I think bonanova was close, but he made one mistake; "A if only B" should be A->B, not B->A.
You're exactly right, I got it backward. Thanks for clarifying.
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Posted 24 August 2007 - 12:40 PM
you guys need to take a logic (discrete structures) class:
to be able to keep the whole statement false, then the part "there is buried treasure" must be true!! if that part was false, then since both parts are false, the whole statement is true so if he was a swindlecant, he wouldn't be able to say this statement.
Posted 21 September 2007 - 02:43 PM
Posted 16 October 2007 - 09:59 PM
Posted 07 November 2007 - 04:28 AM
Posted 27 December 2007 - 08:07 AM
Posted 21 January 2008 - 09:09 PM
I believe you need to review the logic of this again. It seems that you are equating IF-THEN with AND. They are most definitely NOTthe same. I really don't see where you get that equivalence from. IF-THEN creates a causality relationship, AND is boolean operator.
IF-THEN is not the same as AND (or OR). You cannot use it to generate a boolean logic table.
Posted 13 March 2008 - 02:29 AM
Posted 25 March 2008 - 04:29 PM
The answer is - YES - head for the hills and bring your pick and shovel.
But I don't think anyone has given the correct analysis yet.
First, note the statement that was made:
There is treasure only if I am an honest man.
Some have made the mistake of calling this logical equivalence.
It's not. A only if B is logically the same as if B then A.
Logical equivalence is more restrictive: A if and only if B.
The truth tables differ in the case of a false premise and a true conclusion:
"False implies Truth" is True for if; it's False for if and only if.
Thus, we can restate simply as if B then A:
If I am an honest man then there is treasure.
There are two cases: the speaker is a honestant [H] or a swindlecant [S].
 H - the speaker is an honest man
If the speaker is honest, the premise is true [fact] and the logical implication must be true [else he would be lying].
Therefore the conclusion is true: There is treasure.
 S - the speaker is lying.
If the speaker is lying, the premise if false [fact] and the logical implication must be false, also, [else he would be telling the truth.]
But, because a false premise validly implies every conclusion, such an implication is always true.
Thus we must conclude that the speaker could not have been a swindlecant:
one cannot invalidly conclude anything [tell a lie, as a swindlecant must do] starting from a false premise.
Since the speaker must have been a truth-teller, there must be a treasure.
Posted 26 March 2008 - 04:45 PM
I think bonanova was close, but he made one mistake; "A if only B" should be A->B, not B->A. For Example, "the sky is blue, only if 1+1=3" is false.
P = speaker is a Honestant. Q = there is treasure on the island. <1>P -> (P->Q) (given) <2>!P -> !(P->Q) (given) <3>P \/ !P (LEM ... or possibly given, in this context) <4>Assume P: <5> P->Q (from <1> and <4>) <6> Q (from <5> and <4>) ...so if the speaker is an honestant there is treasure on the island. We knew that. <7>Assume !P: <8> Assume P: <9> Contradiction (from <7> and <8>) <10> Q (from <9>) <11> P->Q (from <8> through <10>) <12> !(P->Q) (from <7> and <2>) <13> Contradiction (from <11> and <12>) <14> Q (from <13> ...and there's treasure if the speaker is a swindlecant. <15>Q (from <3>, <4> through <6>, and <7> through <14>)
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