posted
Aha! I knew there were more paradoxes like that, but I could never think of them. *thinks* Still can't come up with anymore though. Anyone else have any?
And Dag... damn you Posts: 3295 | Registered: Jun 2004
| IP: Logged |
posted
Once again, a question that would be easily answered if you simply brandished a weapon and asked it again, only louder.
Posts: 2258 | Registered: Aug 2003
| IP: Logged |
The statement simply has no truth value and cannot be evaluated as either true or false.
But "p = not q" is not true. To lie means "to present false information with the intention of deceiving." Therefore there are cases where false information can be presented without the intention to deceive. Therefore, U, the universal set of statements includes
P, the set of lies Q, the set of truthful statements; and R, the set of untruthful statements
P is a subset of R. R is not a subset of P.
Therefore statements exist which are both untrue and not lies.
posted
I've got a t-shirt like that. The front says: The sentence on the back of this shirt is false. The back says: The sentence on the front of this shirt is true.Posts: 2149 | Registered: Aug 2000
| IP: Logged |
posted
Depends on what you mean by "paradox." There are some other types of paradox (e.g., Zeno/Xeno's Paradox), but sometimes when people use the term "paradox," they mean to refer only to the self-referential sort.
Posts: 14017 | Registered: May 2000
| IP: Logged |
quote:But "p = not q" is not true. To lie means "to present false information with the intention of deceiving." Therefore there are cases where false information can be presented without the intention to deceive. Therefore, U, the universal set of statements includes
P, the set of lies Q, the set of truthful statements; and R, the set of untruthful statements
P is a subset of R. R is not a subset of P.
Therefore statements exist which are both untrue and not lies.
That's simply one definition of "to lie." There is a broader sense meaning something like "to utter falsehood" or "to speak falsely" (OED). I think it's reasonable to say that in this instance, where the options are (1) lying and (2) telling the truth, they are intended to be simple opposites.
Even assuming your narrower definition of "lying" in a broader category of telling untruths, I think it still works.
p = telling untruth with intent to deceive q = telling truth r = telling untruth
p —> q p(x) —> r(x) r —> ~q
Thus p —> q and ~q. So there.
Posts: 9945 | Registered: Sep 2002
| IP: Logged |
posted
Unless you're using a symbol set I'm not familiar with, you're substitution of p for r in "r —> ~q" is simply not supported by any logical operator.
Posts: 26071 | Registered: Oct 2003
| IP: Logged |
posted
He's using conditional introduction, if you can show that assuming one statement (in this case p) will result in another statement (in this case ~q) in a subproof, such as the following:
| p -> r | r -> ~q ---- | | p | ---- | | r //conditional elimination on p -> r and p | | ~q //conditional elimination on r -> ~q and r | p -> ~q //conditional introduction from the above subproof.
Posts: 15770 | Registered: Dec 2001
| IP: Logged |
posted
However, its worth pointing out that logical systems do not completely circumscribe statements in language.
For instance, just because I can say "the set of all sets that do not contain themselves" does not mean such a set mathematically exists.
Posts: 15770 | Registered: Dec 2001
| IP: Logged |
posted
You're focusing too much on explicit information, Dag .
It very well may be that the person stating "I am lying" is intending to deceive as to (the information of) his or her general telling of the truth (perhaps by confusion ).
Posts: 15770 | Registered: Dec 2001
| IP: Logged |
quote:Ah, but we are trying to find out whether it's true or not. Read the first post again:
Yes, but my conclusion was limited to "Therefore you are not lying," and this is what you disagreed with. I purposely avoided the second question, because paradox makes my Mr. Tumnus hurt.
quote:I think we can agree that he is neither lying nor telling the truth.
Certainly. Which makes my first post correct. Posts: 26071 | Registered: Oct 2003
| IP: Logged |
Printer-friendly view of this topic
![[Smile]](smile.gif)
![[Razz]](tongue.gif)
![[Group Hug]](graemlins/grouphug.gif)
![[Big Grin]](biggrin.gif)
![[Wink]](wink.gif)
).
![[No No]](graemlins/nono.gif)
![[Cry]](graemlins/cry.gif)
