Paradox is the Ultimate Truth

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Benjamin Davies

Benjamin Davies

Күн бұрын

The true implications of Gödel's incompleteness theorems.
Go deeper: • Philosophy Has Been So...
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0:00 Hilbert's Program
1:10 Gödel's Incompleteness Theorem
3:56 Tarki's Undefinability Theorem
8:38 Brouwer's Paracomplete Intuitionism
10:20 Priest's Paraconsistent Dialetheism
12:17 Turing's Computability Thesis
13:59 Lucas's Anti-Mechanist Argument
16:10 Hofstadter's Strange Loop Theory
19:40 Bohr's Principle of Complementarity
21:05 Beall's Logical Pluralism
21:49 Paraphilosophy

Пікірлер: 44
@jaye5872
@jaye5872 7 ай бұрын
I've come to this conclusion recently myself. Reality itself is an ongoing neverending paradox. All is one yet all is two at the same time since the unity can only express itself fully through duality and thus it's all a paradox.
@bejdavies
@bejdavies 7 ай бұрын
Spot on 👌
@odievaldez6084
@odievaldez6084 3 ай бұрын
Adam was created in the image of God, and God is one; but Adam as one is a duality of male/female---a unity of opposites...
@isaacm4159
@isaacm4159 Ай бұрын
It's terrifyingly beautiful. I can see why some people run away from it.
@phulbig
@phulbig 5 ай бұрын
I’m in! This was great thanks.
@lucnotenboom8370
@lucnotenboom8370 7 ай бұрын
At 3:34 you say: G: "this statement is unprovable", and if G is false, then G is provable. If G is provable then G is true. Why is it not simply the case that G can be probably false? Provable only means verifiable within a system of conventions, as you can prove that something is false.
@bejdavies
@bejdavies 7 ай бұрын
To prove a statement is to show that the statement can be derived from the rules of your theory (i.e. it is true within your theory). So we don't _prove_ false statements, we _disprove_ them. In classical logic, you can disprove a statement by proving that it contradicts the rules of your theory, or by proving its negation. So yes, you can _prove_ that "it is true that a statement is false", but you cannot prove the false statement itself.
@lucnotenboom8370
@lucnotenboom8370 7 ай бұрын
@@bejdavies I see, thank you. As a layman, it seems there's quite some overlap/redundancy in some of the terms. As if the distinction isn't explicitly made that, however much you might prove something to be true, the proof/symbol/abstraction will never be the same thing as the original thing to be proved. It seems to me like there are actualities/'truths' (e.g. the phone I'm holding) and understandings/symbols/abstractions/'proofs' (e.g. the symbolic knowledge of the phone I'm holding). Understandings/abstractions/symbols encode information about actualities, but never enough for it to equal the actuality. So, G: "this statement cannot be known by the mind" can only be partially understood (like everything else we make abstractions of), and so G is 'true'/actual, it cannot be known by the mind, and we do not need to understand it fully to determine so.
@javiersoto5223
@javiersoto5223 7 ай бұрын
Awesome video! Keep up the great work!
@nickbeighton2183
@nickbeighton2183 7 ай бұрын
great stuff ben
@laurentfaulknerschilling
@laurentfaulknerschilling 7 ай бұрын
Fantastic video mate
@bejdavies
@bejdavies 7 ай бұрын
Thank you Laurent!
@roaldkala
@roaldkala 7 ай бұрын
All that is and all that is not arises in truth. Great video!
@doctorinternet8695
@doctorinternet8695 7 ай бұрын
I once read that "there is no logic, but logics", because, due to our nature as parts of reality, we can't possibly have in our minds a set of rules or representations that apply to reality in all cases. Our minds can have maps, the real territory can never be fully captured. Such would also mean that we must have representations of ourselves and others within ourselves, which would lead to an infinite self-reference 17:50 Also reminds me of zizek's characterization of the subject as the void of self-relating negativity, something that I don't understand enough to explain, but enough to find interesting.
@bejdavies
@bejdavies 7 ай бұрын
Interesting you say that. I believe Zizek's idea comes from Lacan's concept of the "empty square", and I do actually make this connection in my book.
@doctorinternet8695
@doctorinternet8695 7 ай бұрын
@@bejdavies Oh that's so interesting! I'm becoming more and more curious to read your book ;)
@Infoagemage
@Infoagemage 7 ай бұрын
i didn't understand any of this, thank you
@codybast882
@codybast882 6 ай бұрын
Just relax and let it fumigate a bit. You'll get it after the 100th viewing lol.
@buttsnapes450
@buttsnapes450 7 ай бұрын
Thanks!
@bejdavies
@bejdavies 7 ай бұрын
Very kind of you. Thanks!
@buttsnapes450
@buttsnapes450 7 ай бұрын
Your videos are so good and useful! Very skilled thinker! Though I sometimes wonder what this level of thinking does for one’s life, being someone on the diamond mind grind myself. Keep up the good work my guy!
@imjonkatz
@imjonkatz 7 ай бұрын
You are many you are one; ever ending just begun.
@Rhyane490
@Rhyane490 7 ай бұрын
Meaning?
@imjonkatz
@imjonkatz 7 ай бұрын
@@Rhyane490 From a song, I love you and Buddha Too - "You are a unameable You are unknowable All we have is metaphor That's what time and space are for Is the universe your thought? You are and you are not You are many you are one Ever ending just begun."
@redswap
@redswap 7 ай бұрын
Sorry, I know, I'm late watching your video! I hope you don't mind... I had things to do. Very interesting stuff. Keep the good work. 👍
@bejdavies
@bejdavies 7 ай бұрын
In your own time my friend! 🙏😁 Thank you!
@Zlashdashoe
@Zlashdashoe 7 ай бұрын
This was a really cool video! Have you heard of a fella by the name of Iain Mcgilchrist? There seems to be many connections here to his split-brain hypothesis, and he has an incredible book on the philosophy of this and much more. Titled: The Matter with Things.
@bejdavies
@bejdavies 7 ай бұрын
Thanks a bunch. I have been made aware of him, but I do wish I had known about him while I was writing my own book tbh, as I devote an entire chapter to the connetion to the hemispheres of the brain. I'm keen to read the book you mention!
@Zlashdashoe
@Zlashdashoe 7 ай бұрын
That's rad that you talked about it, I've got your book on my list to check out. Iain's book is a monster hahaa, but something of a bible for me at the moment. He also has a great youtube channel with lots of content. Do you have any reccomendations for me to check out?
@lucanina8221
@lucanina8221 7 ай бұрын
What a video
@KeneOliver
@KeneOliver 7 ай бұрын
You are going to get conundrums when you subvert the rule to let true = false.
@bejdavies
@bejdavies 7 ай бұрын
You'd still have 0 = false, and 1 = true. You'd just also have ½ = both. So, no true = false.
@Username5H0
@Username5H0 7 ай бұрын
A new upload? ( • o•)
@alexandernold827
@alexandernold827 7 ай бұрын
Hegel = Gödel. Gödel = Hegel....
@tejarex
@tejarex 7 ай бұрын
The opening statement "consistency and completeness cannot be combined in a single theory" is false in itself. For instance, propositional calculus is consistent and complete, and propositional truth values are mechanically (and usefully) calculable. What Godel said, and the the video immediate implies, is that if a theory is strong (or expansive) enough, then the two properties are incompatible. In particular, if the system includes counting with counts 0, 1, 2, ... and their arithmetic, as counts provide the codes that Godel uses. One can model counts and counting in both set theory and function theory and must be in any general basis of mathematics, and hence any general basis of math cannot be both complete and consistent.
@bejdavies
@bejdavies 7 ай бұрын
That isn't the opening statement though. That statement comes after establishing that we are talking about theories of the foundations of mathematics, which are stronger than propositional logic. Perhaps you skipped the beginning? 😅
@mattphillips538
@mattphillips538 3 ай бұрын
Saying that Truth is equivalent to Proof" is equivalent to presuming Completeness.
@bejdavies
@bejdavies 3 ай бұрын
That's clearly not so. Consider incomplete logics like intuitionism, which are grounded on the constructivist equation of proof and truth. I discussed this in the video, but the equation can be taken in two directions: paracompleteness, and paraconsistency. There are even such logics which are neither complete nor consistent.
@mattphillips538
@mattphillips538 3 ай бұрын
@@bejdavies I don't disagree, I'm just saying that the early starting point of "Truth is equivalent to Proof" you give at the beginning of the video can not be a premise in an argument for Completeness, as it presumes what it intends to demonstrate (i.e., that every true proposition is provable)
@MarxismIsACancerousReligion
@MarxismIsACancerousReligion 7 ай бұрын
So basically don’t nobody know nothing about nothing. I knew it
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