Paradox is the Ultimate Truth

The true implications of Gödel's incompleteness theorems.

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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

[jaye]

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.

[lucnotenboom]

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.

[Infoagemage]

i didn't understand any of this, thank you

[garygoldberg]

The idea that the brain functions in BOTH modes of mechanistic (left hemisphere) AND non-mechanistic or 'organismic' (right hemisphere) 'modes' explains why the vertebrate brain is composed of two distinct cerebral hemispheres. It is also why the concept of 'reentry' is fundamental to organismic organization, including the organization of the human brain. In the frame at 16:06, one can associate the conditions on the left with the right cerebral hemisphere (ie. 'consistent' and 'non-mechanical'), and the conditions on the right with the left cerebral hemisphere (ie. 'mechanical' and 'inconsistent')... so the right answer is BOTH/AND. The real concern is which takes priority--which is the 'pilot' and which is the 'co-pilot'. For a good answer and one that I find convincing, it would be best to read the work of Iain McGilchrist regarding the role of the right and left cerebral hemispheres... one may associate the mechanical machinations of the left hemisphere with a classical computer, and the organismic intuitions of the right hemisphere with a quantum computer. What one needs to be complete is BOTH.

[garygoldberg]

This is the truth of the intuitionistic 'constructive' logic of the right hemisphere of the brain which is involved in willful agency and is dominant for emotion and attentional control. The left hemisphere follows Hilbert's hypothesis and holds to 'analytical' classical logic which is fundamentally intolerant of paradox. There is a very nice approach to this fundamental distinction in George Spencer Brown's book 'Laws of Form'. The issue is the necessity for 'reentry into the form' and the whole idea of reentry is a fundamental organizing principle of the general structure of the brain, as maintained by Gerald Edelman. From a mathematical perspective, the introduction of reentry REQUIRES the incorporation of imaginary numbers as shown in 'Laws of Form'. Which is equivalent to the introduction of a temporal continuum that introduces the reality of mediation that transforms contrarieties into complementarities. Mathematical 'truths' are associated with the function of the left hemisphere which holds to the Law of the Excluded Middle and the Law of Non-Contradiction (ie. that 'contradiction' cannot be tolerated). But the truth of the matter is that living reality is intuitionistic because of the fundamental role of willful agency and 'reentry into the form'. The truth is that any formalism is necessarily incomplete. Humans are not mechanisms and do not comply with the mechanistic formalism--which is the case for all living organisms.

[oliverwashbrook]

I was told to find the fruits of Gödels theorm thank you for this you are a very clever man

[KeneOliver]

You are going to get conundrums when you subvert the rule to let true = false.

[doctorinternet]

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.

[redswap]

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. 👍

[imjonkatz]

You are many you are one;
ever ending just begun.

[roaldkala]

All that is and all that is not arises in truth. Great video!

[PrisonOrDeathPenaltyCongress]

So basically don’t nobody know nothing about nothing.
I knew it

[Zlashdashoe]

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.

[javiersoto]

Awesome video! Keep up the great work!

[tejarex]

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.

[mattphillips]

Saying that Truth is equivalent to Proof" is equivalent to presuming Completeness.

[AmorLucisPhotography]

The verificationist theory of meaning is not stated accurately. That theory states that a statement is meaningful if and only if it is either empirically **verifiable** or analytic. The way you state it, however, empirically false claims -- e.g., I have three arms -- would be meaningless, because it is neither analytic nor empirically true! It is, of course, possible to verify that it is not true, so for logical positivists (and everyone else) it is meaningful. Secondly, the statement that Godel's Incompleteness Theorem signalled the demise of logical positivism is inaccurate. The central problem with LP was essentially internal - it asserted a criterion for meaningfulness that could not itself be meaningful by that criterion. It's much fairer to say that it signalled the demise of logicism (e.g., Russell), but we shouldn't confuse the two. Thirdly, there are many other ways of thinking about truth that do not endorse Tarski's assumptions about what a theory of truth requires (vis-à-vis the T-schema). For example, the redundancy theory of truth.