/sci/ - Science & Math » Thread #11164468

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Anonymous Wed 20 Nov 23:30:09 2019 No.11164468 View Reply Original Report

Quoted By: >>11164578

> REASON & LOGIC

Here I present a video, which I believe may be worthwhile viewing for any and all minds.

It's quite long (twenty minutes), and many of you may have already seen things that are similar, but I've chosen this one for the reason that I found it to be somewhat structured while also entertaining (0:00 - 16:00 being the lead up, 16:14 being the punchline).

>https://youtu.be/xfp4i-yve3o

Anonymous

Anonymous Thu 21 Nov 2019 00:03:48 No.11164557 Report

Quoted By: >>11164560

i aint watching all that shit, nigga. summarize it.

Anonymous

Anonymous Thu 21 Nov 2019 00:04:58 No.11164560 Report

Quoted By:

>>11164557
based and ADHDpilled

Anonymous

Anonymous Thu 21 Nov 2019 00:12:33 No.11164578 Report

Quoted By:

>>11164468
i dont get it

Anonymous

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Anonymous Thu 21 Nov 2019 00:13:34 No.11164579 Report

Quoted By: >>11164654 >>11164680

Short, basic introduction to the logical absolutes:

>https://youtu.be/cuRCF7h7FzE

This leads me godel's incompleteness theorem(s); for which I believe I understand the FIRST (could be mistaken), but I don't seem to be able to comprehend the SECOND.

This is where I am currently positioned - partial understanding of godel's incompleteness theorem(s).

I appeal to all of you wonderful thinkers, how can I better grasp the above?

Anonymous

Anonymous Thu 21 Nov 2019 00:16:19 No.11164583 Report

Quoted By:

*tips fedora*
christfags are really embarrassing too though, desu

Anonymous

Anonymous Thu 21 Nov 2019 00:41:36 No.11164629 Report

Quoted By: >>11164654

alright, i listened to it. what was the point of this thread again?

Anonymous

Anonymous Thu 21 Nov 2019 00:42:47 No.11164632 Report

Quoted By: >>11164636 >>11164654 >>11164686

Now, when I watch Numberphile (you guys like him/they/them, right?) attempt to explain godel's incompleteness theorem(s), I believe I generally understand the concepts being discussed, and the proofs used to show these concepts are valid (in complex systems of arithmetic) - watch here:

>https://youtu.be/O4ndIDcDSGc

Anonymous

Anonymous Thu 21 Nov 2019 00:44:19 No.11164636 Report

Quoted By:

>>11164632
I've seen that video, and yeah, numberphile is alright. What would you like to talk about?

Anonymous

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Anonymous Thu 21 Nov 2019 00:50:04 No.11164654 Report

Quoted By: >>11164663 >>11164667

>>11164629
I don't want to use a name, as I prefer to remain anonymous, but here are my posts, where I hope to be able to pose my current
'big question' to all of you, for input - >>11164579 & >>11164632.

I'm not exactly sure how to word the question, but let me attempt this now:

>aren't the logical absolutes (a much simpler axiomatic system), the foundations of reason, immune to, or, not subject to the incompleteness and inconsistency problem that godel's theorem(s) point out in classical arithmetic systems?

^^ This is the best I can do for now.

Anonymous

Anonymous Thu 21 Nov 2019 00:53:43 No.11164663 Report

Quoted By: >>11164674

>>11164654
I think I understand your question, maybe not. But all logical systems are subject to the incompleteness theorems. There is no "logical absolute" that is immune to it.

Anonymous

Anonymous Thu 21 Nov 2019 00:55:23 No.11164667 Report

Quoted By: >>11164671

>>11164654
Or, another angle:

>wouldn't it need to be shown that godel's incompleteness theorem(s) do in fact apply to the 3 axioms underlying reason and logic?

I could be wrong, but I believe I can see how incompleteness and/or inconsistency are inherit to complex, classical mathematics systems; is it a misunderstanding on my part that I cannot see how this also applies to the basic logical absolutes?

Anonymous

Anonymous Thu 21 Nov 2019 00:58:03 No.11164671 Report

Quoted By: >>11164688

>>11164667
>3 axioms
which are...?
What are the "logical absolutes"

Anonymous

Anonymous Thu 21 Nov 2019 00:58:27 No.11164674 Report

Quoted By:

>>11164663
I thought godel used the complex extension of the three logical absolutes, known as classical arithmetic systems, to show that classical arithmetic systems themselves are subject to incompleteness and inconsistency, NOT the underlying logical absolutes.

Anonymous

Anonymous Thu 21 Nov 2019 01:01:11 No.11164680 Report

Quoted By:

>>11164579
Understanding the thm is one thing, rather easy, and proving it is another. I won't prove it or state it exactly. I'll just say the gist:

In any mathematical theory (system of axioms with the typical logic rules) in which number theory can be described(most nice properties of natural number arithmetic) there exists statements which are true yet cannot be proved within the theory.

What's so hard about this?

Anonymous

Anonymous Thu 21 Nov 2019 01:02:10 No.11164685 Report

Quoted By: >>11164698 >>11164724

If the arithmetic that follows from a set of axioms are subject to incompleteness or inconsistency, then so are the axioms. That's the whole point. That's what is meant by saying a system is incomplete or inconsistent.

Anonymous

Anonymous Thu 21 Nov 2019 01:02:17 No.11164686 Report

Quoted By:

>>11164632
Numberphile doesn't give actual proofs of things. Are you an amateur?

Anonymous

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Anonymous Thu 21 Nov 2019 01:02:26 No.11164688 Report

Quoted By: >>11164696

>>11164671
Taken from https://medium.com/perspectivepublications/wtf-are-the-logical-absolutes-35ffc50b8860, for simplicity:

1) law of identity: “A = A”. Or in other words, something is what it is and isn’t what it isn’t.

2) law of non contradiction- “A ? not-A”. Or in other words, something is not what it is not.

3) law of excluded middle- “A + not-A = everything”. Or in other words, nothing exists outside of A and not-A. Additionally nothing can exist in between A and not-A. Likewise, nothing can be both A and not-A simultaneously.

Anonymous

Anonymous Thu 21 Nov 2019 01:05:46 No.11164696 Report

Quoted By: >>11164714

>>11164688
Can you not see how these axioms are incomplete? Hint: think if you can imagine a situation where ~(~A) does not imply A.

Anonymous

Anonymous Thu 21 Nov 2019 01:07:00 No.11164698 Report

Quoted By: >>11164705

>>11164685
How do we know that this is necessarily true?
Could it not be possible that the arithmetic system (any) was not completely, or sufficiently, or accurately, or properly and perfectly derived from the original axioms?

Has someone excluded this possibility?

Anonymous

Anonymous Thu 21 Nov 2019 01:09:11 No.11164705 Report

Quoted By:

>>11164698
>How do we know that this is necessarily true?
Because that is the meaning of the sentence "this system is incomplete or inconsistent"

Anonymous

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Anonymous Thu 21 Nov 2019 01:10:52 No.11164714 Report

Quoted By:

>>11164696
>Can you not see how these axioms are incomplete?
No, I cannot, that is the express purpose of this thread.
>Hint: think if you can imagine a situation where ~(~A) does not imply A.
I honestly do not understand what this means, in the context of the three stated axioms.. I apologise if I'm missing something obvious.

Anonymous

Anonymous Thu 21 Nov 2019 01:15:33 No.11164724 Report

Quoted By:

>>11164685
Also, the arithmetic of classical systems does not originate from the axioms I have described (the three logical absolutes); classical systems of arithmetic are predicated on complex axioms that are apparently derived from the three I initially mentioned.

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