Kurt Gödel

So in a given situation, right, I have a certain set of concepts, types with their definitions, right? And I've got a certain number of theorems, right? And I might, you know, and

the question is, what can I deduce from that? But as Gödel showed, there are going to be some things that I can't prove with that set of things when you pack them down into axioms.

And the way I read this is, again, in terms of questions versus judgments, what intuitionistic

logic gives you is the structure of questions.

Another person here who's really useful on this is Awadi.

Awadi's paper on bracket types is... basically shows that the double negation construction

that Gödel came

up with for translating

The argumentative power which had been a mainstay, a philosophical mainstay, for 700 years It just evaporated.

And then, some centuries later, Kurt Gödel adopted a modal version of that same argument such that by theological necromancy, the argument, the ontological argument, might live again, valid if not sound and risking modal collapse all the while.

The Renaissance also saw the meteoric rise of a renewed ancient philosophy, Hermeticism.

This Greco-Egyptian philosophy of salvation was heralded by luminaries of the time as a source of primeval wisdom, which would ultimately renovate all of philosophy and spirituality.

I'm not sure where it was in the movie.

Kurt Godel, an Austrian logician and mathematician, is played.

I don't know where he popped up in the movie, but that was James Urbaniak, dude.

That was Doc Venture.

He says it's categorically false, and he uses mathematics to argue his point.

He draws on Kurt Gödel's incompleteness theorem and Turing machines.

How does an equation from the 1930s show my brain isn't a computer?

Let's look at the core concept.

You might get to Ellie J. Brower, intuitionism, constructivism, and bulbaki.

But at some point, you'll probably hit Gödel and Turing, and then you'll likely start thinking about computation.

Computation is the abstraction of computation.

Its avatars include the P versus NP problem, Gödel's incompletions theorems, Turing's imitation game, and many descendants.

As a field, computation leads to some deep, thought-provoking questions, and to some that, once upon a time, I thought held no interest at all.

In particular, I remember learning about computer programs called proof assistants, such as Coq, now Rock.

This will further devastate universities and continue to eat away at the soft money edifice they rely on.

The resulting not-quite-academic findings will be leased back to us at profit, or held closely, developed in secret, and revealed as barely comprehensible jewels of arcana that, like Renaissance mathematicians at court, lend a bit of stature, a dash of rivalry, some injections of cash, and the imprimatur of legitimacy to the shady or primary activities of the companies.

And we can push this mathematical logic to its extreme limits.

This brings us to Kurt Gödel, one of the greatest logicians in human history.

Oh, this part is fascinating.

He is most famous for his incompleteness theorems in mathematics.

But in 1949, Gödel was at the Institute for Advanced Study in Princeton, working right alongside Albert Einstein.

They used to walk home together every day.

What a

duo.

No sé, no sé.

En 1931, el lógico austríaco Gödel, Kurt Gödel, publicó sus, este, famosos teoremas de la incompletitud y demostró algo que hizo temblar a la ciencia y que acá siempre decimos de un modo u otro.

Cualquier sistema matemático lo suficientemente complejo siempre con-contendrá verdades que son imposibles de demostrar.

Y son imposibles de demostrar utilizando las propias reglas de ese mismo sistema.

Si asumimos que el universo está regido por leyes físicas y matemáticas, la conclusión de Gödel nos dice que al estar nosotros atrapados dentro del universo, siempre existirán verdades fundamentales que jamás podremos probar.

Lo que decimos el otro día acerca de los lenguajes.

Cuando está uno dentro de un lenguaje, eh, está preso de ese mismo lenguaje, tiene que salirse para afuera para demostrar cosas de adentro.

The ontological argument holds that you can demonstrate the existence of God just from properly understanding the concept of God.

A version of this argument was made famous by St. Anselm of Canterbury back in the 1100s, and there have been other versions of it, such as one by the 20th century mathematician Kurt Gödel.

who is one of the most famous mathematicians ever and a really sharp thinker.

So I have an intuition that even if some versions of the ontological argument, like Anselm's, need refinement, that I think a version of the ontological argument can succeed.

More than the ontological argument, though, I'm a fan of the contingency argument.