly even worse in that regard, is aesthetics. Is there even anything objective to aesthetics?

Ontology is often classified under metaphysics, but I disagree with that. For example, the question "What is engineering?" does not appear as metaphysical to me.

Concerning metaphysics, to cut a long story short, it invariably degenerates into an exercise of infinite regress.

Concerning ethics, I see the same problem as in metaphysics. Like Aristotle wrote, if nothing is assumed, then nothing can be concluded. So, ethics without mentioning the foundation from which one reasons, is just another exercise in infinite regress.

Logic has been annexed by mathematics in the 19th century. As far as I am concerned, it is no longer part of philosophy.

It is epistemology that I consider to be the true flagship of philosophy. At some point, I thought that category and/or computability could replace epistemology, but I have abandoned that view. Epistemology can never be a ramified, axiomatic theory. It is about patterns that are detected "empirically" in the abstract, Platonic world of knowledge. It is not possible to predict by using some basic rules what new patterns will end up emerging pretty much spontaneously. Epistemology is much more a question of describing correctly what you see.

Is philosophy useful? Is philosophy meaningful? You could ask the same question about mathematics. Using a process of abstraction, we tend to remove semantics, until none is left. All that remains is empty structure. Is an empty structure useful? No. You will need to fill it up again with semantics in order to achieve some measure of usefulness. So, by using abstraction we seek to obtain useless and meaningless structures. We cannot complain at the same time that the results that we seek, have the properties that we actually wanted in the first place.

Yes, I know what you mean. But humanity operates from within the so-called "hermeneutic circle" of its present knowledge and understanding, and does not need any ultimate premise to ground all subsequent ones. It is as though reasonableness is cumulative as understanding grows, but never absolute, or based on any absolute foundation. — Janus

Yes, agreed.

The hermeneutic circle (German: hermeneutischer Zirkel) describes the process of understanding a text hermeneutically. It refers to the idea that one's understanding of the text as a whole is established by reference to the individual parts and one's understanding of each individual part by reference to the whole. Neither the whole text nor any individual part can be understood without reference to one another, and hence, it is a circle.

There is clearly some truth to that. For example, the foundations of (classical) mathematics are considered impredicative (circular). I personally suspect that all mathematics rest on impredicative foundations, but that is not how the problem is traditionally phrased. So, I will limit the problem to "classical" mathematics (but I do not really believe in that limitation).

Still, mathematics may not have ramified foundations, but the remainder of mathematics is still exclusively built on these (possibly) circular foundations and is therefore ramified.

Mathematics is very intrusive and possibly unavoidable in other spheres, if only because logic has been annexed into mathematics in the 19th century. If mathematics -- which is our stock of syntactic consistency-maintaining formalisms -- has that problem already, everything else (which provides the actual semantics to knowledge) will not be any better ...

Think of science: there are certain things it is reasonable to believe in light of science and others things that are not. The premise here would be the totality of scientific understanding as it is now known, or rather attempted to be known. — Janus

Unlike mathematics, science provides real-world semantics. So, the situation will only be worse there. What's more, there is a lot of academically-accredited ideology masquerading as science. But even real science is at best a Platonic-cave shadow of the true laws of nature, i.e. the true but unknown construction logic of the universe. Scientists may not necessarily stick to advocating theories that have effectively resisted experimental testing, i.e. the sound Platonic-cave shadows. They will happily sell opioids and kill a large number of people in the process, based on mere conjecture.

So it would be unreasonable per se, and not merely on some premise or other, to claim that the earth is flat, for example. — Janus

Yes, agreed. There really are sound Platonic-cave shadows. They obviously exist. Not all purported science is produced by opioid-flogging charlatans. There is science that is real science, i.e. Platonic-cave shadows that are impressively resilient to falsification by experimental testing.

Of course, this real science also exists.

Don't see how this follows from your first paragraph. — Banno

Behaviour guided by Reason, means that the behaviour necessarily follows from some premise. This is possible, but in that case, which premise? Hence, the existence of unknown mental faculties that are not Reason and that also inspire behaviour; most likely more often than Reason.

I think this should be "while there is nothing necessarily reasonable about that ultimate premise". — Janus

Well, if this ultimate premise were reasonable, we would be able to demonstrate how it necessarily follows from another, even more ultimate premise ... which is just a recipe for infinite regress. ;-)

Think you are taking a very tight definition of reason here. Rather in most cases the reasons for our acts are given post hoc. Would you agree? — Banno

A lot of our behaviour -- I would even think most of it -- is inspired by other, unknown mental faculties that are not reason itself. Even the behaviour of producing a new theorem along with its proof from an ultimate premise, is not possibly guided by reason. Gödel proved that this would simply be impossible.

Therefore, post factum rationalization is more often than not, nonsensical.

You cannot discover a theorem merely by using reason. You cannot discover its proof from given foundations merely by using reason. You can actually not even discover these foundations merely by using reason. The use of reason is strictly limited to verifying that the theorem necessarily follows from such foundations.

Therefore, given the relatively small role of reason in knowledge, I do not see why there would necessarily be any guidance by reason in every possible act.

You remain free to choose not to follow reason, but you ought not. — Banno

People never "follow reason". If you reason from X, then you are following X. You always follow the ultimate premise from which you are reasoning, while there is necessarily nothing reasonable about that ultimate premise.

I was making a pointed joke about the OP's argument just being another form of Divine Command Theory. Why did Banno have to listen to Reason? Well, Reason is just always right in what it says. — TheWillowOfDarkness

Reason is always right in what it says about X, if what it says necessarily follows from X. At the same time, you cannot use Reason to find X. Furthermore, if X is nonsense, then anything Reason says about X will also be nonsense.

Reason is a function with arity two: reason(C=conclusion,P=premise). It does not say what P should be (It cannot find P). It does not say what C should be (It can generally not find C either). It only verifies that C necessarily follows from P. It is very, very easy to overestimate the power or impact of this mechanical function. Reason is almost never what it is about.

Come on, you gotta listen to the commands of Reason. — TheWillowOfDarkness

There is only "Reason From".

There is no Reason irrespective of what one is reasoning from. So, if you reason from X, the outcome will be determined by your choice of X. What is your ultimate X? Merely ignoring the question will not make it go away ...

The "existential graphs" of Charles Sanders Peirce are an innovative diagrammatic alternative. — aletheist

I was looking for extended definitions for the term "consistency" when either extending the permissible logic language or the permissible truth values.

In simple propositional calculus, inconsistency arises when the theory is capable of generating both $\phi(x)$ and $\neg \phi(x)$.

In first-order logic, introduction of the universal quantifiers $\forall$ and $\exists$, allows for a new form of inconsistency, i.e. $\omega$-inconsistency, where the theory generates both $\forall x (\phi(x))$ and $\exists x (\neg \phi(x))$.

Higher-order logic allows, for example, quantification over sets: $\forall x \forall A (x \in A \wedge \phi(x))$. What new mischief is possible here?

So, I was looking for what the term "consistency" means in higher-order, many-valued logic. What new forms of mischief are not allowed? What new forms of inconsistency can be introduced by further increasing the power of the logic language?

The Wikipedia page on consistency only mentions Henkin's theorem in that respect, but I frankly do not understand what exactly this theorem means ... ;-)

So it is not possible for an act to be both reasonable and wrong. Yes? — Banno

Garbage in, garbage out! ;-)

OK - so an act is good because reason prescribes it. — Banno

Reason can only verify that a conclusion necessarily follows from its premise. At some point, the process of chaining back from premise to justifying premise will end in a basic premise.

Reason cannot say anything about that basic premise. Attempting to do so anyway, will simply degenerate in infinite regress, which seems to be the hallmark of metaphysics.

The basic premise for morality is either arbitrary or supplied by other, unknown mental faculties. It is never supplied by reason.

Reason says don't get your ethics off the back of a matchbox. — Bartricks

Reason cannot say where to find the basic rules for ethics, simply, because discovering the basic rules for anything is not the job of reason. It is always the job of other, unknown mental faculties to achieve that.

The ambition of (some) moral philosophers to discover the basic rules for ethics through reasoning, is in strict violation of Gödel's incompleteness theorems. Their approach is provably nonsensical.

Is our list of valid argument forms complete? — TheMadFool

There is also an alternative version of propositional calculus that only has one inference rule, i.e. modus ponens, and two operators, AND and OR, which allows for axiomatizing the core rewrite rules of Aristotelian/Boolean two-valued logic.

The basic and derived argument forms then naturally follow from this axiomatization of propositional logic.

Two-valued (Aristotelian/Boolean) logic -- with only the TRUE and FALSE values supported -- is actually a degenerate form of logic that allows for single-value negation results. Not all paradoxical results in two-valued logic also occur in many-valued logic. Therefore, two-valued logic often ends up being considered naive and unusable. For example, the IEEE 1164 (9-valued) and IEEE 1364 (4-valued) international standards disallow the use of naive 2-valued logic in electronic design automation.

the Philosopher King concerns himself with what is true. He collects up all the information and then makes the right choice. — PhilCF

A lot of philosophers believe that the discovery of new knowledge is the result of a rational procedure.

That is why they fail to discover it. Reason is limited to verifying that the knowledge conclusion necessarily follows from its justification. Reason by itself cannot discover what conclusion to make nor what evidence would support such conclusion. That is the prerogative of other unknown, mental faculties.

Why and how did Einstein manage to write his seminal 1905 paper that propelled him to fame? We do not know. It is certainly not the result of reasoning or any other purely mechanical procedure, such as "He collects up all the information and then makes the right choice".

It is a mistake to believe that humanity would be characterized by reason, which is merely a mechanical procedure that machines can carry out too. Humanity is characterized by other unknown mental faculties that allow it to discover new knowledge.

Therefore, "collecting information and making the right choice" is a very, very weak principle. This kind of mechanical procedures do not allow for changing the ball game. That is also, absolutely not how Einstein discovered special relativity in 1905. It is rather how the software controlling a robot in a factory steers the details of the production of new widgets.

Science is pretty much a Platonic cave shadow of what the real, unknown laws of nature are. At best, science has an uncanny ability to resist experimental testing. At worst, it is just a citation carousel for which the corrupt, academic journals are so well-known.

That is no different for neuroscience. The human brain is not human technology, and its true construction logic is simply unknown. If you really understand it, then you can build it yourself. Neuroscience apparently can't. Hence, what they know, can only be much more limited than that. The proof is always in the pudding.

What triggers Hate? Do you embrace it? Is hate a good or evil attribute for us to have? — Gnostic Christian Bishop

Since the emotion of hate exists, it must have some kind of useful survival value. Just like all emotions, however, you will need to remain in control of them, because otherwise they could end up controlling you.

I understand that the Theory of Everything is expected to cover all physical phenomena. That human group interactions always has exceptions to any law designed for it indicates either that there can't be a theory of everything or that the mind is not physical. — TheMadFool

In his lecture, Gödel and the end of physics, Stephen Hawking argued that it is Gödel's incompleteness theorems that prevent the discovery of the theory of everything (ToE):

Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery. Without it, we would stagnate.

Existing scientific knowledge is not one unified theory that builds on the true construction logic of the universe, and therefore, does not represent the true laws of nature. Existing scientific knowledge is rather some kind of Platonic shadow of the true laws of nature.

Well it is nice to have opinions. — Bartricks

Reason needs to stick to what it is meant to do, i.e. to verify a conclusion from its evidence.

The idea that you could discover new knowledge by reasoning is preposterous, especially, taking into consideration that it would imply the existence of a purely mechanical procedure to achieve that. Such procedure cannot possibly exist.

Any arbitrary knowledge statement can be encoded as a natural number. The question then arises: Can we run through all natural numbers, and check if the number represents a knowledge statement that is logically true? This procedure cannot possibly exist because it would also solve Alan Turing's halting problem, while we have another proof that guarantees that this cannot be done.

That procedure cannot possibly exist. Assume that we have a sound (and hence consistent) and complete axiomatization of all true first-order logic statements about natural numbers. Then we can build an algorithm that enumerates all these statements. This means that there is an algorithm N(n) that, given a natural number n, computes a true first-order logic statement about natural numbers, and that for all true statements, there is at least one n such that N(n) yields that statement. Now suppose we want to decide if the algorithm with representation a halts on input i. We know that this statement can be expressed with a first-order logic statement, say H(a, i). Since the axiomatization is complete it follows that either there is an n such that N(n) = H(a, i) or there is an n' such that N(n') = ¬ H(a, i). So if we iterate over all n until we either find H(a, i) or its negation, we will always halt, and furthermore, the answer it gives us will be true (by soundness). This means that this gives us an algorithm to decide the halting problem. Since we know that there cannot be such an algorithm, it follows that the assumption that there is a consistent and complete axiomatization of all true first-order logic statements about natural numbers must be false.

Therefore, the approach to use a rational procedure revolving around reason in order to discover new knowledge is nonsense. It cannot possibly work. Knowledge is produced by other, unknown mental faculties that are essential to the discovery of knowledge. Reason alone cannot possibly achieve this.

What is Reason? — frank

This is indeed a really important question.

I think that reason is no more than the ability to verify that a conclusion necessarily follows from its evidence. It is a purely mechanical procedure that machines can also carry out. Reason itself does not produce evidence nor conclusions. That is achieved by other, unknown mental faculties.

In other words, you cannot discover new knowledge merely by reasoning. That is in my opinion the reason why metaphysics, i.e. trying to discover new knowledge by reasoning, is such a worthless endeavour.