There is this widespread view of a long mathematical winter between Greek antiquity and the 12th century AD, i.e. a millennium-long standstill: Is tha...
Stephen Wolfram wrote something very relevant in that regard: Being knowledgeable of say 1% of these 5 million theorems, i.e. of 50,000 theorems, is p...
Totally agreed. While René Descartes is rightfully revered as an indisputable grandee in mathematics, through his highly influential work on coordinat...
It works exactly the other way around. According to the Dunning-Kruger study, intelligence is defined as: Knowing when you do not know. Intelligence h...
Not really. In fact, not at all. Trust is exactly what fuels deception. The more there are who people trust, and the more blindly they trust, the more...
This belief is deeply ingrained but not at all justified. In fact, it is even a dangerous belief. As a matter of fact, we must never "trust" service p...
My current understanding is that there exists indeed a detailed description of the infinite model(s) for real numbers but at this point I am unable to...
Formal knowledge are sentences for which "the paperwork" containing their justification can (conceivably) be verified mechanically. Paperwork concerni...
If you need formal knowledge in order to discover new formal knowledge, how do you get hold of the very first formal knowledge? How do you get the pro...
If I understood the explanations correctly, Löwenheim-Skolem applies to the theory of real closed fields (=first order theory) but not to to the theor...
Religion, more specifically, Islam is strongly opposed to usury: I strongly dislike corporations, especially the banksters, because they are usury-inf...
This is incredible. I didn't know that this was possible. It is so unlike the models of PA: Well, yeah, I wasn't aware of the fact they behave so diff...
Well, the undue influence on the culture and laws of society by corporations is considered evil by religious people, while both left and right are not...
Because of this post, I started reading up on the axiomatization of real numbers, and of course, I have run into issues that I do not properly underst...
The advantage of using a religious regulatory framework for morality, such as Jewish or Islamic law, is that left-wing versus right-wing does not even...
It only applies to some human thought processes, i.e. the ones related to reasoning within or about a formal system. Since the human mind does not onl...
The affinely extended real number system simply adds infinity as two real numbers in a Cantor-like approach: According to the explanations this extens...
Provability is the property of a number. It is a definable predicate. Given Gödel's semantic completeness theorem, all provable numbers are also seman...
Totally agreed. Mathematics is only about abstractions expressed in language. Cantor's work is really interesting in this regard. Countable infinity a...
The same theory will say that the earth did not always exist. How can something that still needs to come into existence be flat or not flat? Furthermo...
In my impression, in logic it certainly is. Other arbitrary, non-logic data can be transformed to logic sentences. For example, the arbitrary statemen...
The use of the term "proof" outside the context of mathematical proof is wrong and misleading, because the mere evidence itself could be wrong or misl...
I have just watched a youtube video, entitled, "Population Control Isn't the Answer to Climate Change. Capitalism Is", that revolves around something ...
U(x)f(x) : (\forall x \in D)f(x) or even U(x,D)f(x) ?(x)f(x) : (\exists x \in D)f(x) or even ?(x,D)f(x) Explicitly mentioning domain D is important, b...
According to proof theory, Descartes' views do not constitute "proof" in any fashion: Like many philosophers in western philosophy, Descartes' argumen...
Love is overrated, and romantic love is very dangerously overrated. It makes sense to get along with people you do transactions with. That is why we a...
Yes. Unicorns exist in their imaginary world. You can construct an imaginary world by describing it. For example, the imaginary world of Star Wars. Th...
If it matters who says it, then what he says cannot possibly matter. The reason why a statement is sound knowledge is because there is paperwork to ju...
The reference section in Wikipedia's page on the diagonal lemma is quite good. I never really read his other work, as mentioned in Carnap's biography ...
Now you assume that some kind of incentive psychology that would govern the behaviour of all experts. How do you justify that? Where is the paperwork ...
My own intuitive belief is that the abstract, Platonic worlds of mathematics exist regardless of humanity, which only discovers them. Concerning exist...
What Kant said, sounds very similar to what Carnap's diagonal lemma suggests about a legitimate existence predicate: it would need to be possible to d...
Well no. If the quote from wikipedia is not attributable because it should be considered original research, then it will probably already have been fl...
Well, it is still clearly his field that would need to make such connection, because mathematics itself will certainly not make any. He may indeed hav...
Well, they are not being "reconciled". Science uses the language of mathematics to maintain consistency in what it says. Mathematics does not tell sci...
The liar paradox is not used in the proof strategy for the undefinability the truth. The main consideration is Carnap's diagonal lemma: There will be ...
I personally think that Tarski's convention T is an elegant and adequate workaround for the undefinability of truth. The video below explains conventi...
Mathematics has no direct empirical take on the world. Its models are always abstract Platonic worlds. It is through its influence on empirical discip...
It took me quite a bit of irritation to understand the gist of model theory. Initially, it appeared to me as nonsensical and absurd. So, in the meanwh...
It could have an impact somehow, but that would have to be investigated/discovered by an empirical discipline. The requirement to maintain corresponde...
Agreed, but the terms syntactic and semantic have unusual definitions in mathematical logic: If you can derive a new rule, i.e. theorem, from other ru...
There is no need for it, but it is also not even possible. Even a redundant existence predicate would be a problem. It would not be merely redundant b...
You are trying to use the meaning of the term predicate to determine if a particular property can be a predicate. I just use a purely syntactic proced...
Given Tarski's undefinability of truth, any system has no other choice but to receive its fundamental truths from a higher meta-system. Tarski beautif...
And there is also an important unmet need for that. For example, there are all these scientific publications supposedly backed by experimental testing...
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