I've had a go at this one: For the aficionados, the javascript program: #!/usr/bin/env qjs //The following is what the French would call "le référenti...
That was an interesting phone call: It still generates a flurry of new articles in 2024! But these articles don't particularly say anything new. They ...
The existence of the multiverse is a Pythagorean belief. It is not possible to prove that the physical universe is part of a multiverse, simply becaus...
The notion of group may indeed be an abstraction, a way of perceiving things, but there are still five people, which are physically there. Fewer diffe...
I do not believe that the universe is composed of numbers. What I believe is limited to the idea that the arithmetical multiverse is structurally simi...
Viewing mathematics as just string manipulation highlights a different aspect of the same thing. The same holds true for structuralism. You can see ma...
I subscribe to the following take on Platonism: In my opinion, you cannot actively do mathematics if you do not believe that its objects are real whil...
In that regard, Victoria Gitman writes the following alarming statement: Even though the law of identity is certainly applicable in the standard model...
Have you found a job already? In my opinion, absolutely nobody can work with you. I guess that you may find a job, but you will not be able to keep it...
Mathematical nominalism seems to be an aberration. If that is true, then Von Neumann ordinals cannot exist. Example 3 = {{},{{}},{{},{{}}}}. It wouldn...
Concerning Cantor, Gödel, and Turing, I have some kind of morbid fascination for what I consider to be a form of disaster tourism. It is akin to a gui...
If you demonstrate that Cantor's theorem is false. (the existence of countable and uncountable infinity) If you demonstrate that Gödel's theorem is fa...
When Kant writes about philosophy of the mind: I generally refuse to engage, if only, because philosophy of the mind is almost never falsifiable. That...
I believe that the soul is non-algorithmic. Concerning "human consciousness", I don't know how much of it is just mechanical. The term is too vague fo...
There is an infinite number of ways to write the same thwarter program. In order to know that the source code does indeed represent a thwarter, oracle...
Not ZF but ZF-inf. It requires removing and denying the axiom of infinity. Of course, they are mutually exclusive. Still, they both provide a perfectl...
The quote is extreme. I don't think, however, that it is incorrect. If mathematics is "just string manipulation" then it is indeed "about nothing". As...
Yes, of course. Hardy famously said: I would add to what Hardy said, that "useful" mathematics has absolutely zero metaphysical implications. That is ...
The reason why moderate formalism has less merit that the most extreme take on the matter, is actually to be expected. If you abstract away almost eve...
It is actually an incredibly productive view. The more you insist that it is about nothing at all, the more it starts revealing secrets about everythi...
There are surprising and unexpected connections between the foundational crisis in mathematics and fundamental metaphysics. In principle, mathematics ...
Agreed. However, the more precise the definition is being phrased, the more impenetrable the explanation tends to be. Therefore, in a multidisciplinar...
I guess so. As you have probably noticed, @Lionino does not talk about metaphysics or about mathematics but about me. That is apparently his obsession...
I think that having "free will" versus having a "soul" are not the same thing. As I see it, the soul is an object in religion while free will is an ob...
Well, no. The term "truth" should be used in a way that is compatible with its model-theoretical definition, which is in fact not particularly negotia...
Yanofsky phrases a generalized Cantor theorem in terms of the sets Y, T and the functions ?(x), f(x), g(x,y). I still do not fully grasp the connectio...
In my opinion, rationality is a tool and spirituality is another one. If your only tool is a hammer, then the entire world will start looking like a n...
For the afficionados, a simple solution strategy implemented in javascript: #!/usr/bin/env qjs //it is possible to generate the solution space automat...
There are multiple solution strategies possible, none of which, however, naturally translate to first-order logic, because the problem is most natural...
Yanofsky seems to say that all paradoxes listed in his paper are somehow the consequence of Cantor's theorem. Even though I understand Cantor's theore...
Superficially, science can indeed appear to fill the symbolic space. That is why scientism exists as an ideology, i.e. a pseudo-religion. In times of ...
Every collection of truth has a sound theory. However, only some part of its truth may follow from it. Say that a collection of truth has 5 sentences:...
The idea is that every physical system has a sound theory, albeit possibly unknown. Every collection of truth has a sound theory. Every claim that nec...
Understanding of a system amounts to having perfect knowledge of its construction logic, i.e. its theory. For example, the axioms of arithmetic theory...
If a program knows a list of things it can do , and it receives the instruction "do something else but not Ak", then it can randomly pick any action f...
Yes, of course, Oracle can perfectly know what is truly going to happen. However, his knowledge of the truth is not actionable. What else is he going ...
In first-order logic, you may want a predicate is(person,identity). Example, is(A,liar) evaluating to true if A is liar. In fact, the solution space i...
The problem is that this is not the only problem. It is just one of the problems. The language in which the foundational crisis of mathematics is word...
It is actually a description of the standard contemporary proof for Alan Turing's halting problem. The oracle must predict if thwarter will print a ze...
There are landmines when in the combined vocabulary of both metaphysics and mathematics. It is overly optimistic to believe that you can always detect...
The misalignment in vocabulary is something akin to a landmine. You become aware of the problem only after the facts. But then again, I don't think th...
I am trying to point out the metaphysical implications of the foundational crisis in mathematics. That is necessarily multidisciplinary, meaning that ...
You got caught up in the vocabulary misalignment. The phrase "incomplete deterministic system" is perfectly fine in computer science or mathematics. I...
The existence of a functioning oracle is equivalent to determinism (with the notion of determinism equivalent to the notion of completeness). The orac...
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