Curry's Paradox

[@whycantiremainanonymous8091]

If I'm not mistaken, this too is a Curry sentence.

[@AR0ACE]

My brain hurts... I guess you're right? Yeah

[@Kentrosauruses]

Kane’s relentless pursuit to prove to me that logic doesn’t work continues

[@fable4315]

This shouldn’t be a problem, only if you subscribe to naive truth theory. In formal logic this paradox does not arrise and has a resolution.

[@error-unauthorized_access]

​@@fable4315how?

[@real_pattern]

if this sentence is true, then curry's paradox is false.

[@stefanmilicevic5322]

if this sentence is true, then curry's paradox is correct. :)

[@KaiHenningsen]

@@stefanmilicevic5322 And if those two sentences are true, then your system is inconsistent.

[@teanutpub]

Pee is true

[@dustinking2965]

Self-reference leads to bugs.

[@Gavlavyus_Rumi]

New patch when? We need uptades

[@BennettAustin7]

This seems similar to saying something like x = x + 1, which would imply 0 = 1.

[@Xob_Driesestig]

or x is infinite

[@BennettAustin7]

@@Xob_Driesestig yes that’s true. And in our case of A->B it seems that this would mean A is some sort of infinite conditional. But I’m not sure if that is well defined

[@fable4315]

@@Xob_Driesestiginfinite is not a number, so x can‘t be infinite. That is the reason for calculus and why we need limits…

[@onty-op5587]

@@fable4315 Cardinal arithmetic is well-defined. Infinity + 1 = infinity can be given a mathematically precise meaning.

[@Fafner888]

A needs to be atomic (or at least analyzable into some atomic sentence) for A->B to make any logical sense, but since 'A' is defined to stand for a non-atomic sentence, you can't eliminate the conditional from A, because if you try to do so you get into an infinite regress. For this reason the 'A' within 'A->B' doesn't really stand for anything and so is the whole sentence really just meaningless or ill defined.

[@fable4315]

In naive truth theory you are wrong, you can try to make sense of such propositions. But in modern mathematical sense you are correct if I understood it correctly, I looked a bit into this and in formal logic the answer would be that there is a existence quantor and a for all quantor implicitly where the substitution doesn’t make sense, because, namely we try to substitute a A -> B into a context where we already statet „there exists A“. So the naming is invalid to claim that this A is the same as the A in the substitution.

[@swank8508]

that was my first assumption, havent finished the video yet though

[@joecampbell2365]

Very clear@@fable4315. Thanks!

[@GottfriedLeibnizYT]

Ah .. the good ol' self-reference.

[@brandonsaffell4100]

Thanks for doing the Tarski Theory of truth before this. Really helps contextualize both of them.

[@thomaslodger7675]

Love your vids on logical paradoxes.

[@horsymandias-ur]

THANK YOU. I’ve been looking for a new handy, generalized argument I can use for a while now.

[@khaliiid6514]

This is so surreal i was literally just now reading about this, (doing a course on lambda calculus). Lol Keep up the good work btw !

[@cynical5062]

lambda calculus is so fun

[@mkrafts8519]

This isn't a paradox in my opinion. Because we are mixing the grammar with the claims the sentence is making. The claims the sentence makes are irrelevant for the sentence structure to be true. But see, when we define "true" some of us are thinking of the claims of the sentence, while others are thinking of its grammatical correctness. True sentence according to grammar: "If this sentence is true, then I will claim whatever I want because the parameters have been set by the initial clause." True sentence according to claims: "If this sentence says something true about God, then God exists." So which is it? True grammar or true claims? The claims are arbitrary. Rather, the parameters of the sentence are dictated in the first clause. Parameters set: "If this sentence is true then" Contingency: "insert any claim here" This means (A) does not -> (A), because a parameter and its contingency are not the same thing logically. The logic is referring to the modal power of the grammar and is not do with the fictional claims of the sentence itself.

[@mkrafts8519]

If we change the sentence to "If this claim is true, then God exists." We start to see the logical flaws. That is, the first clause is not a claim. And because the second claim is dependent on the parameters of the first clause we see the logical flaw.

[@TotalitarianDemocrat]

​​​@@mkrafts8519The first clause (the antecedent) isn't a claim, but that's not what "this claim" refers to: it refers to the whole sentence, which is a claim. The second clause is not a second claim, it's just the consequent (part of the same claim as the first clause).

[@fable4315]

⁠@@TotalitarianDemocratI think the problem is that the „claim“ refrences itself before it was even stated. And in mathematical logic this is exactly the resolution, you need to transform this into something which is satisfiably equivalent (but doesn’t have to be logically equivalent) and then you see that the transformed statement is not satisfiable so this claim is never true.

[@mkrafts8519]

@fable4315 This logical flaw becomes even more apparent when we flip the claim to the first clause: "If God exists, then this sentence is true." Even this sentence is logically fallacious because even if we verified that God exists, it doesn't mean the sentence stated a true claim. Because it never claimed God existed. It only gave the contingency "if". An "if, then" contingency has to be contained in the first clause. Another version: "The sentence is true, if God exists." We verified God exists so does this mean the sentence is true? True about what? The sentence never made a claim. Even if God existed, the first clause is logically disconnected.

[@blackheart7921]

I don't see the paradox. True, if we assume that A=A→B then we can conclude B. But similarly, from ¬(A=A→B) we can conclude ¬B. So in general, A=A→B is simply an equivalent statement to B in all cases, and we can't just assume A=A→B to be true without further justification, the same way we can't just assume B to be true without further justification - not in a way that lets us extract insight into a general assumption-free context, anyway. "If this sentence is true, then X is true" can simply be an incorrect statement the same way that "X is true" can be an incorrect statement, no paradox whatsoever. Incorrect statements do exists and that existence doesn't make them cease to be incorrect.

[@benjamingurevitch4097]

The whole point of the paradox is that we don’t assume A is true (that is, we don’t need to make the assumption that if A, then B is true

[@blackheart7921]

@@benjamingurevitch4097 The whole paradox is however based on the assumption that X is true where X=(A=A→B), which lacks any kind of proper justification for why X can't just be false. If X is true then yes, we can conclude that B is true. But if we just assume X to be true without proper justification, then any conclusions from that are only valid within the assumption context. Ultimately, the supposed "paradox" is nothing more than the statement that "(A=A→B)=B" - which isn't a paradox at all, it's just a normal equivalence. Technically it's "(A↔A→B)↔B" but I don't like that emoji graphic.

[@Eta_Carinae__]

@@blackheart7921 X is a definition. Doesn't need justification.

[@mandobrownie]

I can definitely see why relevance logics and logics in the same vein make sense now lol

[@MrGustavier]

But isn't there a problem with saying A = A→B in the first place ? How can these be equal ? They don't have the same truth table. A→B can be both true of false when A is true, and A→B is always true when A is false.

[@richard_d_bird]

he's inserting a = a>b by simple definition. i guess curry would say it's because a refers to its own truth value as the condition for b, but this is all formal stuff. it's a case of formal arguments referring to their own formal systems, thereby producing nonsense conclusions, and i agree in this case the truth tables kind of neatly say yeah, no don't do that.

[@nicknolder7042]

I think you’re on to something. The only way A is logically equivalent to A (insert some operator) B is if the operator is true when A is true and false when A is false. Let’s call the operator G. So A (A G B) But the truth value of B is not guaranteed either way by A being true or false. B could be true or false when A is true, and B could be true or false when A is false. The paradox relies on the fact that A being true guarantees B being true, but like you said, A (A->B) is false in all cases. In short, I agree with you.

[@Azrael664]

You are one of the few honest men

[@Elisha_the_bald_headed_prophet]

Conversely, B implies (A -> B) for any A, in particular for the self-referential statement A = (A -> B). Thus assuming the truth of the Curry sentence is equivalent to assuming the truth of B straight out (ignoring the admissibility of self-referential statements).

[@italogiardina8183]

Truth conditionals are tricky when used in everyday transactional ordinary language, as in making a deal: for try stating to a sales person 'if the used car is road worthy then it's good to purchase' . This is one sure way to end up with a good lemon.

[@tomrobingray]

The solution to the Curry's Paradox is simply this. Whereas it is true syntactically that every arbitrary statement A entails such a statement B. As soon as we specify what A might be, then the specification of B is necessarily restricted to what follows from A.

[@synchronium24]

Based God

[@frogandspanner]

The _If_ restricts the domain of discourse, and for something as iffy as the existence of a god the domain is infinitessimal.

[@dwbi24]

bro listening to this with airpods sounds like your coming out of the speaker somehow away from me its unsettling

[@fable4315]

I would have liked a little bit more discussion about the paradox, because there are resolutions for this. If I am correct this paradox was first stated in the realm of mathematics but mathematical formal systems have a resolution to this and right now our mathematics is free of inconsistencies like them (but then also provably not complete, which is sad but I can take that). I think we can construct with natural language more than „actually exists“ and I know that this is deeply philosophical and I don‘t know philosophy enough to say what philosophy this is I am subscribing to and what it‘s actual weaknesses are, but it makes intuitively sense for me. Just because we can state anything doesn’t mean it have to make sense in a real world context.

[@fable4315]

Also wouldn’t it be more general to state „if this sentence is true, then false“ then we can claim we derived false and from false we can derive anything?

[@ELPsteel]

Correct me if I'm wrong, but isn't this just an example of both tautology, and infinite regress? I.e. "if this sentence is true, then if this sentence is true, then if this sentence is true" etc

[@BlueEyesDY]

How is it not obvious the problem is with the contraction step in each case? The contraction is only valid if A is true, so it begs the question for the later inference to A.

[@Wasyashock]

It feels like Curry sentences shouldn't be assigned truth or falsity

[@Feds_the_Freds]

Let's try it with the sentence "If this sentence is true, then god exists" to show why this argumentation doesn't work: First, we have to agree, what is A and what is B: A = "If this sentence is true, then god exists" B = "god exists" I hope, we can agree :) Now, step by step and see, where it breaks: (1) A -> A, so "If this sentence is true, then god exists" -> "If this sentence is true, then god exists" Obviously, this is true. (2) A -> (A->B), so "If this sentence is true, then god exists" -> ("If this sentence is true, then god exists"->"god exists") I would argue, that the argumentation breaks here. The problem is that it is an infinite recursion. So what is actually meant with the step above is: ""If "If "If "If "If "If "If [A indefinitely] is true, then god exists" is true, then god exists" is true, then god exists" is true, then god exists" is true, then god exists" is true, then god exists" is true, then god exists" So, I would argue, curry's Paradox fails at step 2 (in this example of the Paradox) because of infinite recursion. Do you argee? Do you think, it breaks later?

[@Anonymous-ru9jv]

The solution to this seems trivial to me. Sentences contain information correlated to physical reality (in the purest sense; including potentially the state of the speaking neural network). There are no metaphysical rules governing the 'truth of sentences'. In other words Curry's paradox misunderstands the nature of language.

[@brandonsaffell4100]

" Sentences contain information correlated to physical reality " They certainly can, but they by no means have to. If your theory of sentences is premised on that, then it's going to be incredibly limited.

[@Anonymous-ru9jv]

@@brandonsaffell4100 I think they do have to, in the physics sense of information, because they're produced by physics

[@fable4315]

I think the mathematical resolution in formal logic is cleaner than that. And I just say I am always talking about mathematical logic because logic with natural language is incredibly weird sometimes as you can see here. Sure we still need natural language to define propositions, but we should not analyze it in a natural language way and here this paradox was presented with many hidden mathematical assumptions which make no sense in modern formal logic.

[@gorricsfalterman3454]

just go substructural blocking contraction, might be helpful to check "Substructural Logic" -Greg Restall

[@Chalisque]

I'm only at 3:10. My thought with "If A is true then" is that you must _substitute_ whatever A is defined to be in place of A before evaluating. Thus if A := "If A is true then God exists", then expands to "If (If A is true then God exists) then God exists"; and then to "If (If (If A is true then God exists) is true then God exists) then God exists", and so on. So we do not end up with a well-defined finite sentence about which we can contemplate its truth. I'll watch on.

[@grivza]

Those are perfectly good sentences, you can even intuitively understand the tautological nature of "If (if this is true then God exists) is true, then God exists".

[@Chalisque]

@grivza The point is that you can't evaluate the sentence until you have substituted the word 'this' for whatever 'this' means. This leads to infinite recursion. Essentially, if you can't eliminate all 'this' and 'that' type references in a finite number of steps, you can't evaluate the original sentence.

[@luszczi]

I get the technical side, but my intuition tells me it's a massive stretch. "A" is obviously no proposition at all in the first place. It's like "G" in GNU (GNU's Not Unix). There is no "G". Do you ever need to construct such self-referential substitutions? I'm guessing this is needed for something or otherwise the paradox is solved by just disallowing this kind of thing as nonsensical. I guess what I don't understand is why this is a problem.

[@СергейМакеев-ж2н]

All self-referential sentences can be restated as non-self-referential ones. Instead of "this sentence", you refer to "the sentence that you get when you apply such-and-such operation to such-and-such string of text". Consider the operation "prepend that string with itself in quotes". For example, if you apply it to the string "abc", you get ""abc" abc". And if you apply it to the string "is a string consisting of seven words", you get: ""is a string consisting of seven words" is a string consisting of seven words" which is actually a true statement. In other words, "is a string consisting of seven words" prepended with itself in quotes is a true statement Now, consider the following statement: "prepended with itself in quotes is not a true statement" prepended with itself in quotes is not a true statement

[@grivza]

You will never need to construct such substitutions, but when you have a big problem with many logical statements, say a very complex formalized proof, you might not be able to spot this paradox, but the logic of the proof will be sound.

[@luszczi]

​@@СергейМакеев-ж2н If you use "itself", then you're not really escaping self-reference, do you? More generally, I think you're trying to avoid a semantic problem by using syntax alone. That doesn't really convince me, since I accept the syntax rules that cause the paradox. My problem is that "A" still doesn't mean anything, so it can be neither true nor false in the first place.

[@luszczi]

@@grivza The reader of the proof might be easily fooled by this, but I think the writer knew what he was doing. :D

[@grivza]

@@luszczi No are you kidding? What type of proofs you think we are talking about, things get incredibly complex, which is anything worthwhile these days. Thankfully we have type theory now, so it's not a matter anymore.

[@heresa_notion_6831]

Philosophical newbie response (and question): It is an interesting characteristic of the consequent -- "God exists" -- that it is not (too) knowable (i.e., it depends on your definition of God), but what about the case where you DO know the truth value of the consequent? 1) If this sentence is true, then triangles have 4 sides. If we consider 1) "false" in this case, because we know a triangle has 3 sides, might we just consider 1) false in cases like "God" and cases like "a triangle has 3 sides"? Are perhaps most logical paradoxes (e.g., liar's and Russell's set- inclusion paradoxes) just "solvable" by defining any statement that allows one to conclude both P and not(P) as being "false"? I'm guessing this would be a "functionalist" response to paradoxes, inasmuch as the "function" of logic is (arguably) to avoid such contradictions.

[@michaeljones1686]

I think that this is just a proof that a curry sentence cannot be defined

[@KaiHenningsen]

... in a consistent theory. Though beware of Gödelization!

[@synchronium24]

@@KaiHenningsen Meaning that we can have either consistency or completeness, but not both?

[@reclawyxhush]

'This sentence has no meaning whatsoever.' Yet we can understand it somehow, a testament to the power of the human mind.

[@grivza]

Cause the semantics of words inside the brain aren't built on the basis of syntax rules or the retrospective definitions we give to them in order to try and formalize them.

[@cavestoryking8761]

It's meaningful and so just plain false, no paradox there.

[@reclawyxhush]

@@cavestoryking8761 I've worked on the subject today. It seems that it is not a logical sentence, so its falsity is not the same as that that can be ascribed to a legit logical sentence. And I would nevertheless argue that while it may feel false at first glance it is obviously not plain false. Assume it is -- in such a case arises question what the meaning of this sentence is then? How can you even think that the meaning of this sentence is the absence of its meaning? It's just as absurd as trying to imagine Nothingness I guess :)

[@cavestoryking8761]

@@reclawyxhush It has meaning because it has words that I know (one might even say I know their meaning) which are all strung together in a gramatical fashion. But it says that it does not. So it is false.

[@reclawyxhush]

@@cavestoryking8761 Does it really have a meaning merely by the virtue of being composed of familiar words arranged in a familiar pattern? This is not what the meaning of a sentence is about. Note that this sentence is not 'This sentence is composed of unknown words and is ungrammatical'. The meaning of a sentence arises as an emergent property of both its words and their structure -- it is of a higher level semantic than particular words and obviously something different than the grammatical correctness.

[@awebmate]

Raise your right arm for yes and your left arm for no. Now answer "are you raising your left arm?" OOOOOH it's a paradox.

[@davib.franco7857]

Yes, that is a paradox

[@bertrc2569]

But does it do anything, get you anywhere? I thought philosophical pursuits in the time of the Greeks was to clarify life rather than bury it.

[@jacksaetveit]

This is just like the proof against dividing by zero where 2=1 and 1=0 and all that. It seems like we could just do modus tollens from the knowledge that the conclusion is clearly wrong and by that infer that something is wrong with the logical structure in this specific case, and if not in this specific case, then in a broader sense.

[@grivza]

What? If you knew that the conclusion was clearly wrong you wouldn't need to try and conclude. This isn't some proof about how everything is true or everything is wrong. This is about the limitations of (untyped) logic. If someone created an automated prover without finding a way to handle this paradox, it would be proving everything, entirely useless.

[@synchronium24]

@@grivza "If you knew that the conclusion was clearly wrong you wouldn't need to try and conclude" I think OP is referring to taking the contrapositive of a Curry Paradox conditional. "If this sentence is true, then combat wombats exist." is logically equivalent to "If combat wombats don't exist, then this sentence isn't true." Combat wombats don't exist, so the entire conditional statement isn't true.

[@grivza]

@@synchronium24 And yet you can prove it is true, and that's the whole paradox.

[@KGTiberius]

Why assume “then”? B has no relation to A except the assumption in “then.” If 2 = 2, then 0. Therefore 2 = 0. Nonsense.

[@silverharloe]

If presented with a conditional where the antecedent is a tautology, reject the conditional.

[@4dtoaster819]

Then we have to reject conditionals that seams clearly true. Like: T -> T It's an identity conditional, and it's consequent is true, so it feels strange to reject it

[@EduardoRodriguez-du2vd]

In my view, it is wrong to suppose that one can prove the existence of something in reality by means of philosophical consideration. Philosophy only produces hypotheses and no amount of hypotheses can prove that something is real. One cannot pass the hypothetical stage without analyzing data from reality. One cannot deduce an existence that is not presupposed in the premises. Deducing is just deploying according to the rules of logic. A proposition is one of the ways of relating a concept to the reality it represents. But a concept is not a closed and independent entity. A concept is one more node in a network of concepts that contextually complete its meaning. When one says "All men are mortal," man is a concept that is supported by other underlying concepts. Biological individual, physical universe, human mind, etc. and these in turn rest on their own conceptual basis. The inevitable thing is to distinguish that all concepts float on an ocean of unknown depth. The level on which we base them is just a convention and depends on how practical we want to be. "Man" is not an independent concept, with a certain limit and our limited knowledge only allows us to extract a probable interpretation of the nature of it. Not a certainty and then, a deduction from a proposition with a concept that is not perfectly defined, in the full extent of its nature, does not allow drawing conclusions of absolute certainty. Thus, philosophy cannot solve the problem of how probable an idea proposed by this discipline is. To do this you need to analyze the probability of each premise and with this probability, determine the probability of the conclusion. Adding these calculations, with data from reality, is what we call science. Philosophy cannot avoid using human knowledge as material for its considerations and human knowledge is only probabilistic. This does not represent any problem within an idealistic interpretation of reality. But in order to do such a thing, one must close one's eyes to reality. --- In this light, A is A implies that A is an independent and complete entity of a given nature that will continue over time. If this were not the case, A would be equal to itself now but then A would no longer be equal to A, in its previous stage. That equality would be circumstantial. (this is resolved with the idea of essence but that is an anachronistic concept with no validity today) One could argue that all possible instances of A can be taken as a whole as coherent with that same group, but our imperfect knowledge leaves us having to calculate the probability that group A does not have stages in which it is equal to something that at some point is also equal to something that is not A. Thus one may find itself in the impossibility of proving that A is different from or equal to B , circumstantially. . And I'm just going for A is true with respect to itself. I see that this is getting too long and esoteric for me. Maybe, with coffee and after having looked out the window, I will still be delirious later!

[@adenjones1802]

Premise 2 seemsva bit shakey. The whole thing rests upon equivicating the two different "A"s. A in this argument entails both that there is a peice of evidence that proves God And it entails in another sentence that modus ponens. If A is the same in both cases, then the problem is with an infinite circularity. A is true. What is A? A = if A then B. Ok but what is the A in that sentence? In that sentence, A= if A then B. And on and on it goes.

[@rath60]

For the sake of proof by contradiction assume a Curry sentence can exit, e.g. p is the statement p implies q. For ease of understanding I'll write p = p=>q. Let p=F and q=F then (p=>q) =T => p=T by our hypothesis p= p=>q . Therefore p=F => p=T . Contradiction. Therefore p is not equal to p implies q .

[@GregoryLopez1]

I don't get the truth schema argument at 14:28 . Doesn't the move from TA to (1) ignore the different language levels? The proper interpretation would be: If A is true, then [if A is true, then God exists]. From there, you can't validly move to (2) via contraction.

[@KaneB]

There aren't different language levels; we're using a "naive" truth predicate here. If we presuppose something like Tarski's hierarchy of languages then presumably we would say that we can't construct a Curry sentence in the first place, so the paradox wouldn't arise for that reason.

[@bigol7169]

Butter Chicken's Paradox

[@cubething-x64]

thank you for the videos on logic. i've been wondering for a while now what happens after classical logic, as i was only taught up to that level (and frankly i didn't do well at it). these overviews are giving me a good chance to quickly improve my broad understanding of philosophy

[@intellectually_lazy]

what did they do to curry for wasting everybody's time?

[@synchronium24]

Not nearly enough.

[@Mon000]

I see you hopping on the "The most" thumbnail trend too, my best salutations to you.

[@Feds_the_Freds]

If I think correctly, this isn't a paradox at all as it has to presuppose A in the first place.

[@blackeyefly]

Where exactly is it presupposing A? I don't think you understood it correctly

[@Feds_the_Freds]

@@blackeyefly "If I think correctly, this isn't a paradox at all as it has to presuppose A in the first place" is A and "this isn't a paradox at all as it has to presuppose A in the first place" is B ;) Ok, seriousely though: I just answered it fast with the joke intended to be that it follows the curry's paradox pattern. So basically, I said anything as it was "true according to curry anyways... I answered with a bit more thought in an other comment: My conclusion was, that it fails because of infinite recursion at step 2. After some research, I found that this was basically the reason that ZFC excluded infinite recursion to be possible. So I would think, this part really poses a problem in logic.

[@blackeyefly]

@@Feds_the_Freds ok I misunderstood your comment, my bad

[@hardryv3719]

That sounds _prima facia_ to be *_batshit crazy._* Where is the work? If that's all accurate, it sounds only like there is an obvious flaw in some simple, logical proof constructions. That crap proves bupkis.

[@Mulakulu]

This sounds like it's just asserting something invalid in a fancy self referential way. Its like saying "If this apple is red, God exists" which clearly doesn't say anything about reality. Theres nothing inherently wrong about self reference. Ask any engineer working with differential equations. Its just harder to make a true satement with them it seems, but yeah. An invalud statement is an invalid statement

[@JungleLibrary]

I'm confused: surely "If this sentence is true, God exists" has two possibilities, it is true or false (or maybe undefined?): if true, God exists; if false, God doesn't exist. I'm not understanding why it isn't an assertion like any other, i.e. "If I'm right, God exists, if I'm wrong, God doesn't." Whereas the opposite, "if this sentence is false, God exists" seems to create a contradiction if God exists, because then the sentence can't be false since it accurately states God's existence - however it seems to me that sentence is actually asserting the non existence of God, making it consistent.

[@MadaraUchiha55910]

Isn’t this just the circular reasoning fallacy.

[@gJonii]

A being FALSE implies A->B. But here, you said A being TRUE implies A->B, which is obviously false. I tried to see if you assume something about B but you didn't list A->B as an assumption ever, so A -> (A->B) is just false. That's not how logic works. ~A -> (A->B) is true, where ~A is the negation of A, that's the closest classical logic can get you to these things. And once you build on top of that obviously false step, everything else is just nonsense, the same as assuming 1+1=5

[@thelordz33]

I don’t see the paradox. Any assertion inherently implies that if it is true it is true. Saying "God is real" and "If this statement is true, God is real" are essentially stating the same thing because in order for the statement "God is real" to be true the statement needs to be true.

[@obkyrush]

you are correct this comment was made by trivialism gang

[@OBGynKenobi]

Ceci n'est pas une phrase.

[@haph2087]

I don't see why this is remotely interesting. You can state however many conditions that A must imply as you like, and A can even imply itself, but that doesn't make A true. Consider: a=>b a=>a Aha! I've proven b! And, just to be sure, truth table time! A B T T Consistent with the propositions T F Inconsistent with the propositions F T Consistent with the propositions F F Consistent with the propositions Oh no... We've failed to consider the case where A is false. If A is false, then it doesn't imply anything about itself, nor does it imply anything about B. But curry's paradox is more nuanced! When a sentence in curry's paradox is "false" it's also true! Because (F=>B) is always true, therefore any curry's paradox style sentence is true! Well, no. That's wrong as well. Any false curry's paradox sentence is a paradox, but that doesn't necessitate that every curry's paradox sentence is true. Logical statements/arguments can have both the potential to be true, and the potential to be a paradox, when their premises are tested. In the case of a false conclusion, it's like an elaborate form of the "this sentence is false" kind of self-referential paradox. An assignment of a particular value requires the reassignment of itself as the opposite infinitely. The difference is that Curry's paradox sentences do have a potential internal state where they are true, so some people wanting to avoid thinking about the paradox will assume they are true. Even if "B" is true in a curry's paradox sentence, the sentence can still be "not" true, because the sentence being a paradox is still perfectly possible. A=>B does not imply B=>A, so knowing B doesn't eliminate the possibility that A is false, which leads to the paradox. In this sense, even if we state, "If this sentence is true, then God exists", and then we by a sound argument prove god's existence, we still cannot be certain whether the sentence was true. We just now can't rule out that it *could* be true. My final description of this type of sentence would be that Curry's paradox sentences that argue for false conclusions are all paradoxes (of the self-referential "this sentence is false" kind), and Curry's paradox sentences that argue for true conclusions are undecidable whether they are true or paradoxical (which adds a new kind of psychological paradox where people wanting to avoid the paradox pretend the sentence is true).

[@ReubsWalsh]

The sentence is not true, if the sentence is to be interpreted as a logic statement, then it's not true, because that dependency does not exist. It is not the case that the true occurences a sentence describe do not occur BECAUSE a sentence is true... It's like, at best, the sentence is unenforceable 🤣

[@bread8176]

This entire argument seems to depend on not being able to tell the difference between words and the things the words refer to, what a nothingburger

[@benjamingurevitch4097]

That’s just not true?

[@tomholroyd7519]

8:21 I'm sorry, I thought this was a more sophisticated argument. I mean A -> (A -> B) isn't even classically true what are you talking about

[@KaneB]

"A -> (A -> B)" follows from "A -> A" in this case, because when "A" is a Curry sentence, "A" is equivalent to "A -> B"

[@Sudhebdurbdhdbd]

@@KaneBthe argument is question begging.

[@tomholroyd7519]

It is challenging. OK so I haven't watched the video yet. But when you say "if it's not true" remember that 4-valued logic exists

[@СергейМакеев-ж2н]

That's the neat thing about Curry's Paradox: it works for a much larger variety of logics than plain old Liar's Paradox. That's because it needs barely anything to work. It just needs Modus Ponens, as well as some kind of contraction.

[@Skyhigh275]

AB A B AB BABLE….

[@justus4684]

🍛

[@teanutpub]

Pee is true

[@AtlasofReality]

indian ahh paradox

[@Azrael664]

🔴⚫

[@truthseeker2275]

Please help: How does the non-sequitur fallacy affect this paradox. It would seem to me that, if you guard against a non-sequitur it is no longer a curry paradox.... or if you commit the non-sequitur then it is an invalid(unsound?) argument?

[@Disappointed_Philosoraptor]

This video was a bit of a mess to listen to. You need to start scripting your sentences and then stick to those scrips word for word. Then, you should cut out poor phrasing, mess ups and repetition.

[@KaneB]

I do that already. This channel probably isn't for you.

[@Disappointed_Philosoraptor]

@@KaneB Well, that's an oddly defensive answer. Was my phrasing a bit too harsh? In that case, I mean no offense when I ask this, but, what makes you think that because I find it hard to listen to a few particular segments where you seem to stumble over your own words a bit, that your channel is not for me? As far as I understood the purpose of the video was to teach people who are not experts in the field how stuff works, correct? In the beginning, you stated your intent to phrase it in leymans terms. I figured that, if this is the case, you'd want your videos to be as easy to follow and understand as possible, no? Well, I'll admist my attempt at constructive criticism was also not very specific. Re-watching the video, I'd say what caught my attention was the segment at 9:30. The mistake there should simply have been cut out. Secondly, what I perceived as you "stumbling over your words" is the large amount of filler words in your sentences, specifically "um", "uh", "like" and "so". Well, at the end, your content is up to you, I was just trying to help because I like it but saw what I consider issues with the presentation.

[@KaneB]

@@Disappointed_Philosoraptor I didn't take offense. It doesn't bother me that my channel isn't for everybody. You can't win 'em all. I replied the way I did because all my other videos have the same feature that bothered you about this one, and they will continue to do so since it's partly intended that way. Indeed, although I don't do this anymore, I used to literally add filler words like "um" and "er" into the scripts. Although all my lecture videos are scripted, I don't want them to feel that way. I want them to feel like a lecture of the sort that you might get if you were sitting in a university lecture hall.

[@chrisdsouza8685]

Kane might be the worst presenter of the paradox ever.

[@martinbennett2228]

God exists here as an idea; there is no argument that the idea does not exist. In the absence of reference to material reality, I do not see a problem.

[@benjamingurevitch4097]

I feel like you just watched the first 5 seconds of the video and missed the whole point of it lol

[@cormacobrien5878]

this is fucking nonsense

[@alterperversersackkk]

so the problem is once again minimalism

[@benjamingurevitch4097]

??????

[@Azrael664]

🔴⚫

[@Azrael664]

🔴⚫

[@Azrael664]

🔴⚫