Jeff_Ray...
Level: Smitemaster

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People can make sentences here.

Like:

The after-next sentence is true
The last sentence is false
The last sentence is true.

I start.

The next sentence is false.
The last sentence is true.

____________________________
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MeckMeck GRE
Level: Smitemaster
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Jeff_Ray... wrote:
People can make sentences here.

Like:

The after-next sentence is true
The last sentence is false
The last sentence is true.

I start.

The next sentence is false.
The last sentence is true.

Every sentence is right expect this one.

Nillo
Level: Smitemaster

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MeckMeck GRE's sentence was false.

____________________________
“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”

Alneyan
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Either this sentence is right, and Nillo is a Solarian in disguise, or the ante-penultian sentence is wrong, and the world is a cleverly designed fabrication made by the Elder Ones.

The Stew Boy
Level: Master Delver
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I am literally not myself, therefore this sentence is literally not itself.

coppro
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The statement above the statment directly to the left of the statement two below the statement above's left-hand side is false.

Darkmatt
Level: Delver
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I am not a true sentence, but if I'm not a true sentence, then this post can't be true.

The Stew Boy
Level: Master Delver
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Both of these statements are false.
Both of these statements are true.

MartianInvader
Level: Master Delver
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If this sentence is true or this sentence is false, then this sentence is true and this sentence is false.

If either this sentence is true, the previous sentence true, or the next sentence is false, then the previous sentence is true.

If I absolutely love apples, then I absolutely love bannanas.

Assuming all three of the previous statements are either false or true, if anyone knows how I feel about apples and bannanas, they will post indicating so.


____________________________
Yes, I very rarely post. But I DO keep coming back to check the forum.

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[Last edited by MartianInvader at 12-13-2005 03:18 AM]

Nillo
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MartianInvader wrote:
If this sentence is true or this sentence is false, then this sentence is true and this sentence is false.

If either this sentence is true, the previous sentence true, or the next sentence is false, then the previous sentence is true.

If I absolutely love apples, then I absolutely love bannanas.

Assuming all three of the previous statements are either false or true, if anyone knows how I feel about apples and bannanas, they will post indicating so.

I'll try. (The following sentences aren't in the game)

The first sentence can't be true because it contradicts itself. If the second sentence was true, the first sentence would also be true, which is impossible. The third one gives no clues at all regarding which sentences are true. This means that the first two sentences are false and the third one is of unknown status.

____________________________
“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”

MartianInvader
Level: Master Delver
Rank Points: 126
Registered: 01-30-2004
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Nillo wrote:

MartianInvader wrote:
If this sentence is true or this sentence is false, then this sentence is true and this sentence is false.

If either this sentence is true, the previous sentence true, or the next sentence is false, then the previous sentence is true.

If I absolutely love apples, then I absolutely love bannanas.

Assuming all three of the previous statements are either false or true, if anyone knows how I feel about apples and bannanas, they will post indicating so.

I'll try. (The following sentences aren't in the game)

The first sentence can't be true because it contradicts itself. If the second sentence was true, the first sentence would also be true, which is impossible. The third one gives no clues at all regarding which sentences are true. This means that the first two sentences are false and the third one is of unknown status.

Heh, you're on the right track. Here's a tip: A statement of the form "If A then B" is true if A and B are true or A is false, and is false if A is true and B is false (hope that made sense). Using this, try analyzing that second sentence a little more closely.

____________________________
Yes, I very rarely post. But I DO keep coming back to check the forum.

Nillo
Level: Smitemaster

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MartianInvader wrote:
Heh, you're on the right track. Here's a tip: A statement of the form "If A then B" is true if A and B are true or A is false, and is false if A is true and B is false (hope that made sense). Using this, try analyzing that second sentence a little more closely.

"If A then B" statements are true if A and B are true or A is false? I am terribly sorry, but I didn't understand one bit of that. I'll summarize how I interpret the second sentence:

If either this sentence is true, the previous sentence true, or the next sentence is false, then the previous sentence is true.

IF First sentence is true
OR Second sentence is true
OR Third sentence is false

THEN First sentence is true.

If we assume that the second sentence is true, the second condition described would be met, and first sentence would be true. And the first sentence contradicts itself if it's true so it can't be true. Therefore the second sentence is false. But if the second sentence is false, it doesn't give me any helpful information, because of the OR conditions. It basically tells me this:

IF First sentence is true
OR Second sentence is true
OR Third sentence is false

THEN First sentence isn't necessarily true.

Please tell me I'm wrong somewhere, because I'm getting headaches trying to get this to make sense.

____________________________
“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”

The Stew Boy
Level: Master Delver
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Registered: 05-10-2005
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At least one of these sentences is incorrect.
At least two of these sentences are incorrect.
At least three of these sentences are incorrect.
All four of these sentences are incorrect.

Which ones are correct?

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[Last edited by The Stew Boy at 12-14-2005 05:32 AM]

MartianInvader
Level: Master Delver
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The Stew Boy wrote:
At least one of these sentences is incorrect.
At least two of these sentences are incorrect.
At least three of these sentences are incorrect.
All four of these sentences are incorrect.

Which ones are correct?

Your first and second sentences are correct, the second and third are incorrect (for a total of two correct and two incorrect sentences).

In my puzzle, I'm using the version of "If A then B" that most logicians use, which is as follows:
-When A and B are true, "If A then B" is true ("If Beethro's brave then he smites roaches" is a true statement).
-When A is false and B is true, "If A then B" is true ("If Beethro is a goblin, then Beethro smites roaches" is still a true statement since Beethro smites roaches regardless of the fact that he's not a goblin).
-When A is false and B is false, "If A then B" is true ("If Beethro's a coward, then I'm Robert DeNiro" is a vacuously true statement since Beethro isn't a coward).
-When A is true and B is false, "If A then B" is false ("If Beethro smites roaches, then Beethro is a coward" is a false statement).
In other words, "If A then B" is equivalent to "Either A is false or B is true"

Here's a basic hint for solving the puzzle:


Here's a version of the same statements without using the "ifs", which makes it a lot easier:




____________________________
Yes, I very rarely post. But I DO keep coming back to check the forum.

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[Last edited by MartianInvader at 12-14-2005 06:36 AM]

TripleM
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Nillo wrote
Please tell me I'm wrong somewhere, because I'm getting headaches trying to get this to make sense.

Saying "If A then B" is false does *not* mean "If A then not necessarily B". It means that A is true and B is false. (If A was false, then "If A then anything" is always true.)

So to finish off your logic, since the first and second statements must be false, and we know that 'either the second sentence is true, the first sentence true, or the third sentence is false', in other words the third sentence is false.

So MartianInvader absolutely loves apples, but doesn't absolutely love bananas.

Nillo
Level: Smitemaster

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TripleM wrote:
Saying "If A then B" is false does *not* mean "If A then not necessarily B". It means that A is true and B is false. (If A was false, then "If A then anything" is always true.)

I disagree - if an "If A then B" statement is false, it doesn't prove anything. When it's true it tells me that B is always true if A is true. When it's false it tells me that B is NOT always true if A is true. I will use an example provided by MartianInvader:

If Beethro is a goblin, then Beethro smites roaches

Assuming that a goblin cannot smite roaches, this statement must be false, since Beethro doesn't smite roaches if he's a goblin.

____________________________
“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”

TripleM
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I'm afraid you're arguing against mathematical logic. If Beethro is a goblin, then 1+1=100. If 1+1=100, then my names Bob. As long as what you are assuming is false, you can prove anything.

Nillo
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What I meant was that I don't know if goblins can smite roaches or not, but for the purposes of that example, I assumed that they couldn't. I can use a different example if you don't think that's okay.

Let's say that I'm planning to buy a game. It costs an irrelevant amount of dollars.
If it had costed 2$ less, then I would spend 2$ less if I bought it. It doesn't actually cost 2$ less, but that doesn't mean the previous statement is false.

____________________________
“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”

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[Last edited by Nillo at 12-14-2005 08:43 AM]

TripleM
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OK, but how is that relevant to the above? There we're saying, if the statement 'If A then B' is false, then A is true and B is false, not the other way around or anything.

krammer
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Logical statements are not quite used the way you would use standard English. I'll give some examples of "If A then B", or indeed, "A implies B" which means the same.

Case 1: Both true.
"If the sky is blue, 2+2=4". True, even though the colour of the sky has no bearing on the value of 2+2. Because the sky is always blue, and 2+2 is always 4.

Case 2: A true and B false.
"If the sky is blue, 2+2=5". False (obviously). The sky is always blue, but 2 and 2 is never 5.

Case 3: A is false.
"If the sky is green, 2+2=5". TRUE. Because the sky is never green, so the question of whether 2+2 does equal 5 is irrelevant. We are making a statement about what happens when the sky is green, which never happens, so we can say this statement is true without invalidating anything.

____________________________
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"Oook!"

Nillo
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"If the sky is green, 2+2=5". TRUE. Because the sky is never green, so the question of whether 2+2 does equal 5 is irrelevant. We are making a statement about what happens when the sky is green, which never happens, so we can say this statement is true without invalidating anything.

Ah, I get it now. Thank you.

____________________________
“Folks say that if you listen real close at the height of the full moon, when the wind is blowin' off Nantucket Sound from the nor' east and the dogs are howlin' for no earthly reason, you can hear the awful screams of the crew of the 'Ellie May,' a sturdy whaler Captained by John McTavish; for it was on just such a night when the rum was flowin' and, Davey Jones be damned, big John brought his men on deck for the first of several screaming contests.”

MartianInvader
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TripleM wrote:

So to finish off your logic, since the first and second statements must be false, and we know that 'either the second sentence is true, the first sentence true, or the third sentence is false', in other words the third sentence is false.

So MartianInvader absolutely loves apples, but doesn't absolutely love bananas.

Correct, TripleM! Have a point. Sorry if the whole "if" statement thing got confusing. I'll try to stick to "and" and "or" statements from now on.

One other thing, Nillo, that might add to your understanding: You were interpreting my sentence "If Beethro is a goblin then he smites roaches" as "If Beethro were a goblin then he would smite roaches. That's dealing with various possibilities and is a much more complicated sentence. Since I just said "If Beethro is a goblin", it's a lot easier to see whether the sentence is true or not.



____________________________
Yes, I very rarely post. But I DO keep coming back to check the forum.

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[Last edited by MartianInvader at 12-14-2005 05:14 PM]

stigant
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This gives me an interesting idea for a card game:

Each player will be dealt <x> cards. Each card will have words on it like:
if
then
and
or
this
sentence
is
true
false
the next
the previous
the last
the first
1
2
3
4 (etc)

The object is to get rid of all your cards.

On your turn, you must form a sentence with cards from your hand. The sentence must be a complete sentence asserting truth/fallacy about at least one sentence on the board. Further, all sentences on the board must be logically consistent. The first sentence played is sentence 1, the second is sentence 2 etc (this is where the numbered cards come in).

If you can't play a complete sentence, then you can change up to (say) 3 of the existing sentences using cards in your hand (switch a card in your hand with a card on the board) For example, you could switch a true into a false, or change a number to a different number etc. After all your switching is done, all the sentences on the board must be consistent again.

If you can't do any of that, then you could draw another card from the deck.

Play goes around the circle. If someone plays a sentence (or changes a sentence) so that the board is no longer consistent, and someone calls them on it, then the offending player must take his cards back into his hand, and the player who caught him should get some kind of a bonus (perhaps discarding one of his cards, or perhaps the option of taking one of the cards that the offending player played).

There should be a few special cards like "remove a sentence of your choice" or "swap the positions of two sentences" etc.

If play goes around the circle without any changes then the board is cleared and play resumes.

What do you guys think? Too complicated or tedious? It seems like there would need to be some sort of automation to check logical validity quickly (this is an np-hard problem, I think).

____________________________
Progress Quest Progress

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[Last edited by stigant at 12-14-2005 05:22 PM]

The Stew Boy
Level: Master Delver
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For that to work each player should have the following amounts of the cards:
if - 3
then - 3
and - 1
or - 1
this - 6
sentence - 10
is - 10
true - 5
false - 5
the next - 3
the previous - 2
the last - 2
the first - 3
1 - 1
2 - 1
3 - 1
4 - 1
or something of the sort. It can't be random.

stigant
Level: Smitemaster

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Yeah, I was thinking that some cards (like 'is') should be freely available rather than having to have one in your hand. But I think cards like 'previous' 'next' 'last' '1' '2' etc should be limited.

____________________________
Progress Quest Progress

Swivel
Level: Master Delver

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May I suggest the addition of the word "This" (This sentence is true if sentence 3 is false? "Is/Are" cards would also be good (not two seperate cards.) "Not" is a word that should definitely be added. I would also suggest nouns and adjectives that either describe or don't describe them, like "the sky" and "blue" (the sky is blue) and "sheep" and "black" (sheep are not black.)

Switching two sentences would mean that all mentions of those sentences would also have to be switched.

Scrabble involves forming words with letters; it is a speller's game. However, this game (forming coherent sentences with words) is more of a game for a mathematician or logician. It could help people with converse, inverse, and contrapositive. If an "if and only if" card were introduced, that would be interesting.

Overall, it's a great game! I might use index cards and play it by myself (assuming that I could play several players at once, which I could try to do.)

This is minorly off-topic, but logic is rather interesting.

Here are fun logical fallacies:
I. Why Erik Should Give Us All Rank Points
We know that if A implies B, then the opposite of B implies the opposite of A.
Suppose that:
1. If DROD wins the GameTunnel contest, then Erik will hand out rank points to all.
2. From this we can conclude that:
If Erik doesn't hand out rank points, then DROD won't win the GameTunnel contest.
3. Give us Rank Points, Erik!

II. Why Mike Rimer is not working on TCB
1. Mike Rimer claims that he's working on DROD:TCB.
2. But Mike Rimer has Gandalf as an avatar.
3. I have nothing to hide as I clearly distinguish who I am in my avatar (it shows my love for platypi). But can Mike Rimer say the same thing?
4. Mike Rimer is trying to hide somthing.
5. Mike Rimer cannot be trusted.
6. Thus, Mike Rimer is not working on DROD:TCB.

III. Why Roaches are Really Kind Monsters
1. The Koran says that roachs are kind. Somewhere.
2. The Koran is a reliable source.
3. Thus, roaches are really kind monsters

IV. Why the 'Neather has Been Seen with Elvis Recently
1. Someone or another saw the 'Neather with Elvis recently.

V. Why Smitemastery is Wrong
1. Slashing people with a sword is wrong.
2. Roaches are people too. Can't you hear them crying? Because they have no mommy. They've been left there to die. They've been left there to be mercilessly slaughtered. Feel, my friends, for the poor roaches.
3. Thus, smitemastery is wrong.

VI. Why Seeding is Impossible
1. When Beethro has an invisibility potion, monsters that can "seed" don't.
2. When Beethro is not in a room, it is the same thing as him having an invisibility potion.
3. Thus, when Beethro is gone, seeding cannot occur.
4. Beethro is a smiter.
5. Thus, when smiters is gone, seeding cannot occur.


____________________________
"Write a wise saying and your name will live forever."
-Anonymous

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[Last edited by Swivel at 12-15-2005 12:55 AM]