Freethought & Rationalism Archive

John Page · 03-26-2002, 12:06 PM

Quote:

Originally posted by Bill_C:
<strong>It seems that these are two cases that could both result in da, ja, da. Am I missing something?
</strong>

Da.

(Sorry, sorry - I just couldn't resist that one)

Now folks, back to reality.....

phaedrus · 03-30-2002, 12:36 AM

Bill C

Quote:

Your first move is to find a god who you can be certain is not Random, and hence is either True or False.

To do so, turn to A and ask Question 1: Does da mean yes iff, you are True iff B is Random? If A is True or False and you get the answer da, then as we have seen, B is Random, and therefore C is either True or False; but if A is True or False and you get the answer ja, then B is not Random, therefore B is either True or False.

But what if A is Random?

If A is Random, then neither B nor C is Random!
So if A is Random and you get the answer da, C is not Random (neither is B, but that�s irrelevant), and therefore C is either True or False; and if A is Random and you get the answer ja, B is not random (neither is C, irrelevantly), and therefore
B is either True or False.

Thus, no matter whether A is True, False, or Random, if you get the answer da to Question 1, C is either True or False, and if you get the answer ja, B is either True or False!

Now turn to whichever of B and C you have just discovered is either True or False � let us suppose that it is B (if it is C, just interchange the names B and C in what follows) � and ask Question 2: Does da mean yes iff Rome is in Italy? True will answer da, and False will answer ja. Thus, with two questions, you have either identified B as True or identified B as False.

For our third and last question, turn again to B, whom you have now either identified as True or identified as False, and ask Question 3: Does da mean yes iff A is Random?

Suppose B is True. Then if you get the answer da, then A is Random, and therefore A is Random, B is True, C is False, and you are done; but if you get the answer ja, then A is not Random, so A is False, B is true, C is Random, and you are again done.

Suppose B is False. Then if you get the answer da, then since B speaks falsely, A is not Random, and therefore A is True, B is False, C is Random, and you are done; but if we get ja, then A is Random, and thus B is False, and C is True, and
you are again done. FINIS.

Nic · 04-01-2002, 03:33 PM

Quote:

Originally posted by Bill Snedden:
<strong>Okay, here's the solution I worked out. I can't claim to have come to it 100% on my own (I had a couple of hints), but it does seem to work.

The "trick", if you will, is to word the questions such that their truth value is either known to you in advance or so constructed that the answers will assist you in eliminating false possibilities. The first step is to attempt to "weed out" the randomly answering god. I started by making a working assumption that A was either the truthful or the false speaking god and addressed my first question to A.

Question one: Does "ja" mean "yes" if you are always truthful AND god B always replies randomly?

The question has three parts, all of which work together to ensure that the truth value of the last part is determined by the answer.

Here are the possibilities based on the assumption that A is always truthful:

1) "ja" means "yes", A is truthful, and B is random - JA

2) "ja" means "yes", A is truthful, and B is not random - DA

3) "ja" means "no", A is truthful, and B is random - JA

4) "ja" means "no", A is truthful, and B is not random - DA

Obviously, the answers are reversed (da for ja) if A is assumed to be false.

So, regardless of the actual meaning of "ja" and "da", a "ja" answer tells us that B is the random god and that A & C are the true/false gods and a "da" answer tells us that C must be the random god and that A & B are the true/false gods.

Of course, this is going on the beginning assumption that A is either true or false. However, if A is in fact the random god, we know that neither B nor C can be. So, we can still proceed based on a couple more assumptions. If A is random and answers "ja", we'll make a working assumption that C is not random. If A is random and answers "da", we'll make the assumption that B is not random. (These assumptions are based on the possibilities table, above.)

So, if we get a "ja" response, we can assume that C is either true or false and if we get a "da" response, we can assume that B is either true or false.

Okay, now on to question two. I asked god B, but you can also ask god C.

Question two: Does "ja" mean "yes" if 2+2=4?

Obviously the truth value of 2+2=4 is already known, so the answer will tell us if B is true or false and it will also give us the meaning of "ja" and "da"!

A "ja" response tells us that B is the truthful god and a "da" response tells us that B is the false god.

Now that we have determined the status of one of the gods, and the meaning of "ja" and "da", we can use that knowledge to phrase a question that will allow us to determine the status of the other two.

Question three: If B is the false god, ask, Is A always truthful?. A "ja" response" indicates that A is, in fact random and so the order is A-random, B-false, C-true. A "da" response indicates A-truthful, B-false, C-random.

If B is the true god, ask, is A always false?. Again, a "ja" response gives us A-false, B-true, C-random and a "da" response yields A-random, B-true, C-false.

Ta-da!

At least, I think so. I can't work out any scenarios where this strategy doesn't seem to work.

How did I do, Kachana?

Bill

[ March 25, 2002: Message edited by: Bill Snedden ]</strong>

Nic · 04-01-2002, 03:40 PM

Having only just joined you I may be missing a point, but surely to assume that all (or any) putative gods use a mathematical system in which 2+2 =4 can only be seen as a leap of faith?

The Admiral · 04-01-2002, 03:49 PM

I don't think that that is the hardest logic puzzle ever. Not that I can solve it. I doubt that anyone can.

The hardest logic puzzle ever is "why is there something rather than nothing?"

The Admiral

The Admiral · 04-01-2002, 03:55 PM

I don't know what happened to mp post, but here it is again.
I don't think that that is the hardest logic puzzle ever. Not that I can solve it.

The hardest logic puzzle is "why is there something rather than nothing?"

The Admiral

The Admiral · 04-01-2002, 04:00 PM

Why is there something rather than nothing?
Or is there something?

The Admiral · 04-01-2002, 04:01 PM

test

The Admiral · 04-01-2002, 04:06 PM

Ah my friends and Oh my foes; my humble apologies for not noticing that there were two pages.

The Admiral

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04-01-2002, 03:40 PM	#34
Nic New Member Join Date: Mar 2002 Location: UK Posts: 2	Having only just joined you I may be missing a point, but surely to assume that all (or any) putative gods use a mathematical system in which 2+2 =4 can only be seen as a leap of faith?

04-01-2002, 03:49 PM	#35
The Admiral Senior Member Join Date: Sep 2000 Location: Racine, Wi. USA Posts: 768	I don't think that that is the hardest logic puzzle ever. Not that I can solve it. I doubt that anyone can. The hardest logic puzzle ever is "why is there something rather than nothing?" The Admiral

04-01-2002, 03:55 PM	#36
The Admiral Senior Member Join Date: Sep 2000 Location: Racine, Wi. USA Posts: 768	I don't know what happened to mp post, but here it is again. I don't think that that is the hardest logic puzzle ever. Not that I can solve it. The hardest logic puzzle is "why is there something rather than nothing?" The Admiral

04-01-2002, 04:00 PM	#37
The Admiral Senior Member Join Date: Sep 2000 Location: Racine, Wi. USA Posts: 768	Why is there something rather than nothing? Or is there something?

04-01-2002, 04:01 PM	#38
The Admiral Senior Member Join Date: Sep 2000 Location: Racine, Wi. USA Posts: 768	test

04-01-2002, 04:06 PM	#39
The Admiral Senior Member Join Date: Sep 2000 Location: Racine, Wi. USA Posts: 768	Ah my friends and Oh my foes; my humble apologies for not noticing that there were two pages. The Admiral

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