Talk:Curry's paradox

message: Cleared up the ambiguity on the natural language section. The previous description offered no explanation as to why it results in 'Santa Claus' existing or elaborating on how it is a paradox. — Preceding unsigned comment added by 124.198.175.237 (talk • contribs) 08:19, 4 November 2010
:I undid the edit because several of its claims are incorrect. The sentence is not just "surprising"; it's a genuine paradox. And it proves that Santa Claus actually exists, not just that he exists hypothetically. — Carl (CBM · talk) 10:58, 4 November 2010 (UTC)
replies: text: I rewrote that section, and changed the example to something more temperate. The old section was overgrown with digressions and, you're right, did not explain how the paradox is derived. — Carl (CBM · talk) 11:36, 4 November 2010 (UTC)

text: This appears to be true only if you aim to prove it to be true. If you aim to prove it true you assume the hypothesis to be true, which results in the conclusion being true. If you aim to prove it false, you assume the hypothesis is false, which results in the conclusion being false. How is this significant?  —Preceding unsigned comment added by 124.198.180.140 (talk) 03:20, 6 November 2010 (UTC)
replies: text: You do not prove a conditional statement false by assuming that the hypothesis is false. However, it doesn't really matter how you would prove it false; the paradox alrady occurs just from thinking about how we would prove the conditional statement is true. — Carl (CBM · talk) 12:10, 6 November 2010 (UTC)
thread_title:  Edit 2010-11-4 

message: please delete or provide a reason why this is notable enough for inclusion and rewrite it in a less in-universe way. because this is actually not a paradox.
"if this sentence is true, Germany borders China" is simply true. if the sentence is true, than Germany borders china, but if it is not, Germany doesn't border China. of course, it is not true, but the sentence doesn't claim to be true. so this is not a paradox. the truth of the first part is not a condition of the sentence itself. 
if i say "if 4 is a symbol meaning "five", than we have 4 fingers on our hands" is also simply true. the sentence is true, but we still do not have 4 fingers on our hands. the sentence doesnt claim we have. just like the previous sentence does not claim Germany to border China. no paradox · Lygophile has spoken 01:56, 8 February 2011 (UTC)
replies: text: The paradox is that (1) we can prove, using only accepted techniques, that "if this sentence is true, Germany borders China" is a true sentence. The sentence doesn't directly claim to be true, but as the article explain we can prove that it is true. And (2) from the truth of that sentence, we can prove "Germany borders China".  This is a paradox because we would not expect widely accepted techniques to lead to a contradiction. — Carl (CBM · talk) 02:11, 8 February 2011 (UTC)
replies: text: then how come "if Poland was called China, than Germany borders China" isn't a paradox as well? or how about "if Germany borders China, than China borders Germany"? why are they not paradoxes just as much?· Lygophile has spoken 00:19, 10 February 2011 (UTC)
replies: text: It's not clear from what you're saying that you've read the article carefully. The article explains in detail how the self-referential nature of the sentence leads to the paradox. The point is that even if we assume that "if Poland was called China, than Germany borders China" is true, it does not tell us Germany borders China. But we can prove that "If this sentence is true, then Germany borders China" is true, and the truth of that sentence then allows us to prove that Germany borders China. — Carl (CBM · talk) 01:06, 10 February 2011 (UTC)
replies: text: i have read it, and it does not make clear why the same thing would not aply to my sentences. Germany borders Poland, so if we assume that Poland is called China, then Germany borders China. except it doesn't. i don't see the difference.· Lygophile has spoken 01:57, 10 February 2011 (UTC)
replies: text: If Poland is called China, then Germany borders China. Poland is not called China, then Germany doesn't necessarily borders China. "If this sentence is true, then Germany borders China" is true (which is proved in the article), and because it refers itself, it also means that Germany actually does border China. There's the difference.79.182.215.95 (talk) 02:07, 19 July 2012 (UTC)

text: i don't see the difference. -- So what? People who can grasp basic logic do. -- 71.102.133.72 (talk) 05:04, 15 September 2014 (UTC)

text: Where I find the problem is at the fact that Germany bordering China has nothing to do with that sentence, despite what the sentence claims. "If this sentence is true, then Germany borders China". What? No! Germany borders China if and only if they are geographically located next to each other; the conclusion does not follow from the premise and the IF .. THEN implication suggested is clearly false. A more accurate sentence would have been "regardless of whether this sentence is true or false, Germany does not border China". I don't see a paradox because the whole sentence seems to me false, therefore the conclusion does not even apply. However, seeing how so many people appear confused by such a silly past-time, I guess an article clarifying how this is not a paradox would not be overdue. 62.37.5.52 (talk) 09:35, 1 September 2012 (UTC)
replies: text: It must be hard for you. You know, being braindead.  — Preceding unsigned comment added by 85.242.102.172 (talk) 08:50, 14 February 2013 (UTC)
replies: text: Now that's just silly. A braindead person cannot type, and therefore your assertion is clearly false. Since you don't provide any other arguments, your contribution becomes meaningless. 80.103.84.224 (talk) 12:04, 23 March 2013 (UTC)

text: Where do stupid and ignorant people get the idea that, if they don't get something, the problem is with that thing, and not with them? -- 71.102.133.72 (talk) 05:04, 15 September 2014 (UTC)
thread_title:  please delete or 

message: 2nd sentence: 
:It is a traduction in minimal logic of Russel's paradox (naive set theory), or Gödel sentence (proof theory).
Is 'traduction' a word? I can't find any reference to it in English, but it's the French word for 'translation' apparently -- is this an error? Or is it meant to read:
:It is a translation in minimal logic of Russel's paradox ...
BrideOfKripkenstein (talk) 06:27, 16 March 2011 (UTC)
replies: text: I also found that sentence very unclear, even if traduction is replaced by translation.  I just removed the sentence. — Carl (CBM · talk) 10:51, 16 March 2011 (UTC)
thread_title:  "traduction" 

message: Far too many Wikipedia users genuinely think this is a paradox. It is not a paraodx, delete the article. 203.206.11.64 (talk) 13:20, 28 July 2011 (UTC)
replies: text: The paradox only exists within a naive calculus of logic. Putting it into natural language immediately demonstrates why the calculus is flawed, so the example is good. However, hiding the explanation in formal rhetoric does not help the reader to understand the flaw in the calculus. I have therefore rewritten the explanation in natural language, which is what the section heading claims to do. Hopefully this answers Harlequin's point, which is validly made. --Gak (talk) 15:34, 5 August 2011 (UTC)
replies: text: This article looks like someone intelligent and knowledgeable wrote it and then some incompetent ignoramus came along and messed it up. -- 71.102.133.72 (talk) 05:11, 15 September 2014 (UTC)

text: The world's logicians -- you know, reliable sources, people who know stuff, people who aren't stupid and ignorant -- think it's a paradox. Therefore Wikipedia properly calls it a paradox and provides the analysis from those reliable sources. People who aren't happy with that should delete their accounts. -- 71.102.133.72 (talk) 05:10, 15 September 2014 (UTC)
thread_title:  That awkward moment when... 

message: This article is unnecessarily hard to read because of ambiguous antecedent choices for "this" in the example sentence.  It seems like the first of these two readings is the one that's meant:
# If this conditional statement is true, then Germany borders China.
# If the antecedent of this conditional statement is true, then Germany borders China.  — Preceding unsigned comment added by 208.26.194.131 (talk) 00:54, 28 October 2011 (UTC)
thread_title:  Um, what's the antecedent of "this"? 

message: I now understand the paradox, but from the comments here, and from the article itself, it is not very clear (as it was not to me, although the article is better at this moment than back then). What must be included is a formal logic proof (as the two I presented) to show that it cannot be false. If one just proves it isn't true you say, "Well, then it's false". It's important to notice it cannot be false either (otherwise it wouldn't be a paradox), basing on the clear definition of the material conditional. JMCF125 (discussion • contribs) 11:47, 11 May 2013 (UTC)
thread_title:  The reason why people believe this is not actually a paradox 

message: ===Proof that the sentence is true===
The following analysis is used to show that the sentence "If this sentence is true, then Germany borders China" is itself true. The quoted sentence is of the form "If A then B" where A refers to the sentence itself and B refers to "Germany borders China". The usual method for proving a conditional sentence is to show that by assuming that hypothesis (A) is true, then the conclusion (B ) can be proven from that assumption. Therefore, for the purpose of the proof, assume A. Because A refers to the overall sentence, this means that assuming A is the same as assuming "If A then B". Therefore, in assuming A, we have assumed both A and "If A then B". From these, we can obtain B by modus ponens. Therefore, A implies B and we have proved "If this sentence is true then Germany borders China" is true. Therefore "Germany borders China", but we know that is false, which is a paradox.
===The paradox===
In a naïve logic, the sentence itself, denoted A, is true. The sentence is of the form "If A then B". Then "A = (if A then B)" is true.  But this reduces to "If A then B" is true. So A is true.  We then apply modus ponens to show that B is true; but this is impossible, because B is "Germany borders China", which is false.
Thepigdog (talk) 03:39, 15 June 2013 (UTC)
thread_title:  Some suggested changes for clarrification only 

message: In a naïve logic, the sentence itself, denoted A, is true. The sentence is of the form "If A then B". Then "A = (if A then B)" is true.  But this reduces to "If A then B" is true. So A is true.  We then apply modus ponens to show that B is true; but this is impossible, because B is "Germany borders China", which is false.
Thepigdog (talk) 03:39, 15 June 2013 (UTC)
thread_title: The paradox

message: I propose a new section for clarification purposes.  I would to group,
* Natural language
* Formal logic
* Naive set theory
* Combinatory logic
under a section Statements of Curry's Paradox
With some opening words like "The Paradox may be expressed in natural language and in various mathematical forms.".
Also I would like to add a section Language Capabailities for Expressing the Paradox under deiscussion and add in the following section Existential Problem.
If no objecttions I will proceed in about a weeks time.
=== Existence Problem ===
This paradox is similar to,
* Liar Paradox
* Russel's Paradox
in that each paradox attempts to give a name for something that does not exist.  These paradoxes all attempt to give a name or representation to a solution to the equation,
: X = ¬X
The paradox arises by naming or representing an expression of the form ¬X to be X.  In the case of Curry's Paradox, the negation is constructed from implication,
: X = X → false = ¬X ∨ false = ¬X
The domain of a boolean variable X is the set {true, false}.  However neither true or false is a solution to the above equation.  So it must be wrong to assert the existance of X.  Modern approaches to these paradoxes denie the right to name such an expression, or they extend the domain.
Thepigdog (talk) 11:19, 19 June 2013 (UTC)
thread_title:  New section 

message: This paradox is similar to,
* Liar Paradox
* Russel's Paradox
in that each paradox attempts to give a name for something that does not exist.  These paradoxes all attempt to give a name or representation to a solution to the equation,
: X = ¬X
The paradox arises by naming or representing an expression of the form ¬X to be X.  In the case of Curry's Paradox, the negation is constructed from implication,
: X = X → false = ¬X ∨ false = ¬X
The domain of a boolean variable X is the set {true, false}.  However neither true or false is a solution to the above equation.  So it must be wrong to assert the existance of X.  Modern approaches to these paradoxes denie the right to name such an expression, or they extend the domain.
Thepigdog (talk) 11:19, 19 June 2013 (UTC)
thread_title:  Existence Problem 

message: Clarify,
2 The language must contain its own truth-predicate: that is, the language, call it "L", must contain a predicate meaning "true-in-L", and the ability to ascribe this predicate to any sentences;
This is not explicitly used in the proof.  I propose removing it.
1 The language must contain an apparatus which lets it refer to, and talk about, its own sentences (such as quotation marks, names, or expressions like "this sentence");
as
# The language must contain an axiom or apparatus which simultaneously names and asserts the existence of an expression in the language.  This allows the expression to refer to, and talk about, itself (such as quotation marks, names, or expressions like "this sentence");
Down further I would like to add.
An expression in a language differs from a statement in that a statement is implicitly true.  That is, asserting a language expression makes it a statement.  Asserting a statement says that the value of the expression is true.
=== Resolution in Logic ===
I am also uncomfortable with the "Resolution in Logic" section.  I think it could be misread as saying that there is some particular difficulty with Currys Paradox which no one can resolve.  That is probably not what the original auther intended. 
I propose some rearrangement, and something like,
The resolution of Curry's paradox (and other similar paradoxes) in logic is difficult, because logic needs axioms from which set theory and the rest of mathematics may be built.  From one perspective, logic and then set theory may be considered as the languages from which mathematics boot straps itself. So even though the problem can be described quite simply, a detailed discussion detailed is limited to a technical discussion of the axioms of logic.
Thepigdog (talk) 12:20, 29 June 2013 (UTC)
thread_title:  More Minor Clarifications 

message: I am also uncomfortable with the "Resolution in Logic" section.  I think it could be misread as saying that there is some particular difficulty with Currys Paradox which no one can resolve.  That is probably not what the original auther intended. 
I propose some rearrangement, and something like,
The resolution of Curry's paradox (and other similar paradoxes) in logic is difficult, because logic needs axioms from which set theory and the rest of mathematics may be built.  From one perspective, logic and then set theory may be considered as the languages from which mathematics boot straps itself. So even though the problem can be described quite simply, a detailed discussion detailed is limited to a technical discussion of the axioms of logic.
Thepigdog (talk) 12:20, 29 June 2013 (UTC)
thread_title:  Resolution in Logic 

message: Banning "this statement" from the language may prevent Curry's paradox from being formed.  However the same problem may be formed in many other ways.  For example if we an add an Eval function to logic that takes a string and converts it into a logical expression, then consider the string,
: s = "Eval(s) → false"
then the expression,
: Eval(s) = Eval(s) → false = ¬Eval(s)
again gives Currys's paradox.  To handle such a situation the boolean type needs a value representing an error situation.
Thepigdog (talk) 18:09, 29 June 2013 (UTC)
thread_title:  Another addition 

message: From what I can understand researchers are suggesting fairly desperate solutions to Currys Paradox.  To me the paradox arises immediately you allow the construction of an expressions whose value does not exist.  This is really easy to do in natural language and any even small addition to logic allows the construction of such value.  I think pure predicate logic may not allow the construction of the paradox, but I am not sure.
In computer programming if given a value that does not fit the domain we would throw an exception.  The equivalent in a functional language would be to return an error value.  This would require extending all domains with,
* Unknown - I dont know
* Error - The value does not exist.
These values dont so much extend the domain as provide an "out" when things get difficulty.  Unknown indicates that the value is not available yet.  So the only valid response is to wait.
Error indicates that an infinitely recursive function has been called, or an expression does not have a value in the domain, or the input data violates the assertions made about the data.  The only valid response is to terminate.
Questions:
* Would somebody knowledgable indicate if such an approach is possible.
* Can Currys Paradox appear in pure logic.
Thepigdog (talk) 19:56, 29 June 2013 (UTC)
thread_title:  The Situation with Currys Paradox is much worse than I thought 

message: Translation of
: r = ( \lambda x.x x \to y ) 
then define,
: m A B = A → B
the translation is,
: T[\lambda x.(m (x x)) y]
: S T[\lambda x.(m (x x)) ] T[\lambda x.y]
: S (S T[\lambda x.m ] T[\lambda x.(x x) ]) T[\lambda x.y]
: S (S (K m) T[\lambda x.x x ]) T[\lambda x.y]
: S (S (K m) (S T[\lambda x.x ] T[\lambda x.x ])) T[\lambda x.y]
: S (S (K m) (S I I)) (K y)
= S (S (K m) (S I I)) (K y)
Thepigdog (talk) 12:17, 1 July 2013 (UTC)
thread_title:  Derivation of Combinatory Logic paradox expression 

message: The comment added under  Statement of Curry's paradox/Lambda calculus needs clarification.  
It also does not fit well with the structure of the article, and its  dramatic purpose. Currently the paradox is shown first, which involves the reader in wanting to understand the resolution.
I am hoping when the author has time that an explanation may be added, and that perhaps some restructuring may be made.  An explanation of how Currys paradox is handled by "proofs as programs" would be valuable.
Thepigdog (talk) 10:53, 21 May 2014 (UTC)
thread_title:  Untyped lambda calculus 

message: In the expression
:r = ( λx. ((x x) → y) )
I don't understand what the arrow (→) means. It doesn't seem do be defined in the linked article Lambda calculus either.
Is it just a variable name? Then, I think, it would be more clear if the expression is written like
:r = ( λx. ((→) (x x) y) )
Is it a part of an extension of the lambda calculus, a link or explanation is needed.
Also, I don't really understand how Lambda calculus expressions can be interpreted as propositions.
Baum42 (talk) 16:56, 8 June 2015 (UTC)
thread_title:  [[Curry's paradox#Lambda calculus | Lambda calculus]]: What does the arrow mean? 

message: Please provide a source for the purported resolution in natural language that has been re-introduced to the article. The claim that the sentence "creates a falsehood if B is false" makes little sense - what does it even mean for a sentence to "create a falsehood"? Similarly, the claim that no value for A satisfies "if A then false" is false, because in natural language "if this sentence is true, then false" gives such an A - that is why we have this paradox! In any case, without a source, it is impossible to improve the paragraph to state whatever is actually intended, and WP:V requires a source when a claim is challenged. I will pause for several days to allow a source to be provided. — Carl (CBM · talk) 10:11, 25 August 2015 (UTC)
thread_title:  Purported resolution in natural language 

message: Relax.  I'm not going to say that there is no paradox.  However, the discussion in the natural language section is confusing and misleading for people who have no understanding of formal logic or lambda calculus.  It doesn't bring them to a point where they can learn why the paradox is important.  It is easy for people to see how the sentence is wrong.  Germany does not border China, therefore the sentence "If this sentence is true, Germany borders China".  They fixate on that bit and can't wrap their minds around the important part.
First, I would suggest linking to the Conditional Proof page to provide some evidence for the technique of assuming the antecedent.  Then instead of simply saying "and by modus ponens", actually spell it out for them.  "Modus ponens" might as well be "abra cadabra" as far as the average reader is concerned.  The key thing that I think should be emphasized is that we assume the antecedent.  However, the antecedent is the whole sentence.  Since the antecedent is the whole sentence the consequent must follow.  By assumption ;-).  This is clearly "a bad thing", but that is the whole reason why this paradox is important.  We have a logical system/lambda calculus that allows this set up.
The last bit is the place where I think this article is falling down the most.  The previous people who commented on this article are pretty much all wrapped up in this misunderstanding.  They feel if you just restate the sentence, you can avoid the paradox.  Which is true, but misses the point entirely.  I suggest they are missing the point because it was never stated in the article: I can prove things that aren't true because my logic calculus has a problem.
Finally, providing some historical context on how the paradox arose and what changes were made to various logical systems to deal with the problem would really go a long way towards making the issue understandable.  It's actually why I came here and was quite disappointed. 59.85.105.186 (talk)  —Preceding undated comment added 14:22, 18 October 2015 (UTC)
replies: text: Thank you - these are very helpful comments. I will try to implement them over time. The historical part is, unsurprisingly, the most difficult. The other changes you suggest should be easier to put in place. — Carl (CBM · talk) 22:44, 18 October 2015 (UTC)
thread_title:  Natural language section is only understandable to those who understand it 

message: OK I don't mind at all if you don't want to use this. But just deleting the section without improving it is a bit annoying. This is not an argument about logical deduction systems. It is an argument about how you would understand this in English, or some other natural language system.
The paradox starts by asserting a statement of the form
: If A then B
Where A refers to the whole statement.
: A = (If A then B)
But if B is false there is no solution for A. All this is explained earlier.
In natural language we are allowed to use natural arguments, that are understandable without a formal system. 
: If (neither true nor false) then B
is not a valid statement in natural language and can be ignored.
I am more than happy for someone to describe this better. 
What follows is a slightly expanded version of what was there before.
3.1 Resolution in natural language
Consideration of the sentence "If A then B" where A refers to the sentence creates a falsehood if B is false, because there is no value for A that satisfies the expression A = "if A then false".
If you put A = true you get,
:true = if true then false ... and this is false.
If you put A = false you get,
:false = if false then false ... and this is false.
So when we use the statement,
:If A then B
Natural language logic assumes that all statements are either true or false. But A is not, so the rest of the argument is invalid because it is arguing from an expression that has no possible value (does not exist) when B is false.
Thepigdog (talk) 02:57, 2 November 2015 (UTC)
thread_title:  Natural Language 

message: I've opened a math.stackexchange question to attempt to understand Curry's paradox better; specifically, the article's explanation of how the paradox can be formulated using combinators or lambda calculus don't make sense to me (see the section on lambda calculus above).
http://math.stackexchange.com/q/1602611/52057
134.217.237.30 (talk) 17:41, 8 January 2016 (UTC)
thread_title:  Math StackExchange post to help clarify lambda/combinator sections 

message: Glad i'm not the only one that is confused by the example given to explain this. "If this sentence is true, then Germany borders China.".
It seems like this sentence should read more like, "This sentence is true, so Germany borders China." -or- "Germany does not border China, so this sentence is false.".
This might be going over my head, but from my understanding from reading previous topics, is that this is better understood with Math than through sentence examples. That sentence example might make sense to some people on here, but it seems, IMO, that the section explaining the example could be worded better for a reader. DrkBlueXG (talk) 21:07, 7 June 2016 (UTC)
thread_title:  Weird example 

message: There is NO implication function according to the Curry-Howard correspondence.
* https://en.wikipedia.org/wiki/Church_encoding
* Church Booleans
* If
Can't this be used to construct the implication operator?
Thepigdog (talk) 04:24, 10 September 2016 (UTC)
thread_title:  No implication operator in lambda calculus 

message: Techincally, Germany does border China. Since Germany has an embassy in the capital of China, and all embassies are considered to be the territory of the embassy's country, we can conclude that Germany borders China, and therefore the example given in the article, If this sentence is true, then Germany borders China, is not actually an example of Curry's paradox. 130.126.255.117 (talk) 05:29, 2 November 2016 (UTC)
thread_title:  Example given not actually a paradox 

message: If this sentence was typed, there are 5 quarters in a whole. 205.142.232.18 (talk) 22:50, 13 December 2016 (UTC)
thread_title:  A Better Example of the actual paradox 

message: The formal logic proof has a step that uses "contraction" as its justification.  I was not familiar with contraction, and the linked page was not at all helpful.  I suggest that additional steps be added as follows:
x -> (x->y)       .... (already in the proof)
(-x) -> (x->y)    .... (if the antecedent of a conditional is false, then the conditional is true)
x OR -x           .... (law of the excluded middle)
(x->y) OR (x->y)  .... (I think you can do this substitution, where each side of the previous step is replaced using of the two steps before it)
(x->y)            .... (Is there a name for the rule that "a OR a implies a"?)
This returns us to the proof.
Another way to accomplish this would be to appeal to the Distributivity of Implication (https://en.wikipedia.org/wiki/Distributive_property#Truth_functional_connectives)
x -> (x->y)       .... (already in the proof)
(x->x) -> (x->y) .... (distributivity of implication)
TRUE -> (x->y) .... (law of identity)
(x->y) .... (modus ponens)
This returns us to the proof.  — Preceding unsigned comment added by 63.138.92.98 (talk) 13:27, 24 April 2017 (UTC)
thread_title:  What is contraction? 

message: 5.249.127.17 (talk) removed a ton of material anonymously, without discussion.
I suggest that he log in as a user. Roll back the changes. Then justify the changes here in talk. Then he can re-apply them.
Thanks for your co-operation.
Thepigdog (talk) 01:17, 19 May 2017 (UTC)
replies: text: I'm afraid I have to disagree. For one, the user also added material. More to the point, the edits have edit comments explaining them, and the removed material was not cited to reliable sources. I suggest reading these edits as WP:CHALLENGEs. They should not be undone without addressing the issues raised by the IP contributor. Paradoctor (talk) 06:43, 19 May 2017 (UTC)
thread_title:  Vandalism 

message: The link at the top of the resolution section links here, but "here" didn't exist until I made this section. Anyway, the section needs reliable sources so I'm opening this discussion in hope of finding some. Hopefully I'll be back with some. HueSurname (talk) 14:34, 2 February 2021 (UTC)
thread_title:  Dispute 

message: An editor has identified a potential problem with the redirect :Curry`s paradox and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 October 15#Curry`s paradox until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  1234qwer1234qwer4 15:36, 15 October 2022 (UTC)
thread_title:  "Curry`s paradox" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: I read this page using white text on a black background, which is generally fine for Wikipedia. Some text isn't visible to me, for instance the displayed material after "by examining the set":
X \ \stackrel{\mathrm{def}}{=}\  \left\{ x \mid x \in x \to Y \right\}.
I don't know what's going on here. I presume that this material is being displayed in black. 2A02:A475:62C9:1:BDBA:6E29:FF67:98FA (talk) 07:02, 17 December 2022 (UTC)
thread_title:  white text on black background: some displayed material is not visible 

message: I hate to add to this discussion page, but if this is to be an educational page I think it's important that the formal sentential logic proof that's provided isn't formal or sentential logic. '=:' isn't a symbol in sentential logic. It's a symbol from the metalanguage, meaning "means the same thing as" or something like that. (It's usually used to state a definition.) This also means that the proof isn't formal, since '=:' denotes a semantic concept. In fact, this paradox (my favorite one!) depends on self-reference, and you can't express self-reference using the vocabulary of sentential logic. Now try substituting material equivalence for '=:' and see what you can prove... Kronocide (talk) 22:23, 28 April 2023 (UTC)
thread_title:  The formal sentential logic proof isn't sentential logic or formal 

message: I've been a programmer for more than 40 years. In writing programs, I have to create comparisons and tests. Based on my background, I don't believe there is a paradox because I can resolve it. Or I'm completely missing the problem. Here is how I resolve the conflict.
I can simply say, we  analyze a sentence as a whole. For example, "If this sentence is true," is a conditional clause. We do not presume it as either true or false until after the condition is evaluated. It depends on a condition antecedent to the clause. Since the secondary clause "Germany borders China" is not true, therefore the sentence is false and no paradox occurs. Now, I think the opposite might be better as an alleged paradox, e.g. "If this sentence is false, then Germany borders China." Yes, the sentence is false, but, truth is that which is concordant with reality. Since the sentence is false, none of its conclusions have any value or relevance, because they have no relation to reality, so they have no validity. Thus, the proposition ""Germany borders China" is irrelevant.
 
Another way to put it is if a sentence is false, that is, not concordant with reality, any claim or proposition within may be ignored. This also resolves the paradox.
 
An example in math is 0*. 0 times anything is 0 regardless of what number follows, therefore any digit or string of digits may be ignored. Same if the entry to the right is a parenthised expression, it may be ignored as irrelevant.
 
So maybe someone can show me where I have misunderstood the paradox? I resolved it in about 10 minutes, it seemed way too easy. The inverse was harder.
"Understanding of things by me is only made possible by viewers (of my comments) like you."Thank you.Paul Robinson Rfc1394 (talk) 12:36, 12 January 2024 (UTC)
replies: text: Indeed, the explanation in section "In natural language" is pretty superfluous in that it omits the details of the "" mentioned in item 1.  Since you are a programmer, you should be able to understand the formal proof in section "Sentential logic", which actually gives all details.  I'll try to come up with a natural language version of it within the next few days. - Jochen Burghardt (talk) 19:27, 14 January 2024 (UTC)
replies: text:  I made a first suggestion; please check if it is comprehensible and convincing. (BTW: In your argument, the step "" is flawed, cf. Material conditional). - Jochen Burghardt (talk) 20:02, 14 January 2024 (UTC)
thread_title:  Curry's Paradox: Either I've resolved it or I don't understand it 

message: Two posters above have alluded to this idea, so maybe there is already consensus that it's not a good approach. Anyway, I suspect that truth tables are more accessible to readers than lambda calculus, combinatory calculus, etc. And it seems to me that truth tables explain what the paradox is concisely. So here is my treatment.
:In general, here is the truth table for an implication P \to Q:
:
P	Q	P \to Q
F	F	T
F	T	T
T	F	F
T	T	T
:In this case specifically, P is "the sentence is true" (or "my claim is true"), and Q is "Germany borders China". But P holds if and only if P \to Q holds. So the only row of the truth table that does not contradict itself is the fourth row, where Germany borders China. So Germany borders China.
Questions:
# Does this treatment capture the paradox correctly?
# Is it not rigorous enough? If its gaps were filled in, then would it be just as verbose as the other treatments given?
# Is it original research? (I think not, because of WP:CALC.)
# Would it improve the article?
Regards, Mgnbar (talk) 14:16, 6 May 2024 (UTC)
thread_title:  Truth table treatment?