Tarskian

It is an existence theorem about a sentence that is supposed to exist in PA. The canonical witness is definitely a sentence in the language of PA: G ?...

Gödel's incompleteness theorem proves that PA is inconsistent or incomplete. That is a perfectly legitimate theorem in PA. It does not prove that PA i...

Yanosky includes the Gödelian statements that cannot be expressed by language. There are uncountably many of those.

The use of logical entailment predates model theory by decades: The page uses it without distinguishing between theory T and its model M: A1..An ? S =...

Gödel's theorem can perfectly be phrased without assuming that PA is consistent. In fact, by introducing the assumption "If PA is consistent", Gödel's...

In "True But Unprovable", Yanofsky insists that unprovably true statements vastly outnumber provably true ones: True and provable statements are denum...

Yes, and once this part has been proven, there is no need to prove soundness theorem, because the model-theoretical construction already guarantees th...

Well, if PA is not sound, then it is actually unusable. So, we have to assume that it is sound. We simply have no other choice. However, proving sound...

Soundness implies consistency. So, if you manage to prove soundness theorem from PA then you have also managed to prove PA's consistency from PA. Göde...

((everything below is in the context of PA or similar)) Gödel's own witness is certainly a corner case, but so are all the witnesses for his incomplet...

You see, I do not want KYC (Know Your Customer), because it allows the ruling mafia to target bank accounts based on nationality and other criteria. I...

I cannot comment on "liberalism" because that term has no precise definition. The people who mine them or somehow buy them. It is the same question as...

We were talking about the taxes at the time of the Pharaohs. They were necessarily simple. "huge issues", "modern slavery", "human trafficking" ... bl...

The Egyptian tax on a farmer's harvest is not the same as modern personal income tax. The farmer did not have to give any information to facilitate th...

What I meant to refer to, was:

The physical laws that we know, are not an axiomatic theory. They are a collection of stubborn observable patterns. They just say that a particular pa...

The Egyptian tax collector would measure the farmer's land and compute taxes based on that information. He would not ask the farmer if he somehow made...

If physical reality has a formal theory, then its model/interpretation may contain inexplicable truths in a similar way as the system of the natural n...

An undecidable problem in logic is undecidable irrespective of how much time or memory you throw at the problem. The P versus NP issue only applies to...

The problem is logic itself:

This would imply that for every true statement about the physical universe, there exists a proof that can be derived from the supposedly canonical and...

Certainly not to the extent that it exists in the West. For example, personal income taxation was introduced only in 1913 while the human race has bee...

PA is short for Peano Arithmetic theory: https://en.wikipedia.org/wiki/Peano_axioms It is the most common theory of the natural numbers. Most true sta...

First of all, if S(t) can be predicted from S(t-1) ... S(0) then the theory T for this system is complete. Non-trivial systems do not have a complete ...

The official ruling mafia defends their monopoly on expropriation, called "taxation". Lions also fight other lions trying to feed on prey in their ter...

Every property of this unstateable number is itself an unstateable truth. Example: Number r is a real number. If number r is unstateable then this sen...

Construct a Richardian number and map it one-to-one to a subset of the natural numbers. This subset is ineffable:

Consider the following proposition: The set X is a subset of the natural numbers. This is trivially true for an example subset such as {5, 67, 257}. T...

I don't think that JTB is inadequate. Most truth cannot be known in terms of JTB. That is not a flaw in JTB. The nature of reality is simply like that...

Then there is still the next level: the beliefs about these ineffable beliefs which are not necessarily ineffable. There is a large literature about R...

If you look at the epistemic JTB account for knowledge as a justified true belief, it means that the overwhelmingly vast majority of true beliefs are ...

There is a one-to-one mapping between the subsets of the natural numbers and the real numbers. So, we can represent a subset of the natural numbers by...

In my opinion , it decisively divorces mathematical reality from physical reality, which is otherwise its origin. Humans, but also animals, have quite...

The distinction between countable and uncountable infinity, originally introduced by Georg Cantor, has always been controversial. When first confronte...

The following is a legitimate proposition: The set {6,8,11} is a subset of the natural numbers. It is true or false. The following proposition is taut...

Requiring proof in science would indeed be unfair, if only, because there is no (axiomatic) theory to prove it from. So, we accept the scientific clai...

In classical law, the burden of evidence is on the prosecutor: However, for offences newly defined in modern times, this is usually not the case. For ...

Proof is what mathematics uses as justification. There is always a disconnection between truth and justification. Concerning physical truth, it is per...

The thing is that computer science started almost a decade before the first computer was built. So, in 1936, Alan Turing dreamt up a machine that coul...

In all practical terms, the term "Turing machine" just means "computer". For the problem of proving a PA theorem in ZF, there is no need for infinite ...

This may be true but I do not agree with Penrose's core argument: How do humans know that a mathematical sentence is true? There is only one way: by p...

The Nostr protocol claims to be censorship resistant: The author claims that it is enough to "distribute data across a network of peers" in order to a...

You gave an example of a statement about the natural numbers that can be expressed in language. That is an exception and not the rule. Take for exampl...

It is actually possible to set up decentralized censorship-resistant information publication networks. For example, Bitcoin is one. The powers-that-be...

This is just one example of the problem. The overwhelmingly vast majority of true statements about the natural numbers cannot be expressed in language...

There are infinite identifiers possible, but still a countable number of them. There are uncountably infinite points in a line. Therefore, it is not p...

You can count identifiers. You cannot count points in a line. So, you will never be able to create an identifier for each point.

Planets are indeed countable. There are uncountable sets too. For example, the individual points in a line.

If you know that there are uncountably many of them, you cannot keep assigning countably many identifiers. You will run out of those. Planets are actu...

If there are more planets than possible words then you can't give each of them a different name. It doesn't matter if you have seen all of them.