'Stunning': Roger Penrose on' Gödel's theorem #maths

[KaiWatson]

Penrose recapitulating Godel is exactly what I needed right now.

[johnzhou]

Very roughly, Godel's theorem says, if you have a bunch of axioms, you can write down a sentence that basically says "I can't be proven from these axioms."
If this sentence is false, then by what it says, we can in fact prove it from our axioms, so our axioms can prove a contradiction, which shouldn't happen.
So the sentence has to be true. But this means this sentence really is something true that can't be proven.

[JasonWalsh-qz]

THAT IS STUNNING. THANK'S FOR CONFIRMING THAT, SIR ROGER PROFFESSOR PENROSE. I AGREE. COSMOLOGY AND MATHEMATICAL PHYSICS IS AWESOME!!!😊

[chemquests]

This only applies to deductions. Since science is an inductive process, proofs aren’t strictly logical, based only on axioms. In some sense we’re observing the truth to infer the rules, but those rules need not be axiomatic.

[seskoneify]

"Inception" film constantly going on in this man's mind

[paulaoh]

This is more easily understood as the liar's paradox: the statement of a liar that they are lying: for instance, declaring that "I am lying." If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. I guess Penrose was surprised that he found the same internal contradiction in mathematical logic.

[hugochavez]

he does not make the essential distinction of truth and proof, Godel proved that there is a sentence that is true but that is not provable.

[UptonSinclairLewis]

I have no idea what he is talking about.

[dallynstevens]

What is proves what isn't and what isn't proves what is.
Stunning nature of consciousness, the unseen realm proving the seen, yet the seen cannot see the unseen... As far as we can tell I've course

[creeperkinght]

This then brings in the point that there are truths that are not provable as fundamental formal concept, but an empirical imperative subject to our own perspective, which then is based on natural phenomena and other complex factors in our very existence of reality, in which we cannot define said truths with simplicity, brevity, or possibility under our current systems of abstraction and depth found in science. Therefore this points out that those truths cannot be proven or have consistent value or effect in our reality or anywhere across the universe in either as static or dynamic axiomatic natural concepts. You can't insert a concept or a constant value that isn't consistent or even compatible with other concepts in a natural system that comes from a moral foundation in a formal manner. It's illogical and arbitrary. One has to accept that there are truths to reality that cannot and will not fit in the current systems that guide in understanding our reality, and accepting the possibility that later systems may or may not achieve the goal of aligning said truths to precise formal empirical interaction for us to understand, if at all. The mathematical axiomatic forms and rejecting these truths under the Gödel Theorem is a clue that there are truths to this universe that we cannot perceive as a species currently. However, due to our natural ambitions and determination, there is a possibility somewhere in the future that these abstract truths that deny us will introduce themselves to our systems and us in open arms. Philosophy is our road and the truths are the abstract forces that guide us to further journeys on that road, leading us closer to the secrets of the universe. Until then we must wait until we can see that opportunity, and if it is beneficial or detrimental to us at all.

[Liamh]

Socially people don’t understand this because it stops at gender…

[mykrahmaan]

TRUTH itself must first be defined. There is no universally applicable definition of the word. Its meaning always depends on the purpose of the relevant task.

For a hungry person TRUTH is "what enables han (her/him) to find food", while for a politician it would mean "what enables han (her/him) to win the election".

[LENSKA]

so basically, you cannot prove things to be true true, they're only true within the rules you set up prior... ?

[bpbp]

Ooh! Is that the green couch on Top Gear? Oh, wait. NVM... 😅

[italogiardina]

The search for rules as "sufficient reason" in life is a dynamic process, shaped by both external circumstances and internal values. We can illustrate this with a thought experiment:

Imagine being stranded on a desert island with a leaky bucket of water. Your survival depends on having enough water, so you need to prioritize your actions.

Initial Assessment: You first recognize the value of the water and the threat of evaporation. Your "sufficient reason" for action is to cover the bucket with coconut fronds to minimize water loss.

Shifting Priorities: Upon discovering the leak, your priorities change. The "sufficient reason" is now to patch the hole, as this is more critical for survival than preventing evaporation.

Internal Factors: Even with a clear plan, your psychology plays a role. If you're overly anxious, you might focus on covering the bucket first, neglecting the leak and jeopardizing your survival.

This scenario demonstrates a few key points:

Sufficient reason is context-dependent: What seems like a sufficient reason in one situation may not be in another. Priorities can shift as new information emerges.
External and internal factors interact: Our values and beliefs influence how we perceive "sufficient reason." Anxiety or other emotions can cloud judgment and lead to suboptimal decisions.
Prioritization is key: In complex situations, we must evaluate multiple factors and prioritize our actions accordingly.
In essence, "sufficient reason" is not a fixed concept but a dynamic process that involves both external observation and internal reflection. Understanding this can help us make better decisions in life, especially when faced with challenging circumstances.

[Artisan_GenZ]

Scientists discovering that the scientific can’t get off the ground without faith that truth exist is hilarious 😂

[JohnDoolan-fi]

I have said this in another form of art music now i will say the same in science by standing on the shoulders of these giants we must reach up 👆 and do better be better not just look up to themb

[rajinfootonchuriquen]

That's why math should have as many axioms as it needs. For example, proving a vector space is span by its basis is dumb.

[ReyDG]

Everything is the truth and yet the rules ensures that there's certainty up to what extent that it may provide under the omniscient truths that it is operating in.

[JenksAnro]

I can't tell if he explained that horribly or I am just a dumbass