Atheist Debates - Curry's Paradox: Is Logic unreliable?
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- Опубликовано: 5 сен 2024
- For a bettery understanding of Curry's Paradox, I'd recommend: plato.stanford...
And: • Curry's Paradox
Developing a basic understanding of logic, logical fallacies and paradoxes is critical to being better at spotting problems in formal logic, which can improve your ability to spot problems in informal logic.
Logic isn't wholly unreliable, and our ability to identify how reliable it is - is a strength.
I’m sure you get these comments often, but I’ll share mine anyway:
10 years ago your material planted the seed of self-reflection and truth seeking in me that led to the fulfillment I feel today. The growth and discovery is continuous, and thankfully so have been your guidance (though that’s probably the wrong word to describe how your material affects my self-led development). Anyway, thank you.
What self-led development? You need other people think for you - That's what you begin with in your comment.
@@VindensSaga seed of self - reflection??
Matt is great with his logic and his knowledge of how epistemology works. And he`s able to explain it in ways that proper lay people can understand. You`re are a great teacher Matt!
Dillahunty admitted that his mind is a soulless chemically induced delusion that cannot be correct. He then cut my chat line when I asked him why anyone should take his thoughts seriously
Any atheist here who can explain the difference between pdf file atheist religion and islame?
Matt is great at lying with full force and confidence.
@@JimCastleberry taqqyya is used by both muslims and pdf file atheists
No he isn't. He is terrible. Like too many people far too deeply invested in arguing with Christians about God his understanding of Logic is wholly restricted to trying to reject frequently recurring arguments about god.
You can tell from this his actual understanding of general logic is limited to what you can learn on the internet in less than 30 minutes.
Logic isn't his forte. His forte is saying "That doesn't prove god exists" over and over again. It's remarkable he is lucky to live in a country so amazingly uneducated and so incredibly overinvested in arguments about god that over there you can literally earn a living just from explaining why you don't believe in God.
Over here in England nobody gives a shit if you believe in God or not because it doesn't say anything useful about you.
Over here if you go for a job interview you won't be asked if you believe in God because it isn't a vocational competence question.
It doesn't even say anything about how logical you are because something atheists love to try to ignore or argue about is you can't prove god doesn't exist any more than you can prove he does. Therefore there is no more honest position on the matter than you don't have the slightest idea if God exists or not.
Curry's is a special case of Gödel's incompleteness theorems, which are also related to Russel's paradox and the halting problem. Matt is absolutely correct in the core problem being the self-reference. The self-reference can be any finite number of steps removed (such as "the other side of this card is true" / "the other side of this card is false" cards). ZFC set theory was invented to get rid of Russel's paradox, but nothing as formal has been established for predicate logic. Good video.
Logic is a model that applies to assertions with truth values. this means that logic is entirely conceptual and independent of the particular universe we live in. Models can be defined without limit, but how applicable they are to their specific problem domains is measured as reliability. Whether self-referential statements are within the problem domain of logic would determine whether they would lower the reliability of logic.
The solution is to recognize that self-referential statements do not have a truth value, and are therefore inapplicable to logic. If reliability means applicability of assertions only with truth values, then logic is still highly (possibly perfectly) reliable, but with a restricted domain. If reliability means applicability of declarative sentences in general, then logic becomes to some degree unreliable, but with a larger domain. There is no benefit to expanding the problem domain if there is no applicability in the larger domain, so it's only reasonable to restrict the domain.
In other words, logic is only suitable to assertions with truth values, or any dichotomies that can map to true and false values.
The misunderstanding in the general public is largely a linguistic problem. In English and most (all?) languages, there is no syntactic difference between a self-referential declarative sentence and an assertion. This combined with the assertion-y feel of these self-references and the ability to chain the self reference back a few steps gives a lot of wiggle room for both bad actors and honest misunderstandings.
All words have the same self reference problem. All words by themselves literally mean nothing. The self is also is like the illusion of language where its literally nothing but we assign meanings to it. You can also put God into this category. You can say everything spawns from nothing and God is this nothing in which everything spawns from.
But when thinking of nothing you can see that it is completely metaphysical. Nothing is a metaphysical concept that does not exist in reality. You cannot point to nothing in reality it does not exist except the void behind you, you experience nothing.
God is nothing but it exists metaphysically before physics. And God is conciousness consciousness cannot be found because its before physics and scientist are trying to use physics to find something metaphysical.
When you try to use logic to find being you are using a diluted form of being to find the truth and cannot be done it has to be experienced first person without logic.
This is mostly correct, up until you speak about self-reference. Godel's Incompleteness Theorems (ICs) make use of self-reference in their encoding of the statement "This sentence is unprovable [in the current system]". So if we accept the ICs as valid at all, we are surely committed to some level of self-reference being within the domain of the applicability of logical formalisms.
And really, logic is less "a model that applies to assertions with truth values" as it is about the preservation of some specific truth value. There's nothing about self-reference that inherently prevents the possession of a truth value. "This very sentence is in English" seems entirely unproblematic and is made true because of self-reference, for example. If your model fails to conceptualize that sentence as an obvious truth from which we can derive others in the appropriate argument, it has a deficit that even naive/natural reasoning works fine with.
@@bumblebemeBut consciousness appears to be a process carried out by a physical entity. So far, only by brains, but I don't find it entirely inconceivable that a machine could house something we would recognize as consciousness.
(I suppose under a broader definition even simpler organisms could be considered 'conscious', but the point is that I am not aware of any consciousness that both exists and is not rooted in the physical world.)
Although we might subscribe to different models of metaphysics.
What he is trying to say is:
If truth values in logic are regarded as fundamental for comprehending and assessing information within a formal system, then their influence on reality is contingent solely upon the acceptance of logical frameworks, if and only if reality's interpretation extends beyond the confines of logical constructs to include empirical observation, experimentation, and subjective experience as essential components for ascertaining what constitutes truth or reality in the external world.
Its logic 101.
@@lasseaukio626 You should reference Penrose on this - amongst others
My Mathematics prof used this example: "It is raining therefore the street is wet" vs "The street is wet but that does mean it is raining".
What your professor said was something like: Every time P is True, Q is also True. Q is True. Does that mean P is was True? No, because P is independent of Q. But in this example, P does depend on Q, because of the self-referential aspect of P.
That's trying to claim that P->Q is equivalent to !P->!Q, which is to say they share the same truth table. And they do not.
When people try to apply this flawed equivalence, it's called appealing to the Fallacy of Denying the Antecedent.
But it could rain, and the street could still be dry. 😱
?
Great example for implication
Love listening to you explain things while I do Amazon Flex deliveries. Thanks for all you contribute Matt!
Anyone notice the wiser he gets the longer and whiter his beard gets. So glad we Atheist have our very own Gandalf.
This isn't even his final form.
Not surprising to see secularists appealing to magical characters like Gandalf and irrelevancies like beard color 😂
@@marionfowler4270 you mean a rotting corpse? (Not fundamentally different from the mere clump of cells secularists already purport him to be)
Not surprised to see someone trolling in the anonymous RUclips comment section.@@protestssopeacefulweneedad2017
@@marionfowler4270 According to atheist religion, Was it evil of lenin to torture people?
I love this content from you. I understand why you get so frustrated on The Line but this is my favourite stuff from you. Calm and collected and your brilliance really shines. You are a good teacher.
Agreed. This is a side of Matt I've not seen before. And perhaps these topics are better for his health. Sante, Matt.
@@emordnilaps oh he is this calm a lot but he is better know for being angry. Watch any of his actual debates. He's calm and collected in those.
love the offhanded comment about the willingness to write things down. on the rare occasion I talk religion in person with a theist, the first thing I do is have them tell me about their religion. I write it down, or if they prefer, they can. "the gospel according to so-and-so". and when I can point out that something written contradicts something else written, and ask them which they'd like to change, and how? they're more likely to question their faith than when they think it's because of fast talking or me taking them out of context.
Great video I'll have to watch again but I kinda get the argument generally speaking. Brought up my first paradox in a conversation and chick was gaslighting me with. And I never would of caught that even a year or two ago. Videos like this are super useful. Thanks Matt
This is a fun video!
Logic is all about what follows from what.
There are legitimate branches of logic for which contradictions do not entail explosion; that is, from a contradiction, it's not necessary that anything follows. They're called paraconsistent logics.
They have real-world applications, like error correction in data. (If you get two conflicting data points, you don't want your data to explode!)
I wish I knew how the various paraconsistent logics handle Curry's paradox.
"All contradictions are false even though some are also true."
According to atheist religion, Was it evil of lenin to torture people?
If Matt puts out a video, then I am happy. Matt put out a video, therefore I am happy.🤣
I see you are a lover of lies.
@@davidcowan4705 Why do you say that? I am happy when Matt puts out a video. Matt put out a video, therefore I was happy when I wrote that comment 3 months ago. Where is the lie that I’m in love with?
@@davidcowan4705 See, this is what ruins your credibility. You randomly post that I’m a lover of lies. I respond back that the statement I wrote was true…I am happy when Matt puts out a video. Matt put out a video, therefore I was happy…and ask you what lies I’m supposedly in love with?
Almost a day later, you still haven’t responded. You must have known that I’d ask what lies. Why can’t you back up what you wrote? Why write empty assertions like this if you’re not going to provide evidence for them?
All in all, this is a massive fail for you, buddy.
Thanks for beginning the video with "yes it is", really saved me a lot of time 😅
Thank you Matt. Sincerely.
This is a good example to help us spot those apologetic 'ifs' and assertions with unfounded rationale.
Are there other types from the superstition purveyors? I think not.
@VaughanMcCue true. They are experts at assembling long, rapid deliveries that appear to the unwitting, to be going somewhere, but then that 'if' sneaks in and suddenly we're over the rainbow with Dorothy.
@@mdug7224
There could be times when they even imagine their deposit in the smallest room in a house does not stink, even though a reluctant outsider will have difficulty determining which end of the apologist's anatomy the stuff is emanating from.
@VaughanMcCue 🤣 mighty analogy.
Thanks Matt. Not the easiest subject to grasp but I think I have a good understanding.
We don't teach affirming the consequence here, but we teach not to confuse between necessary condition and sufficient condition, the confusion between the two is the core of affirming the consequence fallacy.
Curry's paradox is similar to Russell's paradox (Let R be the set of all sets that are not members of themselves). Both are similar to the extent that using naive set theor,y it is possible to create these types of paradoxes and contradictions.
Russell's paradox and then later Hilbert's work were the beginning of work to show that mathematical logic could shown to be complete. However Kurt Gödel's proofs in his Incompleteness theorem proved otherwise, and 'tweaked' Russell's Paradox " to make this:
"This statement is unprovable." There are two possible truth-values for this: If the statement is true, then you have a true statement that is unprovable. If the statement is false, then the statement is provable, which means you have proof of a false statement. So any (sufficiently complex) mathematical-logical system is either incomplete (with statements you know to be true but can't prove) or self-contradictory (with false statements you can prove), or both.
There are many implications to Gödel's theorem, and one of them is that Grand Unification Theories may impossible - Stephen Hawking thought so, although others disagree. But the most obvious implication of the theorem is that not all knowledge is knowable - there are limits to what conscious entities can know.
I want to add that the neat thing about Curry's Paradox is that it needs *only* Modus Ponens, nothing else. Which means it works "out-of-the-box" in basically any logical system. There are many logics, but literally all of them have Modus Ponens - it's, like, *the least controversial* law of logic.
I would also say that the Gödel-sentence is not really "true but not provable", because it's not really *true* at all. The more correct way to say it would be: the Gödel-sentence is neither provable nor disprovable, which (at least in some of the relevant logical systems) guarantees that there are *both* possible worlds where it's true *and* possible worlds where it's false.
They call it "independent of the axioms", and the incompleteness theorem says that these "independent" statements always exist.
This is a little off. Godel's theorems imply that limitation specifically in the case that you're talking about a mathematical formalism in which at least number theory is provable and the logical system is consistent. It is not about all domains of knowledge or a universal limitation on what can be known. That is a rash generalization, I suspect.
@@MindForgedManacle Number Theory is one branch of mathematics. So your point is a bit redundant, when considering mathematical-logical systems in their entirety. Hilbert wanted to show that the system as a whole was: decidable, without contradiction, and thus consistent and therefore complete. Gödel proved otherwise. If one part of the system is incomplete, then the system as a whole is incomplete. If there are propositions that are undecidable or spew out contradictions, then clearly this is a limitation to knowledge, as these propositions are 'unknowable'.
In addition If there are 'real world' problems (such as GUTs) that maybe insoluble because of the predicates of Gödel's Theorem, that too is a limitation to knowledge.
@@peterrauth118 No you're bypassing the actual point I was making. Those theorems apply only to the systems with the features I mentioned. If you're not in such a system, the theorems don't apply. If something is unknowable - or in this case, unprovable from within the affected systems - then it's not something that can be known to begin with. It's not an item of knowledge.
@@user-qm4ev6jb7d There are logics without modus ponens, though. Just take any logic that has no implication connective. And it cannot have modus ponens.
And Gödel sentence is true. If it were false, then it would be provable. But then, by soundness, it is true.
I’ve never heard of this paradox. Thanks for sharing something I didn’t know! Love ya Matt.
Matt is Slowly turning into a Wizard with that beard. Given the etymology of Wizard (somebody who is wise), it seems fitting.
Another secularist appeal to magic. Funny how y'all just can't resist but thinking of yourselves as exalted magical wizard beings 😅😅😅
@@protestssopeacefulweneedad2017 All magic is just the "magician" knowing one or two things more than the audience. I certainly do admit that in some areas Dillahunty knows more than me.
PS. I heard that he does stage-magic as a hobby
Omg you've explained this in a way I actually understand thank you
I hope you'll be able to get Professer Dave back on one of The Line shows. Pleasant vid as usual 👍🖖
That fool thinks he has origin of life all sussed out😅
He doesn't think he knows it all but he does know more than the Fraud and Liar Tour. @@XYisnotXX
@@XYisnotXX He's never said that, thanks for the disingenuous take.
Professor Dave is the disingenuous one.
@@XYisnotXX No, it's the theists who assert they have the OoL all figured out, "god did it". Without a shred of evidence and ignore the scientific method completely. Have any more lies and strawmen?
You got me at "yes it is". 😂 Subscribed
thanks for the reminder to mind our p's and q's with regard to "if p, then q"
"Are you strong because you're Gojo Satoru or are you Gojo Satoru because you're strong."
Hi Matt - I really like all your presentations - your clarity and precision is inspiring.
Strangely, just earlier today, Jeffrey Kaplan on Russell's Paradox showed up in my youtube feed. Something similar to what you are discussing here - might even be the same thing with a different name. I mention it because it seems like a thought tunnel you would really like.
Thanks for all you do.
Fionn
Awesome video!!! This Makes me want to learn more about logic.
Interesting and useful, thank you :D
I just had an image in my head of "Teacher Matt", using markers like Khan Academy or Andrew Millisen to explain The Logicks 😅
Matt vs. Jordan Peterson is a gem of online debates. Matt is just really good at this kind of stuff, I get confused. Lol. Too many words! But I'm hanging in there. If you haven't seen that debate, it's a good one.
Enjoying the series and the episode. I wish the audio were a bit louder.
This doesn't seem like a paradox. It just seems like a misunderstanding of cause and effect. You can have a self-referential statement, but your self-referential statement can't be your cause, because then it becomes circular logic.
Not exactly. In a circular argument, the same proposition occurs as both a premise and a conclusion-the argument validates itself.
@@peterrauth118 Wouldn’t ‘if this statement is true’ have to validate itself?
@@twill5626 No, we deal with "If this statement is true" all the time in programming. that's not what circular means in logic.
Logic isn't about cause and effect. It's a purely formal problem, it isn't causal. You need to go read the actual logic involved.
The statement is conditional and validates nothing as it makes no assertion as to truth or falsehood.@@twill5626
Thanks Matt this definitely needs to be brought to the forefront as from insurance companies to governments they always try to trick us
I tuned my brain out for a moment and upon hearing back all I so aimlessly understood was..
If Matt is working, then Matt is working. As well as if the end of the month is not working then Matt is not working. P Q, Matt is working therefore Matt is working, because Matt is working for Matt is working.
If someone has an argument that seems to define God into existence, I check that by replacing "God" with "The Flying Spaghetti Monster" and see if that sentence still flows the same.
Or define the "the god-annihilating monster" into existence, thus proving that god was annihilated.
A mere mention of The FSM returns the entire conversation to a common sense footing, and reality prevails.
Clearly I have much to learn.
Thank you.
Self-referential sentences are not logical propositions that can have truth value because they are incomplete. Just like these sentences: "One plus one is" (this is not a proposition because it is incomplete so it is neither true nor false), "If A then" (this is also not a proposition because it is incomplete, it has no truth value).
G : If this sentence is true, then Matt is working.
The error in making a truth claim about G is that there is no logical proposition G because the proposition is incomplete. At the time that G is proposed, there is no G for it to refer to. If you attempt to determine whether or not G is provable before you make any claims about it, you find your task impossible. Before G is proposed, is it unprovable? No, we cannot know that yet and since it refers to itself, we can never know it before we propose it. This is true of all self-referential claims.
Other propositions have a truth value or are provable before they are written down. They are true or false prior to being proposed.
J: 1 + 1 = 2
I can know whether or not J is provable and then I can propose K
K: The proposition J is provable.
Since we know that J is provable before we write K, we are not making an incomplete claim when we write K. This is because there is an implied temporal element to all propositions that we usually just assume. All statements include a temporal element which is usually implied. Even statements in symbolic logic have an implied temporal element that they are true or false during the time period that the symbols used in the statement have the meanings used at the time that the statement was written. If the symbols are given different meanings in the future, then the statements written in the past would no longer have the same truth values, not because the truth value was incorrect, but because the implied temporal element was unacknowledged. If we proposed K before J, it would be very clear that K does not have a truth value because J does not exist at the time we propose K. Somehow everyone forgets this problem when proposing self-referential statements.
So called "self-referential statements" are incapable of containing the necessary temporal element because the elements of the "statement" do not exist until the claim is evaluated and after the claim is evaluated the claim changes. If I claim: "John Smith is alive on a date chosen at random". The truth value of the claim depends on the date chosen, so the claim is an incomplete statement until the temporal element is added. The claim is true for all dates on which he is alive and false for all dates he is not alive.
Even the claim: "1+1=2" is only true during the time that the symbols "1," "+," "=," and "2" have the meanings that we currently use. A claim that references itself cannot have a temporal element added because the claim does not exist while it is being written. There is no way to reference the claim being written as existent at the time it is being written and there is no way to reference it as existing in the future because it does not come into existence at some point after it is written either. A claim such as: This statement existed prior to being stated or This statement will come into existence after being stated, is nonsensical because the claim is made during the claim. Neither claim is true because the statement being referenced is in the process of coming into existence while it is being stated.
Take the example: "This statement is false." There is no time period when that claim existed prior to being made because every time that claim is made, the reference changes. The claim itself did not exist at the time that the claim was made. The claim does not come to refer to something at some time in the future because the reference is to what is being claimed in the claim. It is axiomatic that a self-referential claim references itself and therefore it cannot refer to anything that existed at the time that it was being made since it did not exist yet. Since the claim exists when it is written the reference does not come to refer to something at any point in the future. In order to evaluate the truth of the claim we could look at potential temporal values to see when it would have a truth value, just like the other example statements. Did the claim have a truth value at any time prior to the claim being made? No, since the truth value depends on the claim itself, there is no reference prior to the claim being made. Will the claim have a truth value at some time in the future? No, every time the claim is made it refers to the claim being made and does not refer to anything that will happen. Take the claim: The time is 12:14. This claim is true if it was written at 12:14 and false if it was written at any other time, however the value does not depend on when you evaluate it since it does not refer to itself. As soon as you add self-reference, the claim loses its temporal element: The time that this claim is made is 12:14. It appears that this claim is true whenever you make it at 12:14 and false whenever you make it at any other time, but that is because it seems that a new reference is being created every time the claim is made. In fact the claim does not have a reference when it is being made because it does not exist while it is being made, but only comes into existence after it is made when the claim being referred to had not yet existed.
"One plus one is." is in exactly the same grammatical form as "I am"; or "Earth is."
Also: "This sentence is incomplete." is a complete sentence.
@@tgenov No my friend, that is not accurate. The grammatical form of a sentence does not determine the status of the sentence as a logical proposition.
Commands like "Go away!" are complete sentences, but not logical propositions because they cannot have a truth value.
The sentence "I am." is intended to convey the logical proposition "I exist." The word "is" has different meanings which causes your confusion. In the phrase "One plus one is," the word "is" means "equals."
When you say "This sentence is incomplete." You may have written a grammatically correct English sentence, but there is no logical proposition because the thing you are referencing "This sentence" does not have a referent at the time that you are making the reference. In our minds words have meanings, but they also act as pointers to bring our attention to other concepts or ideas in our minds. Pronouns are an easy to understand example of how words reference other concepts or ideas. When you use the word "he" in a sentence, you intend that the word "he" refer to some person, but if there is no reference then your sentence doesn't have a truth value.
Take the sentence "He was a tall man who died in his 60s on the beach in Alaska." Is that sentence true?
Have you heard of Fitch's paradox of knowabililty? It demonstrates that there are true statements that we literally cannot know.
Thanx, Matt.
It's reliable enough to serve its function. Things/concepts don't have to perfectly reliable in order for us to trust them enough to use them. Planes aren't perfectly reliable, yet we fly in them.
"Logic shows that logic is unreliable"
That undermines the premise
I would imagine the rhetort would be something like "how do you know it undemines the premise without using logic to presuppose it does? You can't presuppose logic, that is the thing in question. If you assert that you must use logic, then how can you say that it's a rebuttal to the question of if logic is unreliable?" Eh?? I tried?
@@vermidian_ If their conclusion hasn't been accepted, then I can use logic, and pressupossition isn't required
If they have a flawed premise no reason to accept their conclusion
Nice try, though
That's not showing what you think. Imagine we didn't have hammers to pummel in nails. Call it a clanker, and say this clanker wasn't very good at getting the nails into wooden boards. And I said "From trying to use this clanker, I found out the clanker is not reliable".
Is that a contradiction? No. using a tool and determining it has a limitation or flaw is not a contradiction. You simply don't understand the paradox.
But that's just attacking Matt's wording. Better way to put it would've been 'assuming logic and allowing self-referential propositions, we run into contradictions'.
@@MindForgedManacle hammers are not comparable to logic, so that's a false equivalence logical fallacy
In your example, unless you used logic to determine that the hammer isn't reliable, you're just making a bare assertion.
It's literally just your opinion. Once you have actual data, there's no way to process it in the slightest without logic
Why don't you try explain what you're saying without an analogym
When combined with science and empathy it is reliable .
If it's not the last day of the month, I am not working. It is not the last day of the month, therefore I am not working.
Am I trippin or is your comment 8 days old on a video that’s been out for 3 minutes?😅
Im here 3 mins later and thought the same thing
@@Ichabod_Jericho it's almost like there's a patreon level where you get early access to videos
@@bghiggy guess I didn't realize that the "early access to videos" actually happens on RUclips. I've never paid for something like that, so I didn't know.
@@Ichabod_Jericho Matt pre-records all of his videos on the last day of each month and takes all of the other days off.
Love the intro, but yea... a good epistemology exists, but we can make it better. I already have, but requires the premise to be clear from both parties involved :)
It seems to me that our fundamental understanding of logic is not logic itself. It’s been based on observation of how things always are in any instant and how they interact with change, by inferring the general reliability of our perception.
Perceptions, concepts and statements are fabrications referring to contents which may or may not be. The contents of non-self-referential statements simply are or are not.
If we use logic to formulate a binary math system consisting of 0’s and 1’s, then 2 is not in that system. In this system, the statement “1+1=2” can exist, but that which “1+1=2” refers to does not.
Meanwhile, the statement “A=A” refers to the identity of A. “A” does not actually refer to itself in order to equate itself with itself.
It’s not simply a problem of self-reference, it’s an error of equating the identity of any statement (or concept or perception) with the identity of that which the statement refers to. It violates the Law of Identity, but it’s the only way we can even learn.
I wouldn’t say that logic must be universal, but it’s not logic that seems unreliable, it’s our ability to refer to it that presents issues.
What is and what is not is the foundation of what we observe/infer when we’ve developed and used logic. Not “true” and “false.” “True” and “false” are descriptions of our fabrications… description of things which refer to that which may not exist.
Cool shout out to Kane B, small channel I've followed the last few years, really deserves a lot more views
Discussions about whether logic is valid sound to me like discussions as to why I am the son of my father.
There's no way to discuss anything without logic, even discussions to defy logic.
I don't get it. Isn't "if this sentence is true, then Matt is working" false? Matt says so himself at 6:28. That would make the argument valid, but not sound, which I think the whole Curry's Paradox is. What is paradoxical about it?
One question I have is that you said "the very fact that you can point out that there are places where we can see issues with logic speaks towards its reliability". In other words being able to say "no our logic isn't being reliable here" helps logic to be more reliable. If the opposite were true and we couldn't find places where logic was unreliable, wouldn't we still say that logic is reliable because we can't find examples of unreliability?
My question essentially boils down to what scenario could we be in where we could actually say logic is reliable? Whether or not we can or can't point out when it fails doesn't seem to actually help us tell because either way I feel like we would end up saying that logic is reliable
In cases where we apply logic to true sentences and come to false conclusions. The whole point of (deductive) logic is to start with true sentences and guarantee we come to true conclusions.
So in cases where we use the logic correctly, and we start with true statements, but come false conclusions, we find a limitation to logics reliability. The fact we're reasoning to conclude that does nothing to void the somewhat unreliability we have found. It's not relevant all. We use the tools we have. Logic, applied properly, is mostly reliable. Figuring out what logical system to use and where to use it is the tricky part.
*logical absolutes/axiology/pure tautologies/pure dichotomies/direct opposites/logical negations
*basic set theory - depiction of binary relation
*terms: words and phrases
*premises/propositions: combines two terms, subject(p) & predicate(q) to create assertion
*distributed term: universal/all
*undistributed term: particular/some
*major premise: proposition that contains the predicate of the conclusion
*minor premise:proposition that contains the subject of the conclusion
*synthetic a priori proposition: predicate of which is not logically or analytically contained in the subject
*syllogism: combines premises
*validity and soundness
*modus ponens
*modus tollens
*enthymeme
*affirming the antecedent
*denying the consequent
*fallacy
*falsifiability
*deduction
*process of elimination
*abduction
*induction
*testability
*repeatability
*demonstrability/provability
Jn 11;35
I'm quivering with antici...
Wait. It is?
Well, there you go then. Settled.
You are a great teacher Matt
thanks but sound needs to be louder, difficult to listen on mobile.
Ive love these types of discussions and theories of thought, facts, truths etc. But I think my head is spinning a tad from this one. I think I'm one of those that needs pictures or diagrams. :)
Only 15 of the 256 syllogistic forms are valid in modern syllogistic logic. Nine more are valid in Aristotle’s system.
Greetings from a fellow Gael from the west of coast of Ireland 🇮🇪
I like the way the og philsophers evolved their way understanding how thinking should be. There is no logic without reasoning. I remember the book from a period past. The " age of reason". We continue to evolve; now we have AI,imagine that.
I still think people are wrong about the liars paradox. There are two things you are assessing at the same time and that is the problem. One is the accuracy of truth of the statement and the other is the outcome. Just keep those two things separate and there’s no paradox.
I liked Kane B a lot more before I realized how hung up he is on the fact that tools, even cognitive ones, have limits beyond which they are unreliable
I often wonder what matt dillahunty thinks of gödel incompleteness. or just Kurt Gödel
Took me a bit to understand you were saying: Matt... I heard math. So, I found it a confusing example at the start ^^
Matt, well done sir, what if i may ask was your Nuclear Power School Class? Mine was 8604. thanks for your service
Logic is reliable because we use only the portions of it that we find to be reliable.
The phraseology of logic is nice for clear speaking and writing- being precise about what you mean to say- but whether something is “logical”, to me, lies in the factuality of the statement.
Holy shit! This makes sense. OMG! Logic! How wonderful!
I find the need to debate the existence of a made-up being insane.
So you accept that this 'made up being' is an abstraction?
@peterrauth118 Do you mean people give made-up beings' qualities and ideals?
Try the Incompleteness Theorem.
You seem to be conflating the reliability of the logic with the reliability of the premises.
Haskell Curry, who this was named for, is a hero of and one of the OG computer scientists.
Thank you for more education
I'd be curious to see what's Matt's opinion on whether or not the more recent batch of Artificial Intelligence applications (& the neural nets they typically use to analyse patterns to "learn") are yet at the stage where they could be trained to analyse statements for at least logical validity (if not soundness). I'm fairly sure we could have AI-based apps that are capable of evaluating linguistic arguments for common fallacies, but what about some of the more confusing paradoxes?
Soundness is an entirely different can of worms - especially for an AI that is incapable of having the real-world experiences of a human being.
@atheistreligionandislameis4455 OK, you seem a little confused, so I'll try & clarify things for you.
I didn't say anything about AI being too advanced for human comprehension (as it isn't) - and certainly wouldn't do anything so utterly absurd as to describe an AI as being human - so if you somehow got either concept from my comment, I apologise. Though I would point out that declaring modern Artificial Intelligence Systems as merely being _"advanced calculators"_ is overtly simplistic, if not sadly reductionist.
In my comment, I was asking *Matt Dillahunty (@SansDeity)* - in his capacity as a highly skilled logician (& not as an atheist) - about how he thinks we ought to go about developing an AI/Neural Net specifically designed to analyse Logical Arguments for the two essential qualities of:
▪︎ *Validity* (which should be relatively easy as computer programming is itself largely logic statements), &
▪︎ *Soundness* (which, requiring contextual knowledge about the way real-world things work, is going to be far harder to simulate, likely requiring the AI to be taught through a laborious system of trial & error that's overseen by human minds).
In doing this, I was hoping to add to the discussion about how we might best use these new AI tools to benefit us in our daily lives.
*@atheistreligionandislameis4455*
After reading your comment, I presume that you would use such an AI App to examine the statements of both Theist's & Atheists for Logical Fallacies (both formal & informal) & Cognitive Biases. Excellent. I reckon this'd be a great way to both identify when people (including myself) are making irrational arguments & to improve my rhetoric skills, overall. Good luck with your ongoing education in Rational Thought.
just go to know about this paradox from watching this and searching online. first impression is that curry's paradox only stands if you are willing to accept imprecise language. greater precision in language invalidates it.
If a is true then b is true is logic, but when someone says “if god exists then god created the world” is the same logic, but you feel something is wrong here (not sound). Even the if-part is off. How to handle unknown and undefined parameters?
Reminds me of that one caller: truth tables, therefore god! 😂
What I call "logic" is based on my interaction with the external world that surrounds me every day. My brain processes information a certain way and I cannot change it to satisfy an ancient narrative invented by Hebrew tribes living in the Bronze Age.
I would love to see Matt do a video on the fallacies and faulty logic of flat-earthers, especially the ones who pretend to be experts in logic.
For the algorithm!
I remember I had a couple lessons like this when I was in jobcorps,this "logic" stuff always confused me. And I don't know that my lack of understanding of it implies I'm a low IQ person, I'd like to think I'm smart, I mean everyone would because it's a comforting thought, but is there a difference between your intuition and your actual intelligence? Is your "gut feeling" and it turning out to be right a compliment to your "intelligence"? I'm not a person who believes I'm just perpetually "lucky". Is your intuition a different form of intelligence? I've always thought about this but never really found an outlet to ask the question, or find someone who can understand what I'm asking.
I say this because my ability to forsee events yet to play out has quite literally saved my life, multiple times in my life.I saw a fatality on the highway,nasty car wreck, it was so sad to see. Only thing is, I imagined the crash happening before it did,took the proper maneuvers to avoid crashing myself. Parked, tried to help the best I could and I waited for the police to give a statement as a witness (I was right behind the person who crashed into this Ford F-150 truck.) and hey I'm not hospitalized or dead because of it. I'm not asking this question to stroke my own ego,but I am simply curious.
Have you ever done a video on William Lane Craig's "The New Atheism and Five Arguments for God" on reasonablefaith site? If you have, could you please point me there? If not, could you do one? Some theists seem to think it is brilliant proof and that the logic is as airtight as WLC claims.
Thanks for your time and consideration (if you ever see my comment)
Thai Green Curry
did we use logic to discern that logic is unreliable?
Sounds plausible. After all, if logic gives two different answers to the same question it must be unreliable.
If you substitute a self-referencing sentence into itself, you end up with a new reference to the original sentence, nested within the inserted sentence. So you can do it again and again forever. Thus, a self-referencing sentence only has a truth value if this cascaded structure “converges” in some meaningful way.
Any thoughts?
That's not workable. "This sentence is an English sentence" is obviously true. And it's not trivial, because "This sentence is a Chinese sentence" is false when uttered in English.
Self-reference is not the same as variable assignment. It's making, well, a referent of itself. There is no new referent being made nor a nesting of sentences. As in the above examples, there is only 1 sentence, and it seems immediately coherent.
@@MindForgedManaclethanks for your thoughts.
But “”This is an English sentence” is an English sentence” is a perfect English sentence, and thus true. The convergence is immediate.
Likewise, if you write “Chinese” instead of “English”, it is false regardless of how many nested substitutions you make. Immediate convergence once again.
A non-convergent (in a general sense) example would be “This sentence is false”. It is like connecting the input of a logic inverter to its output, apparently creating the impossible function “X = NOT X”. It’s a bit like dividing by zero. In a physical circuit, X would either oscillate between “0” and “1” (divergent behaviour) or the circuit would burn.
I dunno - this probably has little to do with Curry’s paradox, but it felt like a moment’s clarity. Thanks for the chat.
Matt needs to read Hindu 🕉 scriptures. One of 12 school is Atheism ⚛️ where yoga comes from ❤❤❤
For about the first 2 or 3 times, I thought you were saying Modus Poland, and I thought I had missed the Polish joke.
Doesn't the reliability of logic depend on the reliability of the premises on which you base it? If you start from the premise that angels exist, you can build a "logical" argument on the question how many of them can dance on the pin of a needle. (The answer, of course, being "none" because dancing is the devil's work.)
Matt is usually working on the last day of the month.
It's the last day of the month, so it's likely that Matt is working.
However, he might not be working, just as well, for any reason.
Fear The Beard
as i see it "if this sentence is true Matt is working." is not a paradox. it is in-contemplate syllogism, it is at best one premise. the truth of the sentence is dependent on more info. you need to evaluate the soundness of the premise.
p1 - if this sentence is true Matt is working.
p2 - Matt is working
c - P1 is true
p1 - if this sentence is true Matt is working.
p2 - Matt is not working
c - P1 is false
it is essentially asking "is Matt working"
you can do all the substitutions you link you will never get to the point where stating "if this sentence is true Matt is working." becomes true without first knowing if Matt is working.
----short version Curry Sentences cannot confirm everything, they cannot confirm anything. they are a premise that needs to be evaluated.
It does confirm everything, the problem is the assumption that X = X->Y is possible. In most systems (or theories), something like this is impossible, or restricted in a way that it is impossible for false Y, at least.
It is somewhat related to Russell's paradox, which is also impossible in most systems (or theories).
@@ZiseGzu yes, you can make a strucheraly valid syllogism, but that syllogism cannot be sound as it has a premise of unknowable truth value. if you cannot know if a premise is true you are not justified in accepting it (from a skeptics prospective). if you do not accepting all premises the syllogism is not sound (for you).
if a syllogism is not valid and sound it is not rational to except the conclusion. as stated "if this sentence is true Matt is working." is dependent on knowledge of weather Matt is working or not. as a standalone sentence it is meaningless.
please show me a syllogism that is valid and sound using "if this sentence is true Matt is working." as one of the premise
@@garfnob4832 Syllogismd are too weak of a system to prove a lot of stuff. But you can prove anything it in natural deduction or similar system, if naively using similar sentence.
The problem is more subtle than unknowability, though. The X = X->Y is similar to Russell's paradox when unraveled, so in most systems X of this form does not exist (at least for false Y).
@@ZiseGzu syllogisms are how logic works, they are the only way to prove something with logic. "X = X->Y" is part of a syllogistic structure.
if i understand your argument correctly you are proposing that if you can make a strucheraly valid syllogism you are rational in accepting the conclusion. this is not the case the structure must be valid and the premises must be sound. sound, meaning the premises are accepted as true. i do not see how anyone can accept "if this sentence is true Matt is working." when the truth of the sentence cannot be evaluated with the info provided.
if you do accept the premis "if this sentence is true Matt is working." then yes you can make a syllogism the can prove anything. this point in and of it self is cause you question the premis if not out right deny it
from Wikipedia on Curry's Paradox. the full syllogism is...
1. X := (X → Y)
assumption, the starting point, equivalent to "If this sentence is true, then Y"
2. X → X
law of identity
3. X → (X → Y)
substitute right side of 2, since X is equivalent to X → Y by 1
4. X → Y
from 3 by contraction
5. X
substitute 4, by 1
6. Y
from 5 and 4 by modus ponens
@@garfnob4832 After looking at the example you mentioned, it seems to me, that out definitions of syllogisms differ. I was thinking about a certain relatively weak fragment of first order logic.
In any way, you do not have to accept the sentence as true in order to get a valid argument. If you look at the example from Wikipedia, you can see that this argument has no unreleased assumptions. X is defined as X->Y, X->X is a tautology, derivable from empty set of premises or just valid as a tautology, depending on the system.
However, if you were to look at the truth of sentence X, then you could actually conclude it is true.
If it were false, then ~X = ~(X->Y) is true.
~(X->Y) is equivalent to (X and ~Y). But that formula cannot be true, since X is not true. So, by contradiction, ~(X and ~Y) = (X->Y) = X must be true. This can be formalized in a syllogistic way. And then you can append the example from Wikipedia to prove anything.
The problem with the sentence is not that it is an assumption with disputable truthfulness, but the problem (which I see on Wikipedia, too) is that it is not a valid first order formula (or its interpretation in ZFC is not valid), similar to "This sentence is false.", it can not be interpreted in many "standard" formal systems.
This is great
Using propositional logic on non-propositions may lead to contradictions. So what?
They aren't non-propositions. They have the capacity to be true or false. This is trivial to demonstrate:
"This sentence is an English sentence"
Obviously true.
"This sentence is a Chinese sentence"
Obviously false.
We should learn about logic in school. Maybe 1 or 2 chapters a year in math, so more people actually learn to think logically
I lack a belief in Matt Dillahunty’s intelligence. I’m not claiming he’s dumb; I just reject the claims that he’s smart. Until I see a shred of evidence in his intelligence, it’s the most honest position I can take.
He gave you many examples. Like how sofisticated his knowledge is or that he knows the bible more Than you cultists
When are we going to get the final debate review with That muslim Daniel? (dont ask me to spell his last name...)
Well, I'm awake and I've heard the word Curry many times during this video, therefore I'm hungry. #solidlogic
This was hard to follow. But you’ve brought this paradox up a few times. And i have a point that I need clarified. And maybe there can be other examples of this paradox that don’t deal with sentences.
So when you say “if this sentence is true, then X” and then say “this sentence is true”, what does it mean for a sentence to be true? Because in my mind, sentences carry truth values, but the sentence itself can’t be true or false. It’s nonsensical to say it is, because it doesn’t apply. It would be like saying “the color red is heavy”. So when we say a sentence is true colloquially, what we mean is the idea the sentence conveyed is true. We don’t mean the actual sentence is true.
It makes the paradox seem like nonsense.
The way I’m understanding it is like this:
1. If the color red weighs 5g, then god exists.
2. The color red weighs 5g
3. Conclusion: God exists.
This doesn't really advance the discussion though. If instead of "sentence" we said "proposition", the paradox remains. The truth-bearing object is basically never relevant to any longstanding paradox. It's the logic that matters, not the objects upon which the logic is being applied to.
@@MindForgedManacle wasn’t necessarily trying to advance it. I don’t understand the logic behind the paradox and the use of “sentence” was hanging me up. I couldn’t think past it. And I’m not sure “proposition” really grants more clarity. It feels like the truth-bearing object is carrying all the weight.
@@OrcaneVault Proposition in this case is just the meaning of whatever sentence or thought we're talking about. When we say "truth bearer", we're just saying "the thing that has the property of being true or false". If it's not the sentence itself, it's surely the proposition (the meaning itself).
@@MindForgedManacle can you give me a different example of this paradox that might make more sense to me?
@@OrcaneVault The problem is really that it's just caused by the way "if" statements in logic work. It's not really an example thing, and the fact it could undermine logic in some sense makes it hard to explain.
So let me try with explaining the rule since it's the source of the problem. Say I have a sentence named A1. This is the content of A1:
A1: "If this very sentence is true, the moon is orange".
Now consider this argument based on A1.
1) If A1 is true, then it's true. (That's not controversial for any sentence.)
2) But if the very sentence is true, then "If this very sentence is true, the moon is orange."
3) Therefore the sentence is true, and if it's true the moon is orange.
Look at step 2 and look at the definition of A1. They're identical, we managed to prove it true in the argument by deriving it. And you can put anything on the other side of that IF statement.
The point isn't the content of the sentences. The very basic structure of almost all systems of logic allows this obvious error. It's not invalid, just think about it: If something is true, then it's true. We surely can't deny that.
But if the definition of the thing we're talking about is identical to what we derive, we're effectively proving it. Again, it's not invalid no one thinks it's correct, but there's not an obvious solution that actually works. Restricting self-reference would be the only way, though there's not an easy way of doing that which avoids being arbitrary or wrecking basic language too.
Really, the way "if" statements work would have to be changed, but that's easier said than done because that's an elementary part of logic.
Wait... all of the rulers but one are the same? The same as what? Don't you need at least 2 of them to be the same to have sameness?
If you tried to write out a Curry sentence without using any placeholders such as "P" or "this sentence" you would never stop writing. In the same way, if you try to code a version of Curry's Paradox, it results in infinite recursion and will cause a stack overflow exception. It is essentially a divide by zero situation that should not be considered valid. It is somewhat reminiscent of the "1=2" fallacy found in mathematics.
This is just incorrect and it's caused by too much reliance on a false programming comparison.
Reference in logic (and really in language) is not the same thing as a variable assignment.
It's like, if I say "This sentence is an English sentence", that's obviously true. Yet your above reasoning would suggest you can't actually analyze that sentence at all because "This sentence" degenerates to infinity. You're confusing 2 different things, which is why no one in mathematics rejects the Curry Paradox on the grounds you do. It's been a known, legitimate problem for almost a century, it's not based on something as simple as that.
@@MindForgedManacle"This sentence is an English sentence." is not self-referential in the same way. The Curry paradox relies on self referencing it's own logic in a recursive fashion, which this example does not do.
I agree that my point of removing all placeholders is wrecked by this example., but I do not think it fully refutes my point.
The problem is that the Curry sentence creates an infinite logic expression that is obfuscated through placeholders and is impossible to resolve.
@@rellethesit It refutes the means by which you came to your point though. If you don't have it, you don't have an objection. Curry's sentence does not degenerate to infinity precisely by the example I gave before. You're confusing reference with variable substitution ("placeholders"). They're not the same, ergo it is not infinitely recursive.
It's no different than if I walked up to you and said "It's true that these very words I'm saying are in English".
@@MindForgedManacle Here is what I mean:
(1) A = (A -> B)
(2) A = (((...(((A -> B) -> B) -> B) -> B) -> B) -> B)...
(1) and (2) are logically equivalent.
(2) is impossible to evaluate, and therefore so must be (1).
@@rellethesit Again, you're doing the very thing I refuted. Reference is not variable assignment or substitution. A referent is not a linguistic entity, a variable or value or a variable is only a linguistic entity. If I say "A = the sun" and then I say "The sun is in the sky" I'm not saying the variable named A is in the sky. I'm saying the thing A refers to is in the sky.
The term "This sentence" is not instantiating a variable, so there is no infinite expansion. Again, if your example fails to make coherent an obvious truth like "This sentence is English" you're clearly using a bad analogy. You're basically stuck with asking "What is the sentence?" when you can see the sentence.
And again, this can be entirely avoided:
"The next sentence is false "
'The previous sentence is true"
Now there's no possible way to avoid knowing what each sentence is talking about and it's obvious no variable assignment is happening.
Love how Matt seems to think talking on his own should be titled a debate.
I've always suspected he loves the sound of his own voice
It's hilarious you think no one will notice your silly attempt at misrepresenting this video. You must be an insecure christian superstitionist.
I am sure he appreciates your sincere love. Perhaps it went over your head that *AD* is the channel's title.
When you call into the Line, tell the producer your purpose is for a voice talent comparison and that your fragility precludes discussing content.
Here is mine: Birds have wings given to them by God. Therefore, since humans have no wings, God would have told Moses, it is a sin to fly in airplanes.
Imagine using your logic to understand how the universe was created
Dillahunty you’re probably going to be skeptical due to a lack of evidence but ur basically my godfather
I think these are good types of videos