Can Veeky Forums disprove hell? give me concrete evidence that proofs hell isn't real

According to the soundness and completeness of first order logic, all statements of the form "[x] exists" may be proven or disproven.

>Then what do you make of all those people who claimed that they came to hell/heaven and back>?

people with schizophrenia have all kinds of hallucinations including hearing voices and seeing things. Therefore the brain is capable of producing hallucinations that are indistinguishable from reality for those who experience them. Therefore there is no reason to believe that near death experiences are not a similar phenomenon.

Look, friend, (being deliberately nice here) to be taken seriously those who make claims are the ones who have the burden of providing substantiating reproducible unequivocal proof of those claims. Claims in this context include things like the existence of hell, or the existence of gods, or the existence of leprechauns. That's just the only reasonable approach to getting a handle on what is real and what is not real.

Its like I said initially, there is literally an infinite list of possible things that can not be disproven and it is not rational to believe any of them are real without evidence.

*bracing for negative reaction*

>According to the soundness and completeness of first order logic, all statements of the form "[x] exists" may be proven or disproven.

this is not actually true.

If I propose to you that a being exists in a dimension outside of the reach of beings in our dimension and that the two dimensions never interact then there is by virtue of the definition as I described there is no way to prove that it does not exist.

There are whole categories of these sorts of "things" that can not be proven not to be real.

What I've said is actually irrefutably true. Do you know what first order logic is? Do you know what soundness and completeness are in first order logic? Do you understand the order of logic to which statements of individual existence belong?

We have objectively proven that all statements of individual existence are, in fact, able to be proven or disproven. Your argument is a rhetorical one; mine is based off of things that we know to be unequivocally true.

Only if they are true in all models or false in all models. What reason do you have to believe that "Hell does not exist" is consistent between all models?

In your specific example, yes, I can prove what you say given a wide enough view of the universe. If I fix a language including existence and universal quantification (generalizations), and if I define the predicates, functions, and constants necessary to define reality (the vocabulary), I can include the premises you've given me as axioms in my deductive system. I may then translate your claim to a statement in this formal language, and, by nature of the proofs for soundness and completeness of first order logic, I am guaranteed that I may prove your statement if and only if it is true. In first order logic, proofs are also finite, meaning there is a finite proof for or against your statement.

>What I've said is actually irrefutably true. Do you know what first order logic is? Do you know what soundness and completeness are in first order logic? Do you understand the order of logic to which statements of individual existence belong?We have objectively proven that all statements of individual existence are, in fact, able to be proven or disproven. Your argument is a rhetorical one; mine is based off of things that we know to be unequivocally true.

here, this is a wonderful very good video on logic philosophy (a subject that it seems you are interested in a great deal).

youtube.com/watch?v=5wV_REEdvxo

I am not as good at articulation on the subject as the author of this video.

To put it more plainly, you are assuming the logical validity of S or its inverse, where S is "Hell exists," without justification.

I demand you explain yourself immediately.

Again, by the definition of soundness and completeness. Your claim is false in some model if and only if it is false in all models.

There are many statements in mathematics that are false in some models and true in others. The consistency of arithmetic is a famous example.

First order logic assumes nothing of the existence of 'inverses' or anything else. Your claim that hell does not exist is a claim of the non-existence of an object x in which x does not fit the functional description of 'Hell,' (with respect to predicates that you must fully enumerate within your language and interpret within your model) which is precisely that which you are interested in proving, and that which is precisely guaranteed to be provable by soundness and completeness.

I overstate my case somewhat. We can prve that there are models in which the consistency of arithmetic is false. We merely believe that there are others where it is true.

Still, independence results provide a more accurate example of statements that are not logically valid. Soundness and completeness require logically valid formulas.

Your claim is that negating the existence of a point with a set of well-defined qualities.

I am not fully certain that you understand elementary logic. Arithmetic properties which are not provable are instances of statements which fall within second- (or higher-) order logics. These are the things that we can't prove (see Godel's incompleteness theorem). Your example is a prime example of the sort of sentence which may necessarily be proved due to its ability to be expressed in a first-order logical system.

'Logically valid' means 'true in all models.' Again, I am uncertain of your knowledge of elementary algebra. Soundness and completeness is applicable to all sentences, not simply those which are valid (true).

elementary algebra and logic*

>precisely guaranteed to be provable by soundness and completeness

there are only so many different ways I can tell you that this only applies to logically valid formulas

You have justified neither that "Hell exists" nor "Hell does not exists" are logically valid formulas.

The axiom of choice and its negation are both invalid formulas in ZF.

How could I disprove it when we're posting in it?

Soundness and completeness is applicable to all sentences, not simply those which are valid (true).

No.

Consider a deductive system in first order logic with no axioms. It is sound and complete. But clearly it cannot prove any statements. This is because every possible model may exists, and thus no formulas are logically valid.

Once more, I am uncertain that you understand elementary logic.

"Axiom of choice" -- this is an axiom in a logical system higher than the first order. Again, not applicable.

"Logically valid formulas" is not even a concept. "Logically valid" is a phrase which refers to sentences in a language; a formula is a statement in that language which has a free variable. You do not prove statements with a free variable.

You wish to prove or disprove the -sentence- S = "there exists x such that x ... [exhaustive functional description of the definition of hell within your first-order language of reality]'. According to the soundness and completeness theorems, again, you may prove a sentence if and only if it is true. If it is not true, its negation is true (by the definition of satisfaction of a model). Therefore, you may prove exactly one of S, namely, there exists exactly one of (S) and (not S) within the maximal theory encompassing your set of premises and your accepted set of axioms.

There is no proof. Thats why its considered imaginary.
I might as well ask to prove my butthole isn't shaved.

Again, you're patently wrong. At this point, you're literally arguing against the most elementary definitions within logic.

en.wikipedia.org/wiki/First-order_logic#Validity.2C_satisfiability.2C_and_logical_consequence

Please just admit when you're not familiar with a topic. I don't mind explaining things to you, but it is somewhat annoying to somebody who is attempting to hobble imagined definitions together to try to argue against proven results.

Regarding a first-order system with no axioms: again, wrong. You have the set of logical tautologies from propositional logic. There are sentences that you may prove and disprove. There are also the sets of necessary axioms which you may generate using the definition of satisfaction in model theory.

I am increasingly certain that you don't understand elementary logic.

>"Axiom of choice" -- this is an axiom in a logical system higher than the first order. Again, not applicable.

I don't really believe you, considering all the other things you're wrong about, but fine.

"Logically valid formulas" is not even a concept. "Logically valid" is a phrase which refers to sentences in a language

Validity applies to formulas if you just assign false to every formula with free variables. I'm going to keep saying formulas because it doesn't matter.

S and ~S are not necessarily valid and so completeness does not apply.

No. This is a paradox and so is not in the realm of science to prove or disprove. You just have to wait and see when you die. Hope you've been saving up your good boy points.

Fine. Consider a deductive system in first order logic with no axioms, with S the successor function and 0 zero. Prove or disprove [math]\forall x, 0 \neq S(x) [/math]. By soundness and completeness this should be possible.

I have literally been wrong about nothing thus far. In fact, I have even consulted my old elementary logic textbook while constructing my responses for the sake of accuracy (see: Enderton, "Mathematical Introduction to Logic").

>use of "formula" and "sentence" doesn't matter

It does matter. If you know anything about science or mathematics, you should know that definitions are absolutely vital when attempting to engage in discourse. There are proofs about formulas. There are proofs about sentences. The results are entirely different. Validity only applies to sentences. Literally only sentences may be valid.

>S and ~S are not necessarily valid

One must be. If S is not true, then, for all models and assignments, S is not satisfied. This is precisely the definition of satisfaction for ~S in first-order logic. Another elementary result is that any sentence true in one model must be true in all models.

At this point, you're not arguing against me: you're arguing against the entirety of mathematical logic. At the point when I can point out mortal flaws in your understanding of even the most rudimentary elements of the topic and your only response is "it doesn't matter," I'm clearly wasting my time. When I can explicitly provide you new information (which you may actively confirm using any number of external resources) that contradicts everything you're saying, only for you digest precisely none of it for the sake of clinging to whatever your rhetorical opinion was at the beginning of the conversation, I can only conclude that you lack both the intellectual curiosity and the intellectual capacity to engage in any form of conversation which has any purpose higher than stroking your self-perception as being right.

To those who would engage, I warn you that this person isn't interested in mathematics, science, or even what is true: he is only interested in confirming his opinion that he is right. With that, I am done with this conversation.

an interesting troll

I honestly can't tell if he was serious.

the most interesting part about this thread is the fact that he was right and called you out, but you're still dead-set in believing that you've been right all along. i'm not going to waste as much time on you as the other user, but i think he was trying to do you a favor.

i'm guessing you don't have many friends?

>It does matter. If you know anything about science or mathematics, you should know that definitions are absolutely vital when attempting to engage in discourse. There are proofs about formulas. There are proofs about sentences. The results are entirely different. Validity only applies to sentences. Literally only sentences may be valid.

I gave you an isomorphic definition of validity and you bitch because you only want it to apply to formulas that got their nails painted and their hair did. You need to learn that certain mathematical notions are defined differently and different contexts. Your version of validity is just my version on a restricted domain. They're fundamentally the same function.

>One must be. If S is not true, then, for all models and assignments, S is not satisfied.

Truth only has meaning in the context of a model, so this statement is meaningless. Again, I tell you, which [math] you [/math] may confirm using external sources: there are statements that are independent of given deductive systems in first order logic. These statements and their negations are not valid over the models of that deductive system.

i thought you said you were leaving?

>/x/ thread, person trying to prove hell is real
>enter master fedora, telling us how it is about what can be proven
>enter logic user, blessing us with knowledge logic
>master fedora casts 'NUH-UH'
>logic user leaves

This is why we can't have nice things. Is there anybody else here who knows anything about this topic? I personally enjoy learning about the philosophy and the mathematics surrounding what we can and can't prove.

i thought you said you were leaving?

you've already been shown to be full of shit. just calm the fuck down and be glad this guy left and stopped roasting your ass.

i thought you said you were leaving?

i'm not him, but i do find it genuinely amusing that he got you good enough that you really want the chance to get another go at him.

do you want to pretend that i'm him? would that help you feel better?

Good job on not posting on the minute timeout. I'm actually unsure if its you or not now.

An interesting troll. I'm out.

>"B-b-but p-professor, I gave you an i-i-isomorphic definition!"

That's really creative, even for a brainlet. What's your usual follow-up?

>"c-c-can I get partial credit?"

It's a social construct. Stop oppressing me shitlord

I was there like a decade ago. Unsurprisingly there's a million stores trying to sell "hurr I went to hell XD" shirts

Prove to me that unicorns aren't real using concrete evidence.

What's a uicorn ? Present your explaination with concrete evidence please.