There's one Holy Grail there if one could make it a true mathematical theorem: if that "objective truths in logic and math are typically computable and provable, while subjective ones involve self-reference, evading such formalization" could be made into "objective truths in logic and math are all computable and provable, if there isn't self-reference that leads to subjectivity". Or something like that.You rightly emphasize the subjective-objective distinction in the context of Wittgenstein’s hinges and Gödel’s incompleteness theorems, framing subjectivity as tied to self-referentiality and objectivity as a “view without a viewpoint.” I find this interesting, particularly your point that objective truths in logic and math are typically computable and provable, while subjective ones involve self-reference, evading such formalization. Your reference to Wittgenstein’s Tractatus (3.332–3.333) and his solution to Russell’s paradox is spot-on: Wittgenstein identifies self-referentiality as a source of logical trouble, arguing that propositions or functions cannot contain themselves. This insight resonates with Gödel’s incompleteness theorems, which, as you note, cleverly navigate self-referentiality (e.g., the statement “This statement is unprovable in the system”) without falling into the traps of Russell’s paradox. — Sam26
Yes, once you are an acting part of a universe you are trying to model, the problem arises. Many times when you don't notice the problem, you get to a problem of infinite regress. Yet do notice that self-referential loops can get to a "objective grounding". If we have something like a self-fulfilling prophecy, that can indeed be modeled and computed.In your market e.g., the “hinge” might be the assumption that prices reflect aggregate behavior, but using the model to act within the market introduces a self-referential loop that defies objective grounding (if I understand what you're saying), which is akin to the unprovable truths in Gödel’s systems or the unquestioned certainties in Wittgenstein’s hinges. — Sam26
I agree. The uncomputable are really special occasions to the norm. At least when we try to make objective scientific models.Your point, that “not all systematic thought can be brought back to grounded foundations,” is a helpful perspective, but I’d argue it complements rather than contradicts the my claim. — Sam26
Yes, exactly. There isn't any problem with having Gödel's completeness theorem and incompleteness theorems being true at the same time.The paper doesn’t assert that all thought lacks grounded foundations, but that sufficiently complex systems (epistemic or mathematical) require ungrounded foundations within their own justificatory scope. Simpler systems, like those covered by Gödel’s completeness theorem or basic linguistic practices, may achieve internal grounding, but that the parallel with Wittgenstein and Gödel emerges in domains where complexity has limits, necessitating external or unprovable foundations. — Sam26
• Latvia, Lithuania, Estonia are European countries’ puppets, says Lavrov (TASS · 2025 Jun 10)
After they have been bombed by foreign state, why would Iranians start killing each other?If the Iranian regime will sign quickly a treaty with Trump or Israel, this regime will definitely sign it own death. From the first day that there will be no more hostilities, the Iranians will ask themselves why their regime brought these misfortunes to them --and most probably will start killing each-other. But if the Iranian regime endures, then with the passing of the time I see more and more Iranians being united by the resistance towards Israel. — Eros1982
Are political assassinations in Minnesota, the killing of Melissa Hortman and her husband and the attempt on State Senator John Hoffman and his wife also a - big whoop or are they something else to you?Some populist politician said something inflammatory - big whoop. — Tzeentch
(BBC) Investigators reportedly found a list of 70 "targets", including the names of state Democratic politicians, in a vehicle the suspect drove for the assassination.
Walz, congresswoman Ilhan Omar, Minnesota's two US senators, Amy Klobuchar and Tina Smith, and state Minnesota Attorney General Keith Ellison were on the hit list, according to local media.
Locations for Planned Parenthood, which provides abortions and contraception, were also on the list, a person familiar with the investigation told the Minnesota Star Tribune.
I don't have to imagine that.Imagine you have a homicidal and fanatical enemy in your region that is building a mighty weapon. — BitconnectCarlos
No matter how much you say about the logic and soundness of a pre-emptive attack, it still is an attack and there's no question about who is the attacker. Besides, some say an attack is the best defense. Just take it as a fact, admit it to yourself and don't be such a hypocrite.As a last resort, if you were to attack your enemy's designs, would it truly be you starting the war? Or was it your fanatical enemy who ceaselessly worked towards designing a devastating weapon? — BitconnectCarlos
Let's hope that Trump then doesn't escalate and sticks to his current position then.No, but the situation could escalate. — BitconnectCarlos
So you accuse president Truman to be a fanatic leader with zero humanitarian concern? That's a new one from you, @BitconnectCarlos.Do you have any doubt that we've had national leaders in the past 100 years who would have used a nuclear warhead had they had one at their disposal? Hitler, for one. We've had fanatical world leaders with zero humanitarian concern. Has humanity fundamentally changed since then? We're talking about our fathers and grandfathers here. — BitconnectCarlos
EXCOMM considered the effect on the strategic balance of power, both political and military. The Joint Chiefs of Staff believed that the missiles would seriously alter the military balance, but McNamara disagreed. An extra 40, he reasoned, would make little difference to the overall strategic balance. The US already had approximately 5,000 strategic warheads, but the Soviet Union had only 300. McNamara concluded that the Soviets having 340 would not therefore substantially alter the strategic balance.
That's not the contrary.I was often taught the contrary: That two nuclear powers would never go to war because it would be irrational and mutually assured destruction. — BitconnectCarlos
To take the step and use nuclear weapons, even small tactical ones, is huge. That I agree. Hence I don't think that the IDF would use nukes to destroy the underground facilities that Iran has.Nuclear war isn't the likely outcome, but it doesn't need to be the likely outcome for it to be terrifying. — BitconnectCarlos
Israel started this war, not Iran.Even if we knew there would be no nuclear war: Who loves death more? The secular or the Islamic fundamentalists? Fundamentalist religious countries (like Iran) that are nuclear do not bode well for a West that wants to live and let live. A nuclear Iran has much more bargaining power/influence, plus the possibility of proliferation, where they had their dirty work off to others to maintain plausible deniability. — BitconnectCarlos
The only thing I would thank them if they can deliver on time the weapons systems Finland bought from them.You should be thanking Israel. — BitconnectCarlos
I think it's just simply.... lovely.The military parade is amazing. There should be one every year. — NOS4A2
Lol.Trump tried to fight the lobby and lost. — Tzeentch
Did I say that?Anyone who cheers on rioters flying foreign flags and burning the flags of their host country is not a "normal American." — BitconnectCarlos
There's a long way still to go with the Trump administration.Maybe if Trump starts to abuse his authority further but we're not there yet and the culture war is enough of a distraction currently to get people to accept what's going on. — Mr Bee
Everything is about objectivity and subjectivity, actually. It's not merely a psychological issue, but simply logical. We can easily understand subjectivity as someone's (or some things) point of view and objectivity as "a view without a viewpoint". To put this into a logical and mathematical context makes it a bit different. Here both Gödel and Wittgenstein are extremely useful.A crucial distinction emerges between subjective and objective dimensions of these certainties. While our relationship to hinges involves unquestioning acceptance, this certainty is not merely psychological. These assumptions are shaped by our interactions with a world that both constrains and enables our practices. The certainty reflected in our actions has an objective component, as it emerges from our shared engagement with reality and proves itself through the successful functioning of our practices. — Moliere
3.332 3.332 No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the “whole theory of types”).
3.333 A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself. If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition “F(F(fx))”, and in this the outer function F and the inner function F must have different meanings; for the inner has the form ϕ(fx), the outer the form ψ(ϕ(fx)). Common to both functions is only the letter “F”, which by itself signifies nothing.This is at once clear, if instead of “F(F(u))” we write “There exists g : F(gu). gu = Fu”.
Herewith Russell’s paradox vanishes.
If I understand correctly what you mean by grounded / ungrounded foundations, I would say it differently: Not all systematic thought can be brought back to grounded foundations. Usually we can use axiomatic systems and get an objective model, but not allways.I have argued for a fundamental parallel between Wittgenstein's hinges and Gödel's incompleteness results: both demonstrate that systematic thought requires ungrounded foundations. By examining how epistemic and mathematical systems share this structural feature, we gain insight into the nature of foundational certainties across domains of human understanding. — Moliere
I didn't know this. Thank you!True, but "heart" had a much different meaning in both the Hebrew and Greek context (see below). The heart is often referred to as the "eye of the nous," the inner-most part of the mind that receives the highest forms of intelligible illumination in the Patristics (gnosis). It is not primarily a symbol for "emotion" or "sentiment," but often instead of the deepest possible sort of knowledge. Early Christianity is very much a religion of Logos in a way perhaps at odds with some contemporary sentimentalism. — Count Timothy von Icarus
The idea is that computers (or Turing Machines) follow algorithms. An algorithm is a procedure used for solving a problem or performing a computation and act as an exact list of instructions that conduct specified actions step by step.I find it interesting that you mention computers' inability to motivate themselves. Reason has often been reduced to computation in modern thought (computational theories of mind might play a role here, although the shift predates them by centuries). On this view, the computer is sort of an idealization of rationality. But if it cannot act, does that mean all action comes down to a sort of non-rational sentiment? Something else? — Count Timothy von Icarus
I think that here really lies some awesome axiom that is simply missing from our philosophical and mathematical vocabulary. Once we know that axiom, everything makes far more sense.Completely agree! I think the ‘meta-algorithm’ you refer to might be close to what Roger Penrose was getting at in his Emperor’s New Mind. But overall in agreement with your post. — Wayfarer
What – in layman’s terms – is the trick in Gödel’s incompleteness theorem?
The trick is the same as in the barbar paradox and all other real paradoxes. The trick is to make a sentence, a logical statement and …
1. to refer it to itself (self reference)
2. and then to deny it. (negation)
That’s the whole trick. With this combination, any classic formal system can be invalidated.
A rich foreigner with an agenda can be quite dangerous—probably more dangerous than a foreign mugger. The latter is an obvious threat, while the former has the potential to do quite a bit of harm with their great resources. We must look at the values and allegiances of those entering our countries. Our elite universities in the US are flooded with very wealthy foreign students who have zero allegiance to the US, and I think our country is finally waking up to the fact that we've been sold out. — BitconnectCarlos
Says the person living in a far more multicultural country than Sweden. But how do you get to 60%?Sweden is responsible for managing Sweden. Currently, 80% of the population is native Swedes; would they be okay with this number going to 70%? 60%? What kinds of cultural changes would we see at those levels? Do Swedes value their culture, or is it more defined by its openness and receptivity? What cultures are they importing? — BitconnectCarlos
And just how is your President doing with those mass deportations? Last time he ended up deporting far less than other presidents, including his successor Joe Biden.Maybe mass deportations are needed. — BitconnectCarlos
(BBC 29th May 2025) A US federal court has blocked President Donald Trump's sweeping global trade tariffs, in a major blow to a key component of his economic policies.
The Court of International Trade ruled that an emergency law invoked by the White House did not give the president unilateral authority to impose tariffs on nearly every one of the world's countries.
The New York-based court said the US Constitution gave Congress exclusive powers to regulate commerce with other nations, and that this was not superseded by the president's remit to safeguard the economy.
The White House has asked the court to block the order suspending tariffs while it appeals the case.
Pretty much as I said above. It is, to allude to a rather controversial, but also profound, book, ‘the Reign of Quantity’. One of the discussions that prompted this thread, was about how qualia (an item of academic jargon in philosophy of mind referring to the qualities of subjective experience) can be explained away as illusion. — Wayfarer
The first golden rule is that if it is commonly understood that the foreign people bring money into the society, foreigners will be accepted: nobody has a problem with tourists, with millionaires or needed talented professionals moving into your nation. If somebody is publicly against there being tourists, the person will be confronted by angry people who get their life earnings from the tourist trade. But if those tourists don't bring in money, just roam around and sleep in public parks, they will be immediately despised everywhere. Foreigners that just want to take your wealth and have no desire to appreciate anything else are usually in history called the invading enemy. What people feel about them is quite universal and these attitudes have a long history.There's a difference between accepting immigrants who appreciate the country they're emigrating to & work legitimate professions versus those who come, e.g., due to a religious duty to spread their religion or to exploit resources. Every nation has the right to monitor its borders and set its immigration policies. Some immigrants easily assimilate, while others have no desire to. — BitconnectCarlos
Please focus on what the disagreement here is. I don't think there is a genocide taken place, something like the Turks did against Armenians or what the Hutus did against Tutsis during the Ruandan civil war. There simply aren't the piles of white people lying around with either South African soldiers or jubilant crowds with machetes. A genocide looks like a Zombie movie with the exception that the Zombies aren't the brain eating living dead, but totally ordinary people minding their business whereas the "heroes" in Zombie movie are just like how they are portrayed in the movies, except that they just think that other people are zombies and killing them will make the world a better place.Just because a source is biased or has an agenda doesn't mean it's wrong. — BitconnectCarlos
But if the source is telling that there's a genocide when there isn't a genocide, it's wrong. That there are tensions and hostility against an ethnic group can be totally true.Just because a source is biased or has an agenda doesn't mean it's wrong. — BitconnectCarlos
Have you then read the Israel killing civilians in Gaza and the West Bank?Handwaving it under the banner of 'It's not yet genocide' is not the type of thing I would expect from rational people. — Tzeentch
Or the apologetics of those that think actually Russia was the real victim in the Ukraine war. Yeah, I agree.In fact, it reminds me more of the type of apologetics the Israeli government and its supporters like to spin. — Tzeentch
Reflecting on to other countries and not the one the one you live in is one way to sell a message that otherwise wouldn't fly, because a) it wouldn't be appropriate or b) usually people are aware of the situation in the country they live in.I don't need to defend shit because there's no genocide. You'd rather follow the interpretation of a murderous idiot than sensible South Africans just so it fits in your racist worldview.
Also note that the farmers killed are predominantly not white. So there's that. Sigh. — Benkei
Look, I understand it's a touchy issue for you, but the obvious reality that you indeed have these kinds of politicians in various countries, including Israel. And when there's an outright violent conflict and hatred among the different people, then the there is the real fear of a genocide.Regardless of country, it is terrifying when you have prominent politicians (Malema's party controls 10% of Congress) in mass rallies glorifying the murder of another ethnic group, especially where there are pre-existing ethnic tensions. We should have learned this from Rwanda, where the language used played a key role in dehumanization. — BitconnectCarlos
With the example of Zimbabwe, I tried to show you that this isn't the case. Partisan actors will think this way because they simply won't be interested in something that doesn't promote their cause. Put them aside and there's still the ability to get an objective view about events, even if you need to find it out yourself with a little work.If the shoe were on the other foot and whites were imposing racist laws and seizing land from blacks and screaming genocidal chants at mass rallies, the world would be all over it (and rightfully so). Yet double standards define our times. It is seen as fine when an "oppressed" or formerly oppressed group behaves oppressively, and the politically correct thing is to look the other way and not blame them. — BitconnectCarlos