Graham Priest - Gödel's theorem and paraconsistency (UnB, 2018) - in English

Introduction 01:42
Gödel's Theorem 04:12
Paraconsistent logic 08:23
Inconsistent Arithmetic 23:20
Philosophical issues 37:24
Conclusion 48:15

[@TheParadoxOfParadox]

This is an absolute gem of a video! THANK YOU THANK YOU THANK YOU to the people who made the effort to create it. It has profoundly changed my life!

[@avi3681]

I've been enjoying reading Priest's work; it's really stretching my mind. This talk made me wonder if there a dual relationship between infinity and inconsistency. It seems evident that the paradoxes, when not embraced dialethically, generate infinities. For example, the Liar's paradox leads to the Tarski's infinite hierarchy of language and meta-languages. However, the model of arithmetic Priest shows at the end of the talk which is finite and inconsistent made me think that the opposite relationship also holds. Introducing a contradiction can collapse an infinite structure to a finite one while keeping all the truths about the infinite structure intact. So a contradiction operates as a kind of singularity that encapsulates an infinity within a finite structure. Thinking of these as dual led me to ask whether there is some invariant property that is conserved between an infinity and a contradiction. I would describe the invariant property as unresolvablity. The infinite is temporally unresolvable because it never ends. The contradiction exists all at once so it is resolved in time, but it is semantically unresolvable. There may be some model of this semantic unresolvability as something spatial or topological since so often contradictions seem to arise at conceptual limits or boundaries (as Priest describes in detail in his book Beyond the Limits of Thought). I wonder if there is a way to make these observations formally precise!

[@TristanHaze]

I don't think the models of arithmetic Priest was talking about *were* finite.

[@avi3681]

@@TristanHaze In this talk he presents an inconsistent and finite model of arithmetic. It looks like a line with a loop at the end, so all numbers above some value are mapped into the loop.

[@vladimirkabanov7610]

@@avi3681 I'm not sure that's the case tho: it's not the numbers above some (natural) value that are looped, it's the non-standard ones. Also recall that Prof. Priest explicitly mentions that all the truths of standard arithmetic hold in the collapsed model.

[@vladimirkabanov7610]

@@avi3681 Oh, buddy, forget my earlier comment, I watched the next 5 mins of the video)))

[@fluxpistol3608]

I love how the camera person shows the struggling audience members lol 😆

[@GregoryCarneiro]

That me in yellow hahaha

[@guypaterson-jones8630]

Can we download slides for this talk somewhere?

[@tommaullin1197]

After a bit of digging I found this; lna.unb.br/lna_n01_01_gpriest.pdf It's not slides but it seems to follow the slides very closely (same notation and steps)!

[@daltsu3498]

So our presumption that contradictions cannot exist led to our ability to logically deduce the goings on in the world and yet godels theorem proves that our presumption leads to unprovable systems. Do you guys think this will ultimately lead to us having to develop parallel systems of consistent and inconsistent logic? Or might inconsistent logic one day replace the consistent logic that we've basically always used?

[@behrad9712]

I think inconsistent logic represent the actual world in which we living!

[@raylittlerock1907]

there is a gap between 5:01 and 5:02 , at the most important moment !

[@GeorgWilde]

That calls for the lynching of the culprits!