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@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."

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). 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.

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

Lol this thread has become a high school (and at certain periods an elementary school) math boot camp. @Nemra I don't know how you have this much patience - hats off to you.

@Leo GuraSo 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). Or if you prefer wikipedia: Leo, Im sorry but the truth is that you either have a wrong understanding of this specific subject (based on what I have read on this, feel free to prove me wrong) or you are using very imprecise language (claiming that something is inconsistent is substantively different from the claim that a system cannot prove its own consistency within itself - thats extremely imprecise language and thats being charitable towards you, because if any other person would make this big of a miscommunication, my assumption wouldn't be miscommunication, but my assumption would be that the other person lacks the understanding and thats why hes/she made a demonstrably false statement). Now, its obviously possible that I lack some contextual understanding on this, so feel free to prove my interpretation of the above texts wrong or feel free to point out how it ought to be interpreted and why.

Sure, but all of these limitations are directly applicable to your epistemology as well. Framing it this way is misleading, because my understanding is that both incompleteness theorems are only talking about provability and not about making "is" statements - so the system won't necessarily become inconsistent, it is just that you cannot prove within the system that the system itself is consistent (you need to go outside of the system in order to prove or disprove that system's consistency) - which is different from claiming that the system is inconsistent (because one is a truth claim, the other is a jusification[in this case investigating the limits of proving and proofs] and the truth value of a truth claim can be true or false regardless if I have the ability to prove it or disprove it). 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 but I can be wrong).

Leo, you were changing your claims on the go as you realized ,your claims doesn't make sense or hold up. Starting with "all formal systems are contradictory" to "all formal systems with enough complexity are contradictory" to eventually making a difference between a contradiciton and incompleteness. I see no statement or implication of incompleteness here, I only see the assertion of inconsistency.

I think conflating those terms is a pretty big deal and shows a lack of understanding. Anyone who has a surface level understanding of basic logic wouldn't ever conflate incomplete with inconsistency . How can he make a video on this and not understand the meaning of those terms is baffling to me.

Im surprised that Leo would make such a statement that a finite system necessarily have to contain a contradiciton, when he did make a video about Gödel's incompleteness theorem himself. It seems that he either forgot or wasn't familiar with the "incomplete" option or he is being very vague and unprecise with his words again.

Im not sure what specific challenge you talk about. A Paradox comes with a specific challenge, but not all self referential systems entail a paradox , thats just a subset of the self referential systems.

I am familiar with the liar's paradox. Whats the argument you are trying to make?

A=2B 2A=4B A+2B =2A Show whats the "higher inconsistency that comes up here

"Look guys I have an idea how to revolutionize math, but I don't have an elementary understanding of math." How you manage to not cringe at your own self is impressive. You don't understand that 2^ 0=1 is not an axiom, its an entailment that comes from dividing a number by its own self equals to 1.

You don't have any understanding what powering a number to 0 even means. I already give you a breakdown and nemra gave you a breakdown also. I don't know why you are ignoring both of our answers Its extremely frustrating to engage with you , because you are willfully ignorant and you ignore answers and you trying to critique a subject that you don't even understand the basic concepts about.

IF you have 100 apples and divide it with 100 apples how much you get?

Dude you have to learn basic logic, of course you can create finite systems that are consistent.

(x^n)/(x^n)=x^0=1. This is an easy way to 'prove' it. If you divide a number with its own self you get one - is that different in this physical reality ?

wait, do you even know the justification for x^0=1? But again even if I grant you this, this doesnt really mean much to your original statement - the only conclusion follows from is that there are parts of math that cant be mapped onto physical reality, but it doesn't mean that current math is limited for modelling physical reality. As I already told you math is more than just about describing physical reality.

You are still confused about this. Some parts of math can be used to describe physical reality but there is much more to math than just describing physical reality. What do you specifically mean without being vague - that math isn't in alignment with phyiscs? So far when pushed on this you couldn't deliver anything tangible or of substance.

Whats next? Will you guys demand math to give prescription drugs for you?

You want to transform math to become physics at this point. I don't know why you would want to do that.

I don't know what your model is, but as long as your model isn't defined in a way where you have two mutually exclusive axioms - I think you can create a consistent system.

No (if by math we mean an axiomatic system), but that wasn't your question to him originally. Your question to him was specifically about your system where you presented specific operations.

I don't know why you would imply that he is being bad fath and at the same time demand him to do all the work for you. Some of you guys are lazy and arrogant as hell.