This shows how you really don't understand Europe. You think that US and Russia act and behave in Europe similarly, because they are Great Powers. I a...
From the quote, the only difference between recursion and real recursion, that I can think of, is using recursion for reals, in other words recursive ...
Yes, I understand that it's a part you need in Gödel-numbering, to make the number that holds the logical sentence. Once you have both addition and mu...
Everybody even Ukraine would have been totally happy with Ukraine being neutral... assuming that Russia wouldn't have intension of annexing large part...
Was denazification on the table in 2014? But I agree, Russia has been quite consistent in attempting to annex Ukrainian territory irrelevant of NATO. ...
This is pure "what if" arguments, which are unprobable and now . As noted far earlier in this thread, there were aspirations for annexing Crimea right...
And that was my basic question: why having both addition and multiplication entail incompleteness? How does it entail incompleteness? Is it that with ...
Indeed that's interesting. With Robinson arithmetic you rule out mathematic induction and the axiom schema. But you do have the successor function, ad...
I agree with Lichtman's argument on the power of incumbency. If there are no quagmire-conflicts going on, if the voter's 401K's are up and there is no...
With a formal system with Peano Arithmetic we already get the results of Gödel's incompleteness. Hence this has been shown earlier than Yanofsky's pap...
Without any help from the West Russia would have likely obtained it's objectives. Which would have been even more shitty for the country. Likely they ...
With denazification and all that? Lol. That's what I was writing about. Trump makes absolutely shitty peace deals. The peace deal with the Taleban was...
Aren't these symbolic systems of mathematics extremely useful in the US elections too? Isn't counting the votes quite essential in free and fair elect...
I'm always intrigued why a conversation about math morphs to conversation about physics. Why wouldn't a discussion of mathematics morph into a convers...
Trump has vowed that he could end the war in Ukraine in "one day" when President. Even if it's the ordinary populist Trumpian rhetoric from Trump, we ...
First it was Schiff, then it was Chuck Schumer who have pushed to Biden to give up his candidacy. But the Democrats have really a problem even this wa...
I agree, also with Yanofsky. Cantor's proof is the simplest form of diagonalization that has all the "problematic" consequences, once we start to look...
Definitely. It should be obvious that with infinity or anything infinite, you have incommensurability that you don't have when just handling finite nu...
Thanks to both of you. And no, it isn't nitpicking. Of course we can talk about surjective or injective functions. What for me it's very irritating th...
If Biden continues to be Democratic candidate, I think after yesterday Trump will very likely will be the next President. Now way to deny this photo b...
Calculus or analysis is the perfect example of us getting the math right without any concrete foundational reasoning just why it is so. Hence the driv...
Ok, this is very important and seemingly easy, but a really difficult issue altogether. So I'll give my 5 cents, but if anyone finds a mistake, please...
Writing x^2 means x². A bit lazy to use this way of writing the equation. Exactly. With limits we want to avoid this trouble. Yet it isn't actually a ...
Randomly picking some action from as long as it is not Ak is surely not "do something else". It is an exact order that is in the program that the Orac...
:grin: Both Newton and Leibniz figured out the way to make a derivation by using infinitesimals. Let's say that we want to make a derivation of x^2 = ...
Isn't that a bit too much to put on the Basic Law V? If we have problems with infinite sets, why would you throw away also everything finite? How abou...
I think it's good to go this through here. So the basic problem was that "Naive Set Theory" of Frege had this Basic Law V, an axiom schema of unrestri...
Yes, But notice that the Oracle staying silent can be also viewed as an input. So when the Oracle is silent and doesn't make a prediction, the Thwarte...
Thanks! Again a fine article, @"fishfry", that I have to read. I've been listening to Youtube lectures that Joel David Hamkins gives. They are informa...
The effects of diagonalization are important and should be discussed here in PF. It's great that this pops up in several threads and people obviously ...
And here's then the problem: not only Plato started from counting, but even today Set Theory starts from counting too with the Peano Arithmetic. It re...
Well, we can talk about the set of all natural numbers ?, right? I don't think that it's misleading. Notice that it's just a model showing just how st...
Actually not. The counting starts from the dog that Plato defined to be 1. The action itself defines the whole system of counting, hence the one dog t...
I agree. In group 2 social cohesion and solidarity is far more easier to prevail. And usually group 2 countries are far more smaller, which makes demo...
Well, another reason is that making movies is actually very expensive. If you make a movie in Finnish, basically there's only +5 million people who un...
The whole story is about the problem of definition that math has. And for the Grand Order you refer to, there is the Well Ordering Theorem. In the sto...
It all comes down to rule2 and how we interpret rule1. By rule2 if there is an amount, there's a dog for it. If nothing is an amount, then there is a ...
What do you think yourself then? (Or if you have already given a satisfying view, please refer on what page you did it.) It should be totally evident ...
Well, a dog eating ? of Plato's dog's food amount isn't either a natural number, so would you deny it to be a dog? And what about transcendental dogs?...
What if the positivist are indeed partly right, but they won't get the answer they would want to hear? Hasn't this been obvious starting from Hilbert?...
Yes, but I don't unfortunately believe it. United Kingdom declared war to Finland in December 5th 1941. I assume the both countries were then democrac...
Notice in the story Athena, the goddess of wisdom, might very well know the answer as she did use the two philosophers for amusement for the other god...
If so, please be careful @"Linkey". And welcome to the Forum. All the Russian emigrants living in my country that I've spoken to don't like what Putin...
Before going further, Let's remember first that democracy is a system of government and a state or a country is a different thing. Even if the OP does...
There's many things they don't teach in school when looking at what my children have to study. Usually the worst thing is when the writers of school b...
Not only is it one problem, I think it's been the largest problem there has been in mathematics. Just look at the long historical debate around the ma...
There's a lot that in mathematics is simply mentioned, perhaps a proof is given, and then the course moves forward. And yes, perhaps the more better c...
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