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@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.

It seems that you have read some of my rants . I appreciate seeing some of you holding his feet to the fire as well.

Yeah thats probably true, that they maybe had some physical meaning, but my understanding is that right now math is not depended on any specific empirical fact. Like you could change all the empirical facts that we accept to be true right now, and math would still hold because of its axioms. In other words, I don't see any direct connection between any specific kind of empirical fact and between any specific kind of math axiom. Because if the claim is that there is a direct dependency between a specific empirical fact and a specific math axiom, then my question would be ,which specific empirical fact change would necessitate the changing or the redefining of one of the math axioms?

@Ero Hi , cool that you are here, you can clean this thread up and correct whatever bs we are talking here

Yeah that is a controversial one, because as far as I understand, mathematicians would say that math would be true regardless how the physical world works. This kind of goes back to modal logic - where we talk about certain things being possible in all possible worlds (possible here means logical possibility and the set of all physical possibility is inside the set of logical possibility - in other words, there are much more logically possible things than there are physically possible things). I personally disagree with the idea that math is empirically grounded (meaning the truth value of math propositions are not directly depended on the physical laws of this universe) . Like if we would want to go down that route, there is so much ambiguity that could be applied without the usage of extremely strict mathematical definitions (especially defining very strictly what we mean by identity). For example, I could empirically justify almost anything that would contradict basic math axioms. Like, If I would want to get silly about it, I could say 1+1=3, because empicially if two people fuck, one children will be born (and even this is not necessarily true, because sometimes 1+1=4 or more depending on what we are talking about twins, triplets or anything else) - I could even add here that 1+1=1 or 1+1=0, because when two people have sex and when one of them has a deadly STD, the other could catch that STD and then both of them could die later down the road. - and here we only talked about human sex, if we go to animals even more crazy empirical cases could be brought up that would almost all contradict basic math axioms. I can come up with other silly examples if needed, but the basic point here is that that crux of the issue seem to be how strict our definitions are and this doesn't seem to be about anything empirical. Also where did you empirically observe that 1million*1million=one trillion? - you accept a bunch of mathematical statements that you have never observed or empirically verified in the physical universe ever before - hence why this goes back to definitions imo and to inference rules that we all agree on, regardless whats going on empirically .