Today's Meeting
We started off today's meeting with a few exercises. Jumping Jacks, push-ups, running in place... Just kidding, that's obviously a lie. Or is it? If you're officially confused, you now understand how we felt when we took a journey to the island of Knights and Knaves. (No, this is not an elaborate drug innuendo.) Wes brought a few logic puzzles with him. One of which is called (as you might have guessed): On the Island of Knights and Knaves. It goes like this. (The following puzzles are by Raymond Smullyan.)
On the island of Knights and Knaves, every inhabitant is either a knight or a knave. Knights always tell the truth. Knaves never tell the truth; any sentence uttered by a knave is false. A stranger came to the island and encountered three inhabitants, A, B, and C. He asked A, "Are you a knight, or a knave?" A mumbled an answer that the stranger could not understand. The stranger then asked B, "What did he say?" B replied, "A said that there is exactly one knight among us." Then C burst out, "Don't believe B, he is lying!" What are B and C?
Using the aforementioned knowledge of the island of Knights and Knaves, here is a second puzzle:
One day I went to the island of knights and knaves and encountered an inhabitant who said, "Either I am a knave or else two plus two equals five." What should you conclude?
I'm not going to post the answer. That would be too easy. If you think you've got it figured out, leave a comment with the answer. Feel free to have an open discussion about it.
After we felt pretty good about our solutions to these problems, we moved on to Zeno's Paradox. That led us into a discussion about infinity, mathematical concepts, etc.
Next Meeting (October 4th)
Next time we'll be watching the film Waking Life. I haven't been updated on the location, as of yet, but the meeting will be at 8:00pm. As soon as we've got a room locked down, I'll let you know which one it is. You can see the trailer for Waking Life below.
And now... *drumroll*...
Bertrand Russell, on Smoking.
Hopefully that wasn't too anticlimactic. I tend to find these bizarre little stories about philosopher's lives interesting (and funny).
So, to wrap it up, today we solved puzzles and talked about infinity. Next week's meeting is at 8:00pm and we're watching an interesting movie on philosophy and life. You will be there or you won't. Either way, I'm right.
B is a knave. C is a knight.
ReplyDeleteIf B is telling the truth (that A said that there is exactly one knight among us), then B must be a knight. In this case, A cannot be telling the truth because B just truthfully confirmed A's statement. If A was telling the truth, then that would be two truths and two knights, and so A's statement would be false. A would be a knave. There is not exactly one knight among them.
However, C is claiming that B is lying. According to the above assumption, B is not. C must be lying and is therefore a knave.
The problem is that C cannot be a knave because that would prove A's statement true. There is exactly one knight among them.
A's statement being true makes A a knight, but according to the first paragraph, that is impossible (there can't be two knights according to A). So B is a knave. And if B is a knave and is always lying, C must be telling the truth. C is a knight.
Now if we forget everything I just said and assume that B is lying (so we can forget about anything A might have said), then C truthfully called B a liar. C is a knight. B is a knave.
If you assume C is telling the truth, then you get the same answer. If you assume C is lying (so B would be telling the truth), you can see by the first explanation that that is impossible.
I hope that's right!
The inhabitant is a knave.
ReplyDeleteIf the inhabitant is lying about the correlation between his/her being a knave and 2+2=5, that would mean that both parts of the statement could be true and both could be false. He/she not being a knave would not make 2+2=5.
If the inhabitant it telling the truth about the correlation between his/her being a knave and 2+2=5, then either he/she is a knave, or 2+2=5. But we just said that he/she is telling the truth. He/she cannot be a knave if we can accept this correlation as true. The first part of the sentence is then false under this assumption.
2+2 does not = 5, so the second part of the sentence is false as well.
Because this correlation cannot be based on the rules of this really confusing island, the speaker cannot be telling the truth and is a knave.
...right?