The lemma that the number of possible expressions in language is countably finite is actually a core argument in Yanofsky's paper: There is simple pro...
Wittgenstein's view is not compatible with model theory of which the core understanding is that the provability of a arithmetical proposition is tied ...
I don't hate on individual math professors. They are just pawns in the game. One (or rather two) of the things I don't like, is the combo of academic ...
Agreed. Unpredictable truths in the physical universe are usually not particularly interesting either. The difference is that we can see them or at le...
If you feel threatened by its chaotic nature, it means that it disturbs your ideological beliefs. Someone who really uses them as tools of precision a...
The complete and perfect theory of everything cannot do that. It won't be able to predict everything. It would improve our ability to predict the phys...
Well, Christianity is indeed collapsing. Ever more rapidly. Christianity has indeed turned out to be assailable but certainly not easily or instantly....
Well, yeah, I rigidly believe that we should not give powers to people that only Allah should have, and if Allah does even not exist, then so much the...
The true nature of the universe of mathematical facts makes lots of people uncomfortable. Imagine that we had a copy of the theory of everything? It w...
Modal collapse is not an inconsistency. Who told you that? It just means that the proof reverts to standard non-modal logic. Since non-modal logic is ...
That may very well be in violation of Carnap's diagonal lemma: "For each property of logic sentences, there exists a true sentence that does not have ...
People seem to understand this about the truth in the physical universe. They tend to reject this about the truth in arithmetic. I wanted to point out...
Gödel did exactly that. He provided a mathematically unobjectionable proof. Of course, math never does more than advertised. The witness for the exist...
Originally born a Catholic. In the meanwhile, I came to the conclusions that Christians no longer intend to use the rules in the scripture as a benchm...
I started using unpredictability as somewhat a synonym for unprovability because of how Stephen Hawking put it: So, we are sitting on a system that is...
Since we are talking about proof, it is the mathematical view on the subject that matters. Everybody else should avoid using the term ¨proof¨. What th...
All of this is the result of using just one direction ("soundness"): If it is provable, then it is always true. That is the only direction that we use...
There are two directions. If it is provable, then it is always true. (aka, soundness theorem) In this direction, everything is very orderly. That is t...
That point of view is not a problem. Only a 'yes' or 'no' answer constitutes a real commitment. For 'yes' answer, you need to locate a constructive wi...
Yes, Yanofsky's paper also mentions Chaitin's work: This means that most (but not all) mathematical truth is essentially random. Yanofsky's paper ment...
No, Gödel does not assume consistency. In Gödel's theorems, consistency is exactly the question. In mathematics we implicitly assume consistency. In m...
You can enumerate every sentence in natural language in a list. Therefore, it maps one to one onto the natural numbers. Therefore, their set is counta...
The fact that we can prove that it exists. Let's start from Carnap's diagonal lemma. In the context of Peano arithmetic (PA), for each property ?(n) a...
The paper actually says: So, it only insists that the sentence "PA cannot prove a contradiction" can be expressed in PA itself. In the following paper...
Well, how many additional truth values do we need to invent before all our needs for additional truth values will have been completely satisfied? Seri...
If someone is not interested in the issue, fine, but then his answer should still get mapped to the truth value unknown/maybe. There is no need for an...
That is clearly a straw man. You are attacking an argument that I did not make. You are using Don Quichotte tactics. Who exactly is the sophist here? ...
What are sound ethics? We take a snapshot of a sane society as well as an inventory of its rules. This is a suitable benchmark for ethical sanity. Ben...
I have just found an interesting paper that elaborates on why the overwhelming majority of true statements in arithmetic are unprovable -- and therefo...
Well no. You need to be quite sure that the book is about a sane society. You cannot just invent one. It needs to have historically existed. They are ...
A chaotic system is one that follows a seemingly random path albeit deterministic. If you repeat the path with exactly the same initial conditions, it...
Hitler tried and failed. Concerning the consistency of any theory such as PA (Peano arithmetic theory), it is merely an assumption. Gödel's second inc...
It is not the state of the art in their field. Not because he wants to. There are so many people willing to pay a million dollars just for an 15-minut...
Gödel's proof is considered mathematically unobjectionable. That is why the only mathematical criticism is that it merely proves equiconsistency betwe...
It depends on b() whether they are different or the same. It is a similar situation as whether a ?b is equal to b ? a. It depends on the properties of...
No, they can't. There is no justification for axioms. If an axiom can be justified, it is not a legitimate axiom. Math cannot demonstrate its axioms e...
Knowledge is fundamentally foundationalist: Without basic beliefs, reason is not possible. Therefore, there is no such sharp distinction between reaso...
I accept religion, also because it works. We take a snapshot of a presumably ane society along with its rules and call that our scripture. Now we have...
You need to compare apples to apples: - We can demonstrate that math works. - We can demonstrate that religion works. That is the fair comparison. Or ...
You misunderstand what the Wikipedia page on the matter says. Godel has perfectly demonstrated the equiconsistency between his theorem and the axioms ...
In my opinion, the difference between "absence of belief" and "disbelief" is just language engineering. It implies that the position could also be ind...
In that case, you will need to reject mathematics as it is staunchly foundationalist, i.e. axiomatic. Since science is not viable without math, you wi...
There are three possibilities concerning the belief in God: true, false, indeterminate. Religion believes it is true. Atheism believes that it is fals...
The reasons are similar. The belief in Peano's axioms allows you to use arithmetic theory and maintain consistency in downstream applications. The bel...
Dunning-Kruger is about people who think that they know but in fact they don't. Since atheism requires omniscience while faith in God does not, doesn'...
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