2. Graham Priest, On Contradictions

In this episode, Alex talks to Prof. Graham Priest (CUNY) about paradoxes, contradictions and the metaphysics of logic. Priest is well known for defending a theory, known as 'dialetheism', according to which some contradictions are true. He has also done considerable work on paraconsitent logic and the analysis of paradoxes.

[RideTheSmurfFTW]

Ser Davos Seaworth really enjoys his contradictions!

[stillunspoken]

Hooray! I've been waiting for this part of the conversation to open up for as long as I've been alive and thinking.

[ItsRamzi]

At around the 50:00 mark, you ask a very good question. You ask if classical logic is "recoverable" in, (if not a "limit case"), some subset of paraconsistent logic. His answer is, "In a sense, " but then he repeats what he already said about one system being an extension or generalization of Situations than another system. But, also insightful of you, was the analogy to working in Newtonian physics regarding some subset of reality. I think the spirit of your question was something like, "When taking a fuzzy attitude toward truth or consistency of propositions, for all propositions in reality, is there some epsilon or limit case where paraconsistent logics formally yield classical logic?" And I think that's a formal result that I certainly don't know, and he maybe did not know of at the time. Whereas, the spirit of his answer was like, "There are some situations where classical logic is capable, apples on tables and so forth, but other situations like liar paradoxes where paraconsistent logic is the better machinery for addressing that problem." Like he compartmentalized the problems cleanly, into those addressable by classical logic, and those which require an extension to adequately address. Whereas, I think you were asking about some formal property of fuzzy systems where some epsilon value for truth tolerance or consistency tolerance or something, eventually formally yields classical logic, like how Newtonian physics might fall out of quantum physics or relativity or string theory, for certain size values.

I don't know if I articulated myself well. He put problems into two distinct buckets, whereas you were taking a "paraconsistent attitude" to all propositions in a system where some tolerance value causes the system to lapse into classical logic.

[actrealationalist]

Excellent conversation - I've already read some articles by Priest based off this inspiration!

[stormcloud]

Brain hurts... in a good way. I will watch this one again :)

[MindForgedManacle]

This should be a good listen; always nice to see more Priest content. :-)

[joshuabrecka]

Love the opening theme (and the content). "the things that you're liable to read in the Bible..." Very fitting. Didnt know you were a jazz fan Alex! Thanks so much for doing these.

[Mossedey]

Great conversation! I can sort of see the point about motion in terms of classical physics:
To know everything about a system you need to know both the position and velocity (momentum) of all objects at some instant of time. However this is a bit of an odd picture because we say that in given instant an object has a property, which by definition depends on other points in time (definition of a derivative). So it is a bit "cheating" to say that an object has some velocity at a given an instant, since there is nothing about this instance alone that can say what the velocity is. Yet, velocity is fundamental to the physical picture.

In quantum mechanics however, this is not true (was hinted at by Graham): All you need, and indeed can, know about a particle is its position (or any other basis) wavefunction at some point in time. There is no extra quality which depends on other points in time. So in QM motion isn't a fundamental physical property and so the "movie reel" picture of motion seems very natural.

[isawilraen]

When Alex asks what is different between the 'object in motion at a point in time', and the 'still object at a point in time'... It feels like he's trying to create a pair of visual images in his mind that he can compare and find differences between empirically. I mean, as Graham said, the difference is that one is consistent and the other isn't -- because it makes sense theoretically.

I suppose that one could draw an arrow on a sheet of paper and name the work "Travelling Arrow", and leave another sheet of paper blank, and superimpose them onto each other, and there you go... Sure, the lines would appear weaker in the finished product, but if you were to use twice as much ink to draw the arrow, you'd end up with a picture that looked like the first picture anyway. So to think of it in terms of blurriness or whatever just seems weird.

The theory states that one is consistent, while the other isn't -- and we need to live with it.

Ooooor, time isn't analogous, and genuine flux is just a fantasy, and during small lengths of time, the arrow is still, and then it teleports a tiny distance in space and stays there, completely still, for a small length of time; and speed is perhaps about the length of those time chunks, or about the distance that's teleported, or both.

[chrisg]

In arithmetic we normally observe a principle of explosion by not allowing any two numbers to equal each other. As soon as we were to let say 4=11 then we feel that's it, if 4=11 then you can go on to argue 7=0 and 28=21 and eventually 451=1096 and anything else, ex falso quod libet. So for example whatever we got from say summing a column of figures in a ledger would be right, and if we sum it again and get a different total that's right too, so why bother. But what about allowing controlled explosions so to speak? Here's an example

2(2 +6n) = 3 + 4(2 + 3n),
4 + 12n = 3 + 8 + 12n
4 = 11
What?

Don't despair, take it as a sign to plug in 11 for 4 in the original equation:
2(2 + 6n) = 3 + 11(2 + 3n)
4 + 12n = 3 + 22 + 33n
12n - 33n = 3 + 22 - 4
-21n = 21
n = -1

This time we have an answer. I call this useful method Modus Corrigens. It's a bit like Modus Tollens in classical logic, but we're correcting the numerical value of the original proposition to another, rather than just the truth value.

Also it implies a more intuitive theory of false as leading you up the garden path, or deception. 4 =11 therefore isn't false since it's obviously wrong as a statement of quantities, so how can it fool you? It just means the original equation you derived it from is false.

[jamescantrell]

I swear to God, this world that I'm beginning to immerse myself in is just getting more interrelated and interrelated.

[TheSameDonkey]

Speaking as someone who does suspect a degree of validity to the notion that contradictions do occur, I personally don't see it when it comes to the arrow paradox. We have calculus for that, it does seem a bit odd and fuzzy when it comes to the issue of how long it takes for a point particle to cover a Plank length, but I have a hard time seeing that as a contradiction.

[darkhorse]

It seemed like there was some equivocation over the words moment/instant/frame when discussing Hegels theory of time. With the example of being able to see the 'second' hand of a clock moving.... It didn't sound like it was referring to any contradiction either. We aren't seeing the 'second' hand in 2 places at the same time. I didn't really hear a contradiction at play when he was asked what that instant would look like. It all sounded to start a little like Trey Jadows unintentionality & intentionality existing at the same time and in the same relationship, rather than one emerging from the other.

[johndavis]

Fascinating. Deviant logic is really cool.

[jamescantrell]

@thoughtology Did you ever try to read Priest's book, "One"?

[elephantchang]

Couldn't help wondering what Matt Slick would say about this..

[guiltycynn]

In 29:27 the discussion about the scrambled egg. We define the identity. You are you and if I replace a molecule of you with that of a scrambled egg. You have the option of redefining "you". You + molecule of scrambled egg. After you are 90% scrambled egg, if you can redefine yourself as you+90% scrambled egg, assuming you're still alive at that point, then that would be you. Then if you change 1 more molecule, you're just You (you+90% scrambled egg) + 1 molecule of scrambled egg. Right?

[rocio]

I think dialetheism is false. But by neighbour told me both I and the dialethest are right. Thank God. Now I can sleep well.

[Julian-jcxd]

watched the whole thing. still not sure if i get it. how can be both A and nonA be true (at the same time, same location, same conditions)? isnt that BY DEFINITION wrong? and the criticism against it only a hidden play around with words, location, time, etc? yes sometimes the truth value of a proposition cannot be determined. does that mean that A as well as nonA is true?

[benaberry]

Regarding paradoxs does deflationism theory of truth resolve the issue?