Terrence Howard on Reality

[Salvijus]

Amen. 

[Nemra]

@Salvijus I don't think you understand what I mean.

[Salvijus]

3 minutes ago, Nemra said:

@Salvijus I don't think you understand what I mean.

I'm cool with that

I've had enough math for a lifetime now

[Nemra]

Just now, Salvijus said:

I'm cool with that

I've had enough math for a lifetime now

Then you don't know what hell means. 😁

[Salvijus]

Lol

[Ero]

3 hours ago, Nemra said:

@zurew 😁

People don't know that hell is waiting for them when they get introduced to what a matrix is and how it works. 🥲

Wait till you hear about the General Linear Group and its representation embeddings

[zurew]

@Ero Do you have a disagreement with any of this? (feel free to call out the bullshit, don't hold back)

5 hours ago, zurew said:

So in other words, from system's inability to prove its own consistency doesn't necessarily follow, that that system is actually inconsistent ( at least thats my understanding).

9 hours ago, zurew said:

  Quote

https://plato.stanford.edu/Entries/goedel-incompleteness/

First incompleteness theorem
Any consistent formal system F𝐹 within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F𝐹 which can neither be proved nor disproved in F𝐹.

Second incompleteness theorem
For any consistent system F𝐹 within which a certain amount of elementary arithmetic can be carried out, the consistency of F𝐹 cannot be proved in F𝐹 itself.

Or if you prefer wikipedia:

Quote

https://en.wikipedia.org/wiki/Gödel's_incompleteness_theorems

"Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories."

"The second incompleteness theorem, an extension of the first, shows that the system cannot demonstrate its own consistency."

"Peano arithmetic is provably consistent from ZFC, but not from within itself. "<--- this is a specific example where just because you cannot prove the consistency of a system within itself, doesn't mean that it is inconsistent

 

[Ero]

@zurew I actually wrote a statement that started as:

" Leo, I don’t think zurew is being dismissive here. While from what I can tell you do have a deep understanding of the epistemological and philosophical limitations of math, you are indeed making imprecise statements that are generally not true. " (I referenced a few statements with corrections) "I think locking down on the terms and making sure you are more precise with your statements would help when speaking about math, because whilst I can overlook the ambiguity and understand the bigger point you are making, other people who have a stronger math background may get hanged up, which is something you can generally evade by just using the appropriate terms"

But I decided to hide it, because tbh I am slightly tired of engaging on math topics in this forum, since it requires a certain level of care about the math itself which I don't think Leo himself is really interested in or many of the other people that engage in this discussion. 

[zurew]

26 minutes ago, Ero said:

because whilst I can overlook the ambiguity and understand the bigger point you are making, other people who have a stronger math background may get hanged up, which is something you can generally evade by just using the appropriate terms"

I would slightly disagree with this and would say that he isn't just making a slight language mistake there (like I am not getting hung up on little semantics), but his main point is basically wrong . (claiming that something is inconsistent is substantively different from the claim that a system cannot prove its own consistency within itself) - those are two completely separate claims and not even remotely similar in meaning and in implications (imo).

26 minutes ago, Ero said:

But I decided to hide it, because tbh I am slightly tired of engaging on math topics in this forum, since it requires a certain level of care about the math itself which I don't think Leo himself is really interested in or many of the other people that engage in this discussion. 

Okay, I won't drag you into this debate with Leo ,  i was just checking whether you had any disagreement with me since you have a much higher understanding of math than me and you have been making substantive points throughout the whole thread.

Edited June 18 by zurew

[Leo Gura]

@zurew Set theory is inconsistent as soon as you allow self-reference. 

Self-reference will always make your system inconsistent.

Because Self is infinite and none of your systems can handle Infinity.

The reason you guys keep getting hung up on the technical details is because your entire way of thinking is too narrow.

Edited June 18 by Leo Gura

[zurew]

5 minutes ago, Leo Gura said:

@zurew Set theory is inconsistent as soon as you allow self-reference. 

Self-reference will always make your system inconsistent.

Because Self is infinite and none of your systems can handle Infinity.

The reason you guys keep getting hung up on the technical details is because your entire way of thinking is too narrow

@Leo Gura Whatever you are referencing there cannot be found in any of the two Gödel incompleteness theorems ( in fact, I already showed you a counterexample in my previous post). I linked you two separate links there (one is wiki and the other one is SEP) and highlighted the main things.

Now, its possible that you are talking about something that im not familiar with, but Im confident that whatever inconsistency you are talking about there, cannot be found in any of the 2 Gödel's incompleteness theorems and if you think it can be found there - show me where, please.

Or if you want to change your position to "yes, okay, I was wrong, it cant be found in none of the 2 Gödel's incompleteness theorems" Im okay with that also, just show me something that substantiates this claim "Self-reference will always make your system inconsistent."

[Ero]

2 hours ago, Leo Gura said:

@zurew Set theory is inconsistent as soon as you allow self-reference. 

I think he is referring to Russel’s Paradox. It is true that in ZFC there is a distinction between “pure sets” and the type used in Russel’s paradox, which leads to inconsistency.

[Leo Gura]

2 hours ago, zurew said:

Whatever you are referencing there cannot be found in any of the two Gödel incompleteness theorems

Because what I'm talking about requires a deeper understanding of the epistemic and metaphysical implications of Godel's theorems than is classically taught, which I have videos on. It requires you to actually use your mind to make new connections, not just parrot someone's theory.

Godel showed why the project of logicism is impossible and why formalization of mathematics in set theory is impossible. Yes, Russell's Paradox destroyed the possibility of formalizing set theory due to self-reference problems. Russell then invented a contrived form of set theory which outlawed self-reference in order to make it consistent.

Gotlieb Frege tried his best to formalize arithmetic and he failed because of Russell's Paradox. And then Godel came along and put a nail in that coffin.

Go watch my video: What Is Paradox, which I explain this.

Edited June 18 by Leo Gura

[Yimpa]

 

[Leo Gura]

3 hours ago, zurew said:

just show me something that substantiates this claim "Self-reference will always make your system inconsistent."

Any sufficiently complex system which is capable of self-reference can create statements such as: "This statement is false", which creates contradiction and inconsistency.

Any complex system can be hacked to eat itself.

If you want to understand this, read the work of Douglas Hofstadter: Godel Escher & Bach and I Am A Strange Loop.

In short, strange loops will fuck up any interesting formal system you make.

I have videos explaining all this.

Edited June 18 by Leo Gura

[Ero]

@Leo Gura I am not disagreeing with any of your last statements, they are in fact non-controversial when it comes to people who study the foundations of math.
 

Which is why I said earlier some future form of math will be about modelling the taxonomy of the various models themselves.

You can for example choose which side of the paradox you want to examine (similar to Euclid’s 5th axiom depending on which you can switch between Euclidian, Spherical and Hyperbolic Geometry) in a yellow-stage approach to Math.

The thing is, some of your statements were indeed imprecise, such as “all finite systems are inconsistent”, which you later refined to the more precise statement “any sufficiently complex system will have paradoxes” which is generally true.

Again, my only pushback is not about your epistemological and metaphysical positions, with which I agree (logical formalism is not in fact the contemporary base of mathematics precisely because of Gödel), but rather that at times you state your position ambiguously when referring to terms with precise definitions.

That’s all. I know you don’t like to get hanged up on stuff like that, which is why I removed my original post about this.

Edited June 18 by Ero

[Davino]

4 hours ago, Leo Gura said:

The reason you guys keep getting hung up on the technical details is because your entire way of thinking is too narrow.

I was thinking that you on the other hand usually get the bigger picture right but sometimes become imprecise in the narrow details. It's better to get the big picture right, but be also more eager to polish the technicalities for higher holism in your thinking.

I'm not trying to school you or anything but I wanted to give you this feedback. I know you are aware of it already but I invite you to give it another thought: how not being detailed-accurate is skewing my understanding of Reality?

I'm an abstract big picture thinker and lately I'm trying to polish the detail sharpness inside my macroscopic mind-view.

[Leo Gura]

1 hour ago, Ero said:

@Leo Gura  they are in fact non-controversial when it comes to people who study the foundations of math.

People like to have it both ways. On the one hand they claim Godel's work has no larger, deeper implications, and then at the same time they like to then trivialize the implications once they are forced to acknowledge them.

Many people who study the foundations of math do not understand the limitations of their own models and systems and entire approach to making sense of reality. To fully make sense of math and logic requires that you also make sense of reality itself at the highest levels. You can't just dig your nose into the logical sand. Because you are using consciousness, mind, and understanding to make sense of math. And those functions are themselves non-mathematical and trans-rational.

You can't even make sense of Godel's proof without CONSCIOUSNESS -- which is not accounted for in any of your logic or proofs. All your proofs assume certain levels of consciousness as a given.

It's like you're building a skyscraper using magic and then ignoring that fact that magic was used and just talk about bricks, beams, and screws. That's what going logic is like.

Quote

The thing is, some of your statements were indeed imprecise, such as “all finite systems are inconsistent”, which you later refined to the more precise statement “any sufficiently complex system will have paradoxes” which is generally true.

I refined my statement to make it more technically accurate because I knew that people would try to play gotcha about it.

My initial statements were loose and very high-level. I'm not talking as a logician to logicians. The goal of my work is to point out high-level things. The point was to get you to see that any formal system that has any serious explanatory power will run into contradictions. If your system has very low explanatory power then you can get away with local consistency, but why are we talking about such narrow systems at all? It's meaningless in the context of our work. When I speak, I'm assuming a certain context and purpose for all our work here. And it is not the work of academic logicians. I don't usually speak in a technically rigorous way. My method is to throw out loose statements in the hope that they give you some insight that you'd normally not get elsewhere.

Edited June 18 by Leo Gura

[Leo Gura]

Consciousness is so infinite that not even 1% of it will be captured by all the logic humans have ever done.

There are aspects of Consciousness which are completely orthogonal to logic, language, and mathematics. You cannot even connect to them by those means.

Edited June 18 by Leo Gura

[Ero]

1 hour ago, Leo Gura said:

On the one hand they claim Godel's work has no larger, deeper implications, and then at the same time they like to then trivialize the implications once they are forced to acknowledge them.

It seems like you are assuming a straw man of my position. Without trying to be combative, I challenge you to quote me where you seem to think I trivialize the implications of Gödel or that here are no larger deeper implications.

All throughout this discussion I stressed the fact the metaphysical and epistemological ramifications of Gödel's theory align with your understanding of the limitations of formal systems of reasoning. Nowhere have I claimed math is the "ultimate tool" or that one can describe reality by evading paradoxes. 

I fundamentally use "Consciousness" as my ontology and not some physicalist or mathematical belief system.

My position is that all formal systems, philosophies and such are not "territory" and can as such not "cover it", because Reality cannot be grasped through a "subset" of itself. No ultimate TOE can exist other than the statement that "All is Mind". Math is orthogonal to spirituality, similar to how "enlightenment" work does not substitute development on the spiral. 

However, that doesn't mean that all systems are created equal. If we were to have relied on Terence Howard's "math" we wouldn't have left the caves.

The current iteration of math has allowed for all of our understanding of physics and computation. For example, the "AI" you changed your position on and have recently been examining more deeply is all math. Furthermore, I contest that the ability to construct literal intelligence out of silicon and electrons will fundamentally rely on all of contemporary mathematics and very possibly more than that. You cannot have an "AGI" system that equals human intelligence if you cannot embed mathematics, a human creation. That is not even mentioning the functorial relationship between an ML model and its "neuromanifold", i.e parametric space/ descriptive dimension. But it won't be Terence's or Salvijus's models that do that. 

Is math "incomplete" in the imprecise sense - of course. But that doesn't mean there isn't value in examining its dimensions.

1 hour ago, Leo Gura said:

Because you are using consciousness, mind, and understanding to make sense of math.

This is in fact a realization I had a year ago on 300 ug of LSD that pushed me deeper into math - that it in fact occurs in consciousness and that the mathematical realms are no less "real" than physical reality. (I was remembering Ramanujan's biography - an almost spiritual access to these realms without needing "proofs" - the formal logicist's ontology). In a similar fashion to how you explore consciousness, I examine these realms because of the clear value they have in building more refined understanding of our current dream - UFOs, intradimensional travel and communication, artifcial inteligence, synthetic life, genetic engineering - I contest that all these God-like technologies will only be possible through some future version of mathematics - post-rational, holistic and complex in ways we yet don't fathom. But that will not happen without rigour and technically-inclined individuals. 

1 hour ago, Leo Gura said:

I refined my statement to make it more technically accurate because I knew that people would try to play gotcha about it.

I have watched all your videos on deconstructing science and paradoxes before I even started to study math more deeply. Nowhere was I being inflammatory, combative, or  "playing gotcha". I was simply communicating to you that while people without a math background may not find issue with the less precise, you are possibly missing the opportunity to communicate your ideas to people that are more mathematically educated (I am again stressing the fact that I do not have resistance to your ideas due to you not phrasing them technically, as I said earlier). Similar to the pre- and post-fallacy, I believe that integrating the correct terminology and being careful about making precise statements when discussing these topics only would benefit you and the world by making your ideas more accessible, . It is creating unnecessary resistance to your ideas that I believe would benefit greatly the precise people that may conflate you with a woo-woo podcast armchair philosopher, the likes of Terence Howard. That is all. I respect the work you are doing and believe it is important for more people to listen to it. 

Edited June 18 by Ero