Jourdain Paradox (card paradox)

[Ben_Sinner]

en.wikipedia.org/wiki/Card_paradox

There is a paradox similar to the Liar’s Paradox, except this one is not self-referential.

The paradox goes like this:

There is a card.

The front side of the card says ‘THE SENTENCE ON THE OTHER SIDE OF THE CARD IS TRUE’

The back side of the card syas: 'THE SENTENCE ON THE OTHER SIDE OF THE CARD IS FALSE.

Does this prove that both sentences is true and false at the same time and would violate non-contradiction?

 

[PumpkinCookie]

Are you studying philosophy of language now or something?

I think one possible solution to this problem is to suppose that the sentences on the card do not have a discernible truth value since they don’t refer to anything other than themselves.

There is no way to verify the truth value of either sentence without self-reference. There is no empirical reason to suppose either sentence has a truth value, and no reason to suppose either sentence is a priori true. Therefore, we might be able to say that the sentences don’t actually refer to anything meaningful and therefore the apparent paradox is an illusion and a trick of our language.

This problem really isn’t so different from this other (in my opinion):

The following sentence is true.
The prior sentence is false.

Although there are two sentences, they are both self-referential. “Following” and “prior” are indexicals which have no meaning or a radically different meaning without context. The context here though, is self reference, and therefore we cannot reasonably expect a truth value. “Other side of this card” is similarly indexical and also self referential.

So, in my opinion, neither sentence has a truth value and the paradox emerges from a self referential quirk of language. Just like M.C. Escher’s staircases don’t actually descend or ascend forever, but appear to because they are proper or appropriate stairs, these sentences appear to be both true and false because they aren’t sentences with discernible truth values. Not too sure though. There is some interesting literature on this subject.

 

[Rhubarb]

Are you studying philosophy of language now or something?

I think one possible solution to this problem is to suppose that the sentences on the card do not have a discernible truth value since they don’t refer to anything other than themselves.

There is no way to verify the truth value of either sentence without self-reference. There is no empirical reason to suppose either sentence has a truth value, and no reason to suppose either sentence is a priori true. Therefore, we might be able to say that the sentences don’t actually refer to anything meaningful and therefore the apparent paradox is an illusion and a trick of our language.

This problem really isn’t so different from this other (in my opinion):

The following sentence is true.
The prior sentence is false.

Although there are two sentences, they are both self-referential. “Following” and “prior” are indexicals which have no meaning or a radically different meaning without context. The context here though, is self reference, and therefore we cannot reasonably expect a truth value. “Other side of this card” is similarly indexical and also self referential.

So, in my opinion, neither sentence has a truth value and the paradox emerges from a self referential quirk of language. Just like M.C. Escher’s staircases don’t actually descend or ascend forever, but appear to because they are proper or appropriate stairs, these sentences appear to be both true and false because they aren’t sentences with discernible truth values. Not too sure though. There is some interesting literature on this subject.

+1

 

[You]

You can think of language as a dogs bark, tis all just sounds. You can think of the dog, the card or the ink as true things, as they exist. The true contradiction would be a real anti-dog, anti-card and anti-ink existing in the dog, card and ink. Language is just sounds of dogs, sounds proposing contradictions are not true contradictions themselves they do not truly exist as real things yet, barking… and barking, and barking, and barking, and barking, and barking, and barking, and barking,

 

[inocente]

The front side of the card says ‘THE SENTENCE ON THE OTHER SIDE OF THE CARD IS TRUE’

The back side of the card syas: 'THE SENTENCE ON THE OTHER SIDE OF THE CARD IS FALSE.

Does this prove that both sentences is true and false at the same time and would violate non-contradiction?

I don’t see how that’s a genuine paradox. For instance, take a card and write “All bachelors are unmarried” on the back, then the first sentence on the front, which will therefore be correct.

Now take another card and write “All squares have eleven sides” on the back, then the second sentence on the front, which is therefore also correct.

Now stick the cards back to back. That doesn’t make them refer to each other, it’s just a magician’s trick since you can peel the cards apart again.

 

[SimmieKay]

en.wikipedia.org/wiki/Card_paradox

There is a paradox similar to the Liar’s Paradox, except this one is not self-referential.

The paradox goes like this:

There is a card.

The front side of the card says ‘THE SENTENCE ON THE OTHER SIDE OF THE CARD IS TRUE’

The back side of the card syas: 'THE SENTENCE ON THE OTHER SIDE OF THE CARD IS FALSE.

Does this prove that both sentences is true and false at the same time and would violate non-contradiction?

I think the classic non-paraconsistent solution to the liar paradox is:

1. 
   *]Sentences themselves don’t have truth values, only the propositions they express do
   *]Not all indicative sentences express a proposition, only some do
   *]“This sentence is false” is a sentence that does not express a proposition
   *]Hence, since “This sentence is false” does not express an proposition, it cannot be said to be true or false
   
   One could use the same argument by applying point (2)/(3) to the two sentences in this scenario as well. So, considering the liar paradox alone, the criteria for “indicative sentence that does not express a proposition” must be extended from just self-referential sentences to circularly referential sets of sentences (to handle Jourdain’s paradox), to members of certain infinite sets of sentences (to handle Yablo’s paradox).
   
   I prefer the paraconsistent / dialetheic approach, however, because the criteria of “which sentences express a proposition” becomes more and more complex, as one considers additional paradoxes such as Jourdain’s and Yablo’s; and because as those criteria become more and more complex, they begin to feel more and more contrived (i.e. they’ve been concocted just to save the law of non-contradiction, they don’t seem to have any independent justification from that aim).
   
   Another objection to the classic non-paraconsistent approach, is that not only does it say that “This sentence is false” is neither true nor false, but it says the same thing about “This sentence is true”, even though there is no paradox in asserting its truth.
   
   Labelling some sentences as neither true nor false does not reject the law of the excluded middle. The law of the excluded middle is only about propositions, it does not apply to all sentences (e.g. questions and commands don’t have truth values). So long as all propositions have a truth value, the law of the excluded middle survives.
   
   Simon