2. Graham Priest, On Contradictions
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- เผยแพร่เมื่อ 5 ต.ค. 2024
- 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.
We recommend his book, 'In Contradiction' (1987), and his website which features hundreds of free papers (grahampriest.net).
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Ser Davos Seaworth really enjoys his contradictions!
Hooray! I've been waiting for this part of the conversation to open up for as long as I've been alive and thinking.
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.
Excellent conversation - I've already read some articles by Priest based off this inspiration!
Brain hurts... in a good way. I will watch this one again :)
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.
Many years later, I now know this is not "It ain't necessarily so" and instead is "Exactly like you". Still learning...
This should be a good listen; always nice to see more Priest content. :-)
Thank you! :D
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.
The motion argument confuses me a little, progress feels as though a relation between instants rather than a property you can apply to an instant itself. Any thoughts?
@@TheJosh12694 Since progress is a little mysterious, I am going to replace it with velocity. Velocity is indeed by definition depended on many (potentially infinitely many) instants, and there is no way to talk about velocity with only one moment. That said, we can easily talk about the velocity in specific instant, it just takes into account times surrounding our instant.
In classical physics we need both the positions and velocities of the objects in our system in order to fully describe it, which means that we in fact need more than one instant to fully describe our system. You can then start asking questions like how does the particle knows how fast to move? does it "remember" previous moments in time?
I don't really know if we should be bothered by these questions, and I am more of an empiricist anyway, but I do find it interesting that these questions simply vanish in quantum mechanics - one instant of time is completely sufficient to describe our world.
@@Mossedey Thanks a lot for the clarity, I wasn't expecting such a quick reply on a 2 month old comment. Appreciate it.
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.
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.
I swear to God, this world that I'm beginning to immerse myself in is just getting more interrelated and interrelated.
Great video, thanks!
Couldn't help wondering what Matt Slick would say about this..
peter nicholson: Slick doesn't even seem to understand basic formal logic, he'd probably respond with nonsense.
True if it was presented to him his inflated ego would kick in resulting in nonsense as you say.
Fascinating. Deviant logic is really cool.
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?
Toha_BangBang: You misunderstand. The argument for why certain statements can be true and false at the same time has nothing to do with indeterminacy. Rather, the argument is that for statements like the Liar Sentences, giving them any truth value results in a contradiction. But that means it is a true contradiction, so we cannot say that all contradictions are incorrect if you accept the argument.
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.
If contradictions don't exist then it's possible I don't exist and then well, who is the author exactly of what you are reading right now. That's knock down enough for me.
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.
It's perfectly fine to be a dialetheist and to believe that dialetheism is false?
Good one 😂
I guess yes and no
I think dialetheism is false. But by neighbour told me both I and the dialethest are right. Thank God. Now I can sleep well.
@thoughtology Did you ever try to read Priest's book, "One"?
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?
Just because you are thinking of a system which resists preserving the identity with the slippery slope argument, doesn't mean that we can't think about a different kind of system which does preserve the identity with the slippery slope argument. Priest's point here is that we should reject as silly systems which tolerate telling us things like that we're eggs or frogs, but that systems with liar paradoxes are not similarly intolerable. He is biting the bullet and say there are genuinely contradictions sometimes, like liar paradoxes, but this tolerance doesn't overextend itself into allowing absurdities like that you're a scrambled egg.
Regarding paradoxs does deflationism theory of truth resolve the issue?
bena berry: No.
Mind-Forged Manacles why not? Adding is true in some instances adds nothing additional to some statements.
bena berry: Because to be a deflationist about truth, one has to accept the T-Schema in full generality. The issue is that it has been know for almost 80 years that accepting the T-Schema as such creates the Liar Paradox, as follows:
T(A) ~T(A)
Dialetheists are perfectly fine in accepting the T-Schema, provided they also accept Paraconsistent Logic (as they do). Deflationary theories of truth cannot solve the paradox for this reason.
It's easier to accept when you notice that it arises naturally. Just as i, the square root of -1, is the solution to a particular equation that otherwise has no solution, you can create an "imaginary" truth value (but don't call it that, it's not imaginary, it's constructible). You find that x and not x = true becomes the irreducible polynomial x^2 + x + 1 = 0 in the finite field Z2, using Boolean Algebra. Its well known solution is the finite field GF4, where the *two* new truth values satisfy not x = y; if you identify them, there's an isomorphism, and in fact the lattice P3 is embedded in GF4 (along with several copies of Z2). So you get a three valued logic immediately just by solving The Liar in Z2. That logic is LP and you can derive RM3.
English?
😭
Can you explain for me simpler if possible or direct me to someone where I can learn about it.
Since I am sympathetic to the liar paradox but didn’t know it had rational routes in mathematics.
For the arrow they need to do some physics. Take a photograph. It always takes some time to gather the light so the photograph will have some blur indicating motion. The concept of an instantaneous position is a nonexistent idealization. Physics works, philosophy doesn't.
this maybe nieve, but... doesn't quantum physics say that there are particles that both in one place and at the same time somewhere else. Thus, doesn't this match Hegel's concept?
Being at a location and being somewhere else is not a contradiction. What would be a contradiction is to say that you're at a location and not at the location. Something called "quantum logic" was developed in response to quantum mechanics, but it was eventually shown that quantum mechanics could be formalized in classical logic.
Awesome conversation! One question - wasn't the paradox of the arrow was solved by Isaac Newton as taught in introductory calculus? He basically says - how small is an "instant"? If you look at the arrow in any time-frame, it will be moving. You can cut the time-frame as much as you like, you will see movement of the arrow. What you in fact can say is that the amount of time when the arrow is not moving is 0, therefore it is moving and there is no paradox.
stenlis yeah, that is often said. However, I've read Graham say that calculus is itself technically inconsistent, so it isn't going to be ultimately acceptable if you want to avoid contradictions. However, I must admit that I don't know the details well enough to comment. I can dig out the reference for where he says that if you like.
Alex, I'd be ubterested ti see how calculus is technically inconsistent. It would be very surprising as it got humans to moon and back, but I'd certainly like to see Graham's reasoning.
stenlis: You misunderstood him. He was saying that Newton's/Leibniz's calculus was inconsistent (in how it treated infinitesimals). It's not inconsistent anymore though
I think dialetheism is at the same time both true and false. How about that ;o)
Eskil Wadsholt: Well, that actually the case, since the semantics of dialetheic logics entail that dialetheism is both true and false. ;-P
elaborate
@@MindForgedManacleso we can reject dialetheism since it is false
And others can support ir since is true.
Nothing to complain
@@androidvariedades6867 ahaha
This was thoroughly enjoyable, thank you! Regarding your question of how a moving object would look in freeze-frame on Hegel's account, I offer some ideas. Would the notion of a frozen frame have been conceivable prior to photography? Could it be the source of confusion over the apparent contradiction of "both here and somewhere else"? Prior to cameras, we could observe what Priest called "flux" as an object moves smoothly in time. This all seemed very much related to limits in calculus... You covered a lot of interesting ground, thanks again.
>Would the notion of a frozen frame have been conceivable prior to photography?
Yeah, unless cavemen had cameras that we're unaware of; people have portrayed galloping horses since quite early in human history.
>This all seemed very much related to limits in calculus
Why? Because it's about movement? I mean, calculus is about infinitesimals, which are distinct from point particles; theyre the closest thing to point particles, but non-zero quantities nevertheless; and they're needed in order to "capture" movement, precisely because Newton assumed moving objects being still at POINTS in time, and never said anything about them being in a contradictory state of 'here' & 'not-here.'
"This sentence is false" should go to the same category as "Color of sound is tricycle". It is not contradiction but few words put together to create nonsense. Since this is purposely created to be nonsensical why talk about it? We can create all kind of sentences that make no sense. Any explanation why we would take "this sentence is false" more seriously than any other meaningless set of words put together?
Well you can abstract meaning out of it you just can’t tell what the truth value of that meaningful claim is at first glance. You can’t make any grammatical sense out of “colour of sound is tricycle”. We can usually go about answering whether sentences have truth values, even self referential ones; “this sentence has nine different words and is true”.
@@noobslayeru If the sentence is true or false is outside of the sentence so it goes like this> Sentence "this sentence has nine different words and is true" is true. However > Sentence "this sentence is false" is false. Also no contradiction when evaluated from outside. The sentence is false because it does not provide a truth value. You can embed reference to self but it is not self reference how you evaluate something. Evaluation must be outside of thing being evaluated. It is just nice wordplay that sometimes you can do self reference and accidentaly it makes sense.
Frankly as a non- philosopher, I died a bit trying to listen to this. Is there any practical use for such talk or thinking? What is the point? “What I’m about to say is not true” seems to me either the person is lying and all off what he says next is going to be true, despite the fact he said it will not be, or he is telling the truth and all of what he has to say next will not be true. No contradiction either he is telling the truth or not , there is only true and false, in fact the person given the puzzle is committed to using an Aristotelian approach to determine if the statement is true or false. The rest is just word games which give philosophers a bad name, why sit around navel gazing and talking about pointless puzzles. You create hypothetical puzzles which have no bearing on reality and no practical use. Bit like saying “can God make a rock so big he can’t lift it”! Weird hypothetical that sounds quaint and deep, but has no practical significance because he never would, sure I suppose it has some merit in defining omnipotent , but not worth making a TH-cam on , let alone a whole line of philosophy. But I can see the popularity of this type of thinking in the crazy postmodernism era that we live, where it is popular to violate the basic law of non-contradiction
We have to use the tools of critical thinking when deciding what to believe and what to do. We need the right tools to explore questions that are much more than navel gazing, like whether God exists, what it means to be a man or woman (a prominent question of our current time), or what it means to be a good person. So the value in these talks is to see what tools we're working with and how powerful or limited they are. For example, Graham Priest implies in this interview that if dialetheism is true, then argumentum ad absurdum, a useful tool, is weakened, which to my mind is an argument against dialetheism!
Everything is always true because: it is about perceiving one's own body and the behavior of what it does, one's own mind and the thoughts and emotions which appear in it and the world/environment and the seemingly external events which happen in it SIMILAR to each other. So there is no differentiation between what happens outside or inside; what is culturally defined as the physical boundaries of a person. We normally say 'I think, I breathe and it rains'. if you look closer, some people say 'I think, it breathes and it rains'. but you do not control any of your thoughts; they appear like the rain; so better 'it thinks, it breathes, it rains'. But if you have a felt experience of this (classically called a mystical experience or in atheist terms an ecological experience); you understand that 'It is I'; because 'you are It'. So 'I think, I breathe AND I rain' is suitable real. If 'it rains' outside, YOU are raining, because thinking, breathing and raining are just a temporary CONTENT of who you are; the KNOWING REALITY in which all content happens. Content and context are the same; they are your reflected constructs. This does not mean that you have the personal volition to change them; but by the personal unconditionally accepting of what is; the continuous acceptance of change; you impersonally construct the whole of reality which will (as a consequence) benefit you personal. The felt moment this makes sense for you; aka the very moment just before you reflect on all of this with your thought, you experience what is called grace. And that HERENOW-experience of Self (outside spacetime) is the felt container in which the bodymindworld (or all phenomenal content) happens.
Everything is always true? Try walking across a busy road, the car is coming towards you, no it’s not, step out….? Just because you think something is true doesn’t make it so, belief is not truth , it is the substance of that belief that is all important