Agreed. Mathematical sentences, such as X=X, are constituent rules of the mathematical theory that defines them, and are true only in the model(s) for...
I disagree with Churchill. Democracy is doing something that even the worst communist dictatorship never did. It has taken control over marriage and d...
Well, no, it isn't. With S the successor function, and x+1=S(x), and 1=S(0), we can see that 1+1=S(S(0))=2. You can trivially prove it by using PA's r...
You can safely assume that this man, first and foremost, wants sex. This man may not be thinking it over properly, because nowadays there are very dan...
A set of propositions is isomorphic under encoding to the set of the Gödel numbers of these propositions, and therefore isomorophic to a set of natura...
It is just a tool like any other tool. Not really. I have learned to speak with utmost respect about religion. Seriously, I do not shit talk religion,...
Religion can be as much a tool by the ruling elite as one against it. That last bit is really important, because otherwise, as a single individual, yo...
I came to the field in a completely different way. I was customizing software, maintaining software, writing new programs, and otherwise doing really ...
I have finally received an answer for the issue that you have raised. The function that you describe, looks like this: f(\ulcorner s\urcorner) = \neg ...
That is not a requirement for the diagonal lemma. The statement of the lemma says: The liar sentence is handled in a downstream theorem that makes use...
The version in wikipedia indeed revolves around self-reference. When you look at the lemma's statement: s \leftrightarrow f(\ulcorner s \urcorner) The...
Yes, agreed. That is what I wanted to say. I was still looking for a succinct way to put it. This is indeed what it is about. What you just wrote, is ...
A first remark to make is that Carnap's lemma does not need Gödel's first (syntactic) incompleteness theorem (G1SI). It is the other way around. So, i...
I didn't. By the way, the original proof does not seem to use the condition either. I just kept the condition around, because the original proof does,...
At first glance, getting into the NBA could be just 1 chance out of 1 million or so, over the population of all Americans. However, it is probably 1 c...
The user can filter the list of hotels for a location, time period, amenities that you require, and sort the list from lowest to highest price. They s...
Well, you don't need a degree for software engineering. All programmers are essentially self-taught. The other ones invariably drop out. I was program...
Before cashing out from my startup, I always worked as a contractor. For various reasons, I strongly preferred that arrangement. I never had a "boss"....
That is how they fix issues with drones during their flight. Of course, these flights are closely monitored. There isn't anybody suggesting that fligh...
No, we don't. We also no longer need taxis, because we have things like Uber. We don't need hotels, because we have things like Airbnb. All these tech...
Since licensing for parents can only limit births in the country that introduces it, I see wholesale immigration of "unlicensed" people, born in unreg...
You can look at how things are going for contemporary philosophy stars like Nassim Nicholas Taleb, who is a grandee in the epistemology of randomness....
We haven't needed pilots to fly planes for over thirty years now. In fact, we use a lot of drone technology already, which is safer, better, and cheap...
The reason for licensure is first and foremost to restrict competition in the field and increase profits for the cartel that controls it. Regulatory c...
That is how it works for physical property. For crypto-assets, it has nothing to do with any legal rights. I own all unspent output in address: 1GomQs...
The ruling elite cannot be trusted. In theory, the ruling elite protects your property rights. In practice, they are also the worst threat to them. Th...
An infinitely dense starting point for the universe is indeed clearly an issue. Either they figure out how all the matter of the universe could be con...
Agreed. Property rights only exist when the powers-that-be recognize them. If they refuse to enforce such property rights, then you do not have them. ...
The first law of thermodynamics doesn't actually specify that matter can neither be created nor destroyed, but instead that the total amount of energy...
It is the Church that dismantled the tribal and patriarchal network in Europe. For obvious reasons, this is not an option in Afghanistan. Furthermore,...
It is perfectly ok that your views are not universal, but in that case, do not try to present them as such. There are multiple belief systems on the g...
Yes, agreed, and based on my experience, let me emphasize that we should not even want a democracy in these matters. The populace should have no say w...
In my opinion, someone who tries to prove the existence of God, is not truly a believer in God. In that sense, you never really believed. You only som...
Propositional logic is an axiomatic theory, derivable from 14 arbitrary, speculative beliefs with no justification. We have no clue as to why these ax...
Nowadays, Hume's intuition about the sun is considered to be quite right: The Solar System will remain roughly as we know it today until the hydrogen ...
All states are actually, equally probable. Therefore, you see the elements in all other states too, but because they have no interest in staying in th...
You reject a very fundamental notion of the Platonic realm: The interest of isomorphisms lies in the fact that two isomorphic objects cannot be distin...
For example, "2+2=4" is not identical to "two plus two is four" but these expressions are still isomorphic under translation. That is why the equality...
Quite a bit of behaviour emerges from learning how to react to a posteriori information, in Kant's lingo. Still, pure reason, i.e. a priori cognition ...
There is a Platonic intuition that senses that there is somewhere a connection between mathematics and the physical universe, but we (should) never ma...
Yes, but most of these permutations are useless for these parts. According to game theory, these parts will only pick those possibilities that substan...
That is science. Science is simply another activity, and absolutely not the same activity as mathematics. Scientists spend an inordinate amount of eff...
What does system-less so-called "ethics" translate into? Well, obviously into: The Special-Interest effect: Increasing The Size, Scope, and Cost Of Go...
We cannot be far away from witnessing with our own eyes how the $22 trillion of debt and $46 trillion of unfunded liabilities are going to pan out, in...
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