Hatrack River Forum: Answer Me This

This is topic Answer Me This in forum Books, Films, Food and Culture at Hatrack River Forum.

To visit this topic, use this URL:
http://www.hatrack.com/ubb/main/ultimatebb.php?ubb=get_topic;f=2;t=033063

Posted by Alcon (Member # 6645) on :

When I say "I am lying", am I lying or telling the truth?

Posted by AntiCool (Member # 7386) on :

Blue.

Posted by HesterGray (Member # 7384) on :

Yes. [Smile]

Posted by Dagonee (Member # 5818) on :

Lying involves intent to deceive.

Deception involves conveying information contrary to fact.
The statement "I am lying" conveys no information.

We can presume you are aware of this by your posting the question, so you are obviously not intending to deceive.

Therefore you are not lying.

Try it with "This statement is false." [Smile]

Posted by Lyrhawn (Member # 7039) on :

What about "I don't know anything"

If you know enough to know you don't know, then you know more than nothing.

Posted by Alcon (Member # 6645) on :

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 [Razz]

Posted by Teshi (Member # 5024) on :

...and Dag is definately a lawyer...

Posted by Jon Boy (Member # 4284) on :

Better yet:

p = lying
q = telling truth
p = not q

p —> q

but

p —> not q

so

p —> q and not q

The statement simply has no truth value and cannot be evaluated as either true or false.

Posted by King of Men (Member # 6684) on :

Mu!

And at that moment, Alcon was enlightened.

Posted by Teshi (Member # 5024) on :

Hatrack [Group Hug]

Posted by Book (Member # 5500) on :

Once again, a question that would be easily answered if you simply brandished a weapon and asked it again, only louder.

Posted by Teshi (Member # 5024) on :

Book, are you named after Book?

Posted by Dagonee (Member # 5818) on :

quote:
Better yet:

p = lying
q = telling truth
p = not q

p —> q

but

p —> not q

so

p —> q and not q

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.

Dagonee

Posted by Verily the Younger (Member # 6705) on :

Try this one:

The following sentence is true.
The preceding sentence is false.

Posted by Miro (Member # 1178) on :

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.

Posted by Jay (Member # 5786) on :

LIAR!

Posted by Mike (Member # 55) on :

1. Exactly one of these three statements is true.

2. 2 + 2 = 4

3. I am da bomb. [Big Grin]

Posted by scottneb (Member # 676) on :

*duck-tapes head back together*

Posted by Miro (Member # 1178) on :

Something I've been wondering about: Are there any paradoxes that are not self-referential?

Posted by Mike (Member # 55) on :

KoM, would you like some djinn with your tonic?

*Hands Miro a copy of Gödel, Escher, Bach*

Posted by ClaudiaTherese (Member # 923) on :

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.

Posted by Little_Doctor (Member # 6635) on :

The below statement is true.

The above statement is false.

Posted by Morbo (Member # 5309) on :

The post above is true.

This post is not.

Posted by Morbo (Member # 5309) on :

Neither is this one.

Posted by Jon Boy (Member # 4284) on :

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.

Posted by Dagonee (Member # 5818) on :

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.

Posted by fugu13 (Member # 2859) on :

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.

Posted by fugu13 (Member # 2859) on :

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.

Posted by breyerchic04 (Member # 6423) on :

AHHHHH Geeks! *runs away*

Posted by Jon Boy (Member # 4284) on :

quote:
However, its worth pointing out that logical systems do not completely circumscribe statements in language.

And fugu wins.

Posted by Dagonee (Member # 5818) on :

Regardless, with no intent to deceive, he's not lying.

Therefore we know p as defined by Jon is not true.

Therefore we can stop. Remember, we're not trying to find out if "I am lying" is true or not. We're trying to find out if it's a lie.

Premises:
p: intends to decieve
q: statement is true
r: statement is untrue
l: the statement is untrue and there was intent to deceive

r -> ~q
q -> ~r
l -> r & p

~p (we know there is no intent to deceive)
.:~l (l-> r & p taken with ~p)

We're done.

Dagonee

[ March 29, 2005, 12:43 PM: Message edited by: Dagonee ]

Posted by Dagonee (Member # 5818) on :

quote:
And fugu wins.

The only linguistic arguments on the floor are my original one, which is correct, and Job Boy's OED definitions argument.

Therefore I win.

You can say you won, too, if you want. But if you accept that "I am lying" has no truth value, then it's not untrue, and therefore not a lie.

So I win again. [Razz]

Posted by fugu13 (Member # 2859) on :

You're focusing too much on explicit information, Dag [Razz]

.

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 [Wink]

Posted by screechowl (Member # 2651) on :

This is the kind of reasoning test that has been used in stories to trip up androids. I will not fall for it.

[No No]

Posted by Dagonee (Member # 5818) on :

But if he's intending to deceive BUT telling the truth, he's not lying either.

I know a simple way to solve this:

*knocks Alcon to the ground*
*says emphatically, "Who's lying now, mister?"*

Posted by Jon Boy (Member # 4284) on :

quote:
Therefore we can stop. Remember, we're not trying to find out if "I am lying" is true or not. We're trying to find out if it's a lie.

Ah, but we are trying to find out whether it's true or not. Read the first post again:

quote:
When I say "I am lying", am I lying or telling the truth?

I think we can agree that he is neither lying nor telling the truth.

Posted by Mike (Member # 55) on :

quote:
The second statement is false.
2+2=5

Are you implying I'm not da bomb? [Cry]

Posted by Dagonee (Member # 5818) on :

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. [Razz]

Posted by Jon Boy (Member # 4284) on :

But your first post only addressed the issue of the statement being a lie. [Razz]

Posted by Dagonee (Member # 5818) on :

I didn't say my conclusion was complete. I said it was true. [Big Grin]