/sci/ - Science & Math

Do the incompleteness theorems actually rely on a version of the liar’s paradox? I hope not, because paradoxes are all bullshit.
>this statement is false
How the fuck do people buy this? This doesn’t even mean anything.
>this statement is true
See? Nothing is actually being said here. It becomes worse when you define “true” within the statement:
>this statement corresponds with reality
>this statement follows from xyz axioms
Absolutely meaningless.
>this statement does not follow from xyz axioms
Even if this were true, it would be true according to more fundamental axioms of truth and logic. So it WOULD be provable and true (they are the same thing).

I’m just not sure how the incompleteness theorem about true but unprovable statements works. Sure, a lot of systems can’t prove statements that are true in a larger system, but why does this mean that math is never complete?

>>11972690
**teleports behind you**

The world is rational.
Human reason can, in principle, be developed more highly (through certain techniques).
There are systematic methods for the solution of all problems (also art, etc.).
There are other worlds and rational beings of a different and higher kind.
The world in which we live is not the only one in which we shall live or have lived.
There is incomparably more knowable a priori than is currently known.
The development of human thought since the Renaissance is thoroughly intelligible (durchaus einsichtige).
Reason in mankind will be developed in every direction.
Formal rights comprise a real science.
Materialism is false.
The higher beings are connected to the others by analogy, not by composition.
Concepts have an objective existence.
There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.
Religions are, for the most part, bad– but religion is not.

>>11059122
>It's about ideas expressed by symbols, together with manipulation rules of those symbols that can be communicated by books, in a way that two different people can come to the same formal conclusions,
*completely btfos your shitty ideology*

reminder TOE is not possible as per Godels incompleteness thereom

that is all

reminder infinite sets exist, and any one that denies this quite literally just dosent have the capacity to conceive of one. You shouldnt attack finitists, you should feel sorry for them. They are trying, but make sure to point out where they are retarded without being to harsh.

There is a real science that studies them.
There is an absolute theology that studies, with accuracy, the highest abstractions of the human mind.
This is not the only plane of existence we live on, or will live in.
There are different beings of a higher and more intelligent type accessible through abstraction and reasoning

thank me later

we know that you can, through godel numbering, enumerate every wff in any given formal system, meaning they are actually countably infinite, but can you enumerate every conceivable formal system?

>The Soviet historian I. Y. Depman claimed that even earlier, in 1486, Spanish mathematician Valmes was burned at the stake for claiming to have solved the quartic equation.[3] Inquisitor General Tomás de Torquemada allegedly told Valmes that it was the will of God that such a solution be inaccessible to human understanding.[4] However Beckmann, who popularized this story of Depman in the West, said that it was unreliable and hinted that it may have been invented as Soviet antireligious propaganda.[5] Beckmann's version of this story has been widely copied in several books and internet sites, usually without his reservations and sometimes with fanciful embellishments. Several attempts to find corroborating evidence for this story, or even for the existence of Valmes, have failed.[6]

why does everyone lose their shit when i say that im a mathematical realist? I dont think there is some magic world that contains abstract entities, i just believe there exists underlying structure and a priori intuition that needs to be accepted in order to ascertain synthetic math.

1: the set of all sense impressions of the human mind is finite and countable, and can therefore be associated with a natural number by some coherent function
2:all potential conscious states of mind are necessarily derived by a more general universal set that maps things in themselves to sensory experience through a function
3:this set-function P that maps essence to phenomenon is contained in the absolute set itself
4:For every element E in the absolute set, there exists P that maps E into reality/state of mind.
5:any P is simply another E in the absolute set

Conclusion: The mind independent reality contains more then a countably infinite amount of elements

>>10177847
Based Godel shittin on anti-realists