I disagree. Science can exist even if such a theory is impossible. It isn't essential to science IMO, so it cannot be its 'ultimate' goal. — boundless
https://www.scientificamerican.com/article/will-scientists-ever-find-a-theory-of-everything/
Wrangling the final (and, surprisingly enough, weakest) force, gravity, is a much harder task: Electromagnetism, as well as the strong and weak forces, can be shown to fundamentally follow the strange-but-calculable quantum rules. Yet gravity is, at present, best described by Einstein’s general theory of relativity, which concerns the universe at larger scales. These two frameworks do not play nice with each other; quantum mechanics and relativity effectively dictate separate and contradictory rules for the cosmos.
https://nautil.us/do-we-need-a-theory-of-everything-237888/
We need a theory of quantum gravity because general relativity and the standard model are mathematically incompatible. So far, this is a purely theoretical problem because with the experiments that we can currently do, we do not need to use quantum gravity. In all presently possible experiments, we either measure quantum effects, but then the particle masses are so small that we cannot measure their gravitational pull. Or we can observe the gravitational pull of some objects, but then they do not have quantum behavior. So, at the moment we do not need quantum gravity to actually describe any observation.
https://philosophy.stackexchange.com/questions/49613/why-do-we-want-to-achieve-unified-theory-of-everything
During its early phase our cosmos was a world with extremely high energy enclosed in an extremely small domain of space. There was the very active interaction of particles and radiation in a highly curved spacetime. These phenomena cannot be explained by applying the theory of relativity and quantum field theory in separation. We need a unified theory, a theory of quantum gravity. Such theory does not exist up to now.
It is actually the ultimate goal of science:Says who apart from you? Can you cite some source for this opinion? — apokrisis
https://en.m.wikipedia.org/wiki/Theory_of_everything
A theory of everything (TOE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe.[1]: 6 Finding a theory of everything is one of the major unsolved problems in physics.[2][3]
https://www.hawking.org.uk/in-words/lectures/godel-and-the-end-of-physics
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.
And why would maths be a judge of how physics proceeds anyway. — apokrisis
https://www.newscientist.com/article/mg26134773-000-why-physicists-are-rethinking-the-route-to-a-theory-of-everything/
Why physicists are rethinking the route to a theory of everything
Physicists’ search for a theory that explains all reality in one framework appeared to have stalled. But now they are reinvigorating the hunt by exploring a wild landscape of abstract geometry.
That’s how physicists feel about the theory of everything, a putative “final” framework that would explain all reality in one fell swoop. This is the ultimate goal for physics, with Stephen Hawking once memorably writing that to find it would be to know “the mind of God”.
https://www.hawking.org.uk/in-words/lectures/godel-and-the-end-of-physics
Thus a physical theory is self referencing, like in Godel’s theorem. One might therefore expect it to be either inconsistent or incomplete. The theories we have so far are both inconsistent and incomplete.
These are sweeping statements. But are they more than your own personal opinion? — apokrisis
And isn't that the healthy outcome? Some kind of mutual connection between maths and physics as cultures of inquiry? No need to make it a contest between logical rigour vs experimental validity. We have to come at nature from both these directions to grasp its truth. — apokrisis
Meanwhile, it is crucial not to say, "G can not be demonstrated from the axioms of mathematics", since that is plainly false. — TonesInDeepFreeze
So what? The incompleteness theorem has nothing to do with that, since the incompleteness theorem regards formal theories in which the axioms are explicit and such that theorems are strictly from explicit axioms. — TonesInDeepFreeze
Isn't a lot of what you write based on the fact that science doesn't explain science, mathematics doesn't explain maths, and so on? — Wayfarer
https://www.hawking.org.uk/in-words/lectures/godel-and-the-end-of-physics
Thus a physical theory is self referencing, like in Godel’s theorem. One might therefore expect it to be either inconsistent or incomplete. The theories we have so far are both inconsistent and incomplete.
I didn't read the whole speech but Hawking said this about incompleteness — TonesInDeepFreeze
"G can not be demonstrated from the axioms of mathematics." That's really bad and it is the kind of thing that leads people (who don't know the theorem) to make unfortunate inferences about the theorem. — TonesInDeepFreeze
https://en.wikipedia.org/wiki/Axiomatic_system
In practice, not every proof is traced back to the axioms. At times, it is not even clear which collection of axioms a proof appeals to.
Logic might more easily describe physics. — Fire Ologist
I suppose, the Persians had a larger oppression of the lower classes by the rulers. The Persia was an Oriental Despotism, and the Greeks considered all Persians as the slaves of their king. — Linkey
In all these empires, the monarchs and his feudals took a lot of women from the lower classes into their harems, and I heard that rather often the men from the lower classes remained without women because of this. — Linkey
The point of an education is to lift us above the socio-cultural constraints of an oral world order – socially constructed in words – to a technocratic or rational world order. — apokrisis
Thank you, you spent a lot of time gathering all those sources, to manage not to answer my question whatsoever. This is a masterpiece. Once again, I asked "Any solid proof? And not just isolated cases, but a systemic critique: embezzlement... And what about other organizations?" And, instead of providing statistics, a global proof, scientific studies, you wrote about isolated cases from a very few organizations, actually mostly just one. — LFranc
Also, in other threads I've commented on the matters of the incompleteness theorem in philosophy of mathematics. I don't have comments at this time on the incompleteness theorem in connection with science, epistemology, ontology and metaphysics. — TonesInDeepFreeze
I usually take a (logistic) system to consist of a language, axioms and inference rules. And I take a theory to be a set of sentences closed under provability. A theory may be the set of theorems in a language and derivable from axioms with rules. So, with each system, there is the theory induced by that system. — TonesInDeepFreeze
You don't have to go into details merely to avoid egregiously mischaracterizing the subject. I stated the theorem in just one sentence, and using only ordinary words. Plus the other dangling sloppiness in what you wrote. — TonesInDeepFreeze
But you start out by mentioning logic in general, thus giving the impression that systems in general are incomplete, thus adding to the general confusion so prevalent on this point. — TonesInDeepFreeze
Incompleteness doesn't pertain to systems in general. Only to systems of a very certain kind. — TonesInDeepFreeze
"know the construction logic of". What is a "construction logic"? Maybe you mean the construction of the syntax? Better yet, just to say "the syntax rules". — TonesInDeepFreeze
What are some criticisms in mathematics of the identity of indiscernibles? — TonesInDeepFreeze
Principle 2, on the other hand, is controversial; Max Black famously argued against it.[5]
Black, Max (1952). "The Identity of Indiscernibles". Mind. 61 (242): 153–64.
Unlike your post, that quote seems at least fairly clear and doesn't make an overbroad mischaracterization of incompleteness. — TonesInDeepFreeze
http://www.sci.brooklyn.cuny.edu/~noson/True%20but%20Unprovable.pdf
There are more true but unprovable statements than we can possibly imagine.
We have come a long way since Gödel. A true but unprovable statement is not some strange, rare phenomenon. In fact, the opposite is correct. A fact that is true and provable is a rare phenomenon. The collection of mathematical facts is very large and what is expressible and true is a small part of it. Furthermore, what is provable is only a small part of those.
Agreed. The identity of indiscernibles is criticized in other areas of mathematics.No, you said that the only law that "withstands scrutiny" for constructivism is non-contradiction. And that is false. — TonesInDeepFreeze
The law of identity is allowed by constructivism. It "withstands foundational scrutiny" by constructivism. No strawman.
13m — TonesInDeepFreeze
That is ridiculously overbroad and vague. — TonesInDeepFreeze
https://www.hawking.org.uk/in-words/lectures/godel-and-the-end-of-physics
What is the relation between Godel’s theorem and whether we can formulate the theory of the universe in terms of a finite number of principles? One connection is obvious. According to the positivist philosophy of science, a physical theory is a mathematical model. So if there are mathematical results that can not be proved, there are physical problems that can not be predicted.
And constructivism uses the law of identity, so it is not the case that the only one of those three laws allowed by constructivism is non-contradiction.
1h — TonesInDeepFreeze
n context of modern logic, 'decidable' means either (1) the sentence or its negation is a theorem, or (2) There is an algorithm to decide whether the sentence is a member of a given set, such as the set of sentences that are valid, or the set of sentences that are true in a given model.
LEM is not that. LEM syntactically is the theorem: P v ~P, and LEM semantically is the theorem that for a given model M, either P is true in M or P is false in M (so, either P is true in M or ~P is true in M) — TonesInDeepFreeze
The law of identity, the indiscernibility of identicals, and the identity of indiscernibles are different. What specific problem with the law of identity are you referring to? — TonesInDeepFreeze
You think that the only law that constructivism allows is non-contradiction? You've gone through all other laws and found that they are not constructivisitically acceptable? — TonesInDeepFreeze
https://en.wikipedia.org/wiki/Law_of_thought
The title of George Boole's 1854 treatise on logic, An Investigation on the Laws of Thought, indicates an alternate path. The laws are now incorporated into an algebraic representation of his "laws of the mind", honed over the years into modern Boolean algebra.
So what exactly did Godel add to our body of knowledge? — Gregory
There being cases in which a law does not apply. — Lionino
https://en.m.wikipedia.org/wiki/Constructivism_(philosophy_of_mathematics)
Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded middle. This law states that, for any proposition, either that proposition is true or its negation is. This is not to say that the law of the excluded middle is denied entirely; special cases of the law will be provable. It is just that the general law is not assumed as an axiom.
The law of non-contradiction (which states that contradictory statements cannot both be true at the same time) is still valid.
https://en.m.wikipedia.org/wiki/Law_of_noncontradiction
The law of non-contradiction is alleged to be neither verifiable nor falsifiable, on the ground that any proof or disproof must use the law itself prior to reaching the conclusion. In other words, in order to verify or falsify the laws of logic one must resort to logic as a weapon, an act that is argued to be self-defeating.
But for the natural speaker what is lacking is a relation between the two things. — Leontiskos
The ruling class "listens" to the general public so long as they remain inside of their designated theater of action. — ucarr
https://www.britannica.com/topic/kulak
Kulak, (Russian: “fist”), in Russian and Soviet history, a wealthy or prosperous peasant, generally characterized as one who owned a relatively large farm and several head of cattle and horses and who was financially capable of employing hired labour and leasing land.
At the end of 1929 a campaign to “liquidate the kulaks as a class” (“dekulakization”) was launched by the government.
The standing army is the guard rail that prevents everyman crossings into elite circles: — ucarr
If science does not and cannot explain knowledge AT ALL ...This is why philosophical thinking is "privileged": — Constance
Since the Republicans are turning away from the vision of the Founding Fathers towards the ancient blood royal system of governance by divine rule of monarchs, and the Democrats are holding firm to the vision of the Founding Fathers who turned away from royal blood to individual freedom — ucarr
Even if that's true about the Dubai, it does not contradict what I have said: the rulers of UAE can't allow themselves to become despots, because otherwise they will get a revolt. — Linkey
Bananas still don't grow on Burj Khalifas. — BC
BTW, readily available education, housing, and medical care are not a frill -- they are essential components of a successful society--both socially and economically. — BC
One might well ask the residents of Dubai where they will get their food when the age of oil is over --certainly not by their own efforts, being in the desert as it is. Bananas don't grow on Burj Khalifas. — BC
to extrapolate this kind of action is ridiculous and flawed — QuixoticAgnostic
The food that the city consumes does not come from the fields immediately next to it... — Lionino
And Dubai isn't zero tax. It has import/export taxes, property taxes, service taxes, etc. It just doesn't cut money out of your income directly. — Lionino
If it had zero tax it would collapse — Lionino
So I wonder why every Instagram/Youtube clown wants to move to Dubai, but not engineers and philosophers. — Lionino
Because it is in the desert. — Lionino
They can... they are both surrounded by fields. — Lionino
Dubai is a bubble built on luck — Lionino
We all know what the rich Arabs of Dubai pay Instagram models to do on their bodies. Dubai is much more degenerate than it meets the eye. — Lionino
If they had found no oil, there is no universe in which Dubai would have been more than a fishing village, like it was 50 years ago. — Lionino
That's perfectly reasonable. Except that the ideal is impractical. Everyone has to make their living somehow. Independence is a mirage. We have to settle for an independent mind, which is not impossible, though difficult - and requires courage. — Ludwig V
Leiden or Bologna — Lionino
The Emirate of Dubai offers just one product, which is globally tremendously and increasingly popular, i.e. freedom from the aberrations caused by democracy:Martin Luther said that people were better off being ruled by a smart Turk than a dumb Christian. — BC
https://en.m.wikipedia.org/wiki/Dubai
Dubai has been ruled by the Al Maktoum family since 1833; the emirate is an absolute monarchy.
The city has a population of around 3.60 million (as of 2022).[19] More than 90% of the population are expatriates.
461,000 Westerners live in the United Arab Emirates, making up 5.1% of its total population.
Dubai is the second most expensive city in the region and 20th most expensive city in the world.