"the sentence or its negation is a theorem" ignores the existence of true but unprovable sentences. So, it should rather be "the sentence or its negat...
You can perfectly know the construction logic of a system but that does still not allow you to know its complete truth. So, even if we manage to figur...
The most problematic foundational law in logic (Boole's "laws of thought") is in my opinion the law of the excluded middle (LEM), which implicitly ass...
The natural speaker assumes that there is somewhere some justification. Formal languages may expect that too. That is actually the main difference bet...
The best example of popular delusion is their demand to "tax the rich". The core of the wealthy class are the ruling mafia themselves, along with the ...
Science discovers, expresses, and duly tests stubborn patterns observable in the physical universe. The resulting output of scientific activity are sc...
In my opinion, the Republicans remain firm supporters of the principle of rule by the mob, i.e. democracy. They are not "true" conservatives at all. S...
A revolt by foreigners? Because that's 90% of the population. Theyd rather jump on the first plane out of there. The Emirati themselves are too much p...
I view Emirati with respect. I may not always agree with all the nitty gritty details of what they are doing but on the whole I consider their post-oi...
The Dubai Emirati do not pay for education, healthcare, housing , or retirement benefits for the 90% foreigners of their population. All of that are n...
Dubai doesn't live of oil today already. What you are seeing today, is already their post-oil strategy. There are 3.3 million people in Dubai of whom ...
Totally agreed. I give to less fortunate relatives and to people that I can physically see around me. I consider everything else to be an online scam ...
I don't think that the people in Leiden or Bologna want to turn their neighboring countryside into a concrete jungle of endless suburbs. Wealthy peopl...
No, not because they are in the desert. Because they don't need to give out handouts in order to expand. And where are they going to grow the food, if...
Anonymous moral advice is the best, actually. It is a question of establishing an almost "cryptographic" protocol. When moral advice is justified, I'd...
The global poor want to move there because they can get handouts, i .e. free housing, free healthcare, free education, welfare benefits, and so on. Wh...
The Emirate of Dubai offers just one product, which is globally tremendously and increasingly popular, i.e. freedom from the aberrations caused by dem...
Exactly. It represents an entailment A ? B, and not just a simple implication A?B. Logic makes all its decisions by only looking at truth values while...
According to the page on the subject, determinism and predeterminism are "closely related": If you believe that everything has a reason, it does not m...
For Jews: Mosaic law ? isMoral(behavior) For Muslims: Islamic law ? isMoral(behavior) As far as I know, everyone else does not have enough of a docume...
It is probably a mixup between the implication, which is just a truth table, and the entailment, a ? b, which means that consequent b necessarily foll...
"(2+2=5) implies (Kamala Harris is prime minister of China)" is also true in classical logic. It actually does. It just means that knowledge as a just...
Eventually, you will even need to add quantifiers (? ?) and predicates to express in logic something as simple as: All humans are mortal. Socrates is ...
1) Religion matters. Agreed. Humans seem to need spirituality as well as a definition for morality. 2) Some truth can be obtained by practicing religi...
In my experience, democracy is a severely flawed system. You can easily find a democratic majority for ideas that sound good but that are otherwise su...
I agree with the following comment: I disagree with the following comment: That is only going to make the problem worse. In my opinion, it is preferab...
The original article that establishes and proves the bi-interpretability: I have already linked to this original publication in a previous comment. Th...
I did. I wrote: "There are sentences that are like this. There are sentences that are like that. Both could exist." There's a lot of syntactic noise a...
There exist sentences that are true or there exist sentences that are false, or both. "Or both" means: Potentially, there exist as well true as false ...
I left out that detail because it is obvious. So, with the details: It is more accurate but also much more impenetrable than: The resulting syntactic ...
It has always been an explanation about the diagonal lemma: S <-> ¬F(r(#S)) Meaning: (S ? ¬F(r(#S)) ? (¬S ? F(r(#S)) Meaning: (S is true and F is fals...
P(S) := S <-> S Is indeed impossible in PA. However, you can implement it as: P(n) := n=n The diagonal lemma is still perfectly satisfied for the iden...
First, we replace F by ¬F. If F is a property then its negation is also a property. So, the following is an equivalent statement: Next, we replace S <...
I wrote that about the diagonal lemma, i.e. Carnap's theorem. Of course, there are conditions for when it applies. The context required, is PA or equi...
The identity predicate in PA is: P(n) := n = n It cannot be implemented as: P(S) := S <-> S You are trying to do something that is not supported in PA...
In arithmetic theory, the argument n in P(n) must be a natural number. You cannot apply the predicate to S. You can only apply it to its Godel number....
I guess you meant to write: Let P be the property: P(S) if and only if S is equivalent with P(#S). In that special case, P is actually Tarski's truth ...
The diagonal lemma: (By the way, there seems to be a mistake in the page: "formula" should be "sentence"). Equivalently replace F by ¬ F: ? ? ¬ F(°#(?...
Take for example Oxfam, known for exchanging sex for access to taxpayer-funded aid: Highly-paid expensive expat jobs just for westerners while the loc...
That is a bit of a mystery. Any simplification to Robinson's arithmetic will make it complete: https://en.wikipedia.org/wiki/Robinson_arithmetic. It j...
My initial interpretation of the term "better" was "more faithful", but indeed, this doesn't necessarily make an abstraction more useful. That does in...
Noson Yanofsky's paper, "True but unprovable", is about arithmetical truth, also called "true arithmetic": I have used the term "mathematical truth" i...
There's a big difference between saving a child from drowning in a pond and giving money to people who say that they will be saving drowning children ...
Comments