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Author Topic: Random Stuff Part III  (Read 650164 times)

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ThetaSigma12

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Re: Random Stuff Part III
« Reply #2900 on: October 14, 2017, 07:31:48 am »
0

Wow, this is confusing. You can say "some things I say are true" and be lying, for example if the only things you say are that and "1=2".
How does that work with the negation of "some things i say are true" being the paradoxon "everything I say is false"?
Well in your example the statement is true I think. If you only say that "Some things I say are true" and "1=2" (waiting for the edgecasers on that one) then "Some things I say are true" can be true, if it refers to itself. It's the equivalent of saying "This statement is true."
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Witherweaver

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Re: Random Stuff Part III
« Reply #2901 on: October 14, 2017, 07:58:51 am »
+1

There is a class of phrases that can not be assigned a truth value.  Basically, metalanguage falls into this.

So in generality, there isn't a true/false dichotomy but rather a true/false/NA trichitomy.

I suppose that's why reducto ad absurdum does not work. To show false cannot he true is not the same as showing true.
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ThetaSigma12

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Re: Random Stuff Part III
« Reply #2902 on: October 14, 2017, 08:10:38 am »
0

There is a class of phrases that can not be assigned a truth value.  Basically, metalanguage falls into this.

So in generality, there isn't a true/false dichotomy but rather a true/false/NA trichitomy.

I suppose that's why reducto ad absurdum does not work. To show false cannot he true is not the same as showing true.
Where does the law of non-existent middle come into play then? Are you saying paradoxes like "Everything I say is false" fall into the same category as "What's the weather like?" and "Go put on your shoes!" or other sentences with no truth value? That wasn't really the way I learned it but I suppose it makes sense.

Regarding Reductio Ad Absurdum, I think it doesn't apply because "Some things I say are true" isn't an argument, it's just a premise.
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pacovf

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Re: Random Stuff Part III
« Reply #2903 on: October 14, 2017, 09:52:40 am »
+2

There's a puzzle I enjoy that exposes the problem, I think.

Assume there's two chests in front of you. One has treasure inside, the other is trapped. In front of the one on the left, there's a sign that says "This treasure is trapped"; in front of the one on the right, there's a sign that says "Exactly one of these signs is truthful". Which chest do you open?

Solution:

If the sign on the right is truthful, then the one on the left has to be false, hence the treasure is on the left. But if the sign on the right is false,
then the one on the left still has to be false, so the treasure is on the left still. So you should open the chest on the left.


You follow the logic and decide which chest to open. Yet, just before you open either:

I come in and switch both signs with each other, so that the one that used to be on the left is now on the right, and viceversa.

What do you do now? Which chest do you open?

This shows that you were starting the problem with a wrong assumption, which is that all statements are either True or False, which logically leads to spurious results, as all wrong assumptions are wont to do.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2904 on: October 14, 2017, 09:56:02 am »
0

There is a class of phrases that can not be assigned a truth value.  Basically, metalanguage falls into this.

So in generality, there isn't a true/false dichotomy but rather a true/false/NA trichitomy.

I suppose that's why reducto ad absurdum does not work. To show false cannot he true is not the same as showing true.
Where does the law of non-existent middle come into play then? Are you saying paradoxes like "Everything I say is false" fall into the same category as "What's the weather like?" and "Go put on your shoes!" or other sentences with no truth value? That wasn't really the way I learned it but I suppose it makes sense.

Regarding Reductio Ad Absurdum, I think it doesn't apply because "Some things I say are true" isn't an argument, it's just a premise.

Hmm.. I suppose I was only referring to assertions, that you could otherwise evaluate as true or false, but it's actually nonsensical to do so.
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silverspawn

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Re: Random Stuff Part III
« Reply #2905 on: October 14, 2017, 04:03:52 pm »
+1

There's a puzzle I enjoy that exposes the problem, I think.

Assume there's two chests in front of you. One has treasure inside, the other is trapped. In front of the one on the left, there's a sign that says "This treasure is trapped"; in front of the one on the right, there's a sign that says "Exactly one of these signs is truthful". Which chest do you open?

Solution:

If the sign on the right is truthful, then the one on the left has to be false, hence the treasure is on the left. But if the sign on the right is false,
then the one on the left still has to be false, so the treasure is on the left still. So you should open the chest on the left.


You follow the logic and decide which chest to open. Yet, just before you open either:

I come in and switch both signs with each other, so that the one that used to be on the left is now on the right, and viceversa.

What do you do now? Which chest do you open?

This shows that you were starting the problem with a wrong assumption, which is that all statements are either True or False, which logically leads to spurious results, as all wrong assumptions are wont to do.

That puzzle doesn't show anything. You have two signs which say things, then when you switch them they say different things. The old signs have truth values and the new signs may have different truth values because they are different statements.

Every statement is either true or false not not distinctly defined. Paradoxes are either things which are confusing or highly unintuitive or so mething but can actually be resolved, or they are about non-distinct definitions.

silverspawn

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Re: Random Stuff Part III
« Reply #2906 on: October 14, 2017, 04:05:45 pm »
+1

"Everything I say is false" is not well defined because it references itself. You can do countless stuff like that.

Kirian

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Re: Random Stuff Part III
« Reply #2907 on: October 14, 2017, 05:07:03 pm »
0

"1=2" (waiting for the edgecasers on that one)

1.49999 and 1.50001 round to 1 and 2 respectively if you're only using 1 significant digit, but are much closer to each other.  That's about the best edge case I can come up with.

This is the same as "2 + 2 = 5, for sufficiently large values of 2," where 2.3 is sufficiently large.
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pacovf

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Re: Random Stuff Part III
« Reply #2908 on: October 14, 2017, 05:07:45 pm »
0

I am confused, you both say that a statement can only be either true or false, then you say that a statement can also not be properly defined. In the second case, you are agreeing with me.
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scott_pilgrim

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Re: Random Stuff Part III
« Reply #2909 on: October 14, 2017, 05:14:47 pm »
+2

"1=2" (waiting for the edgecasers on that one)

1.49999 and 1.50001 round to 1 and 2 respectively if you're only using 1 significant digit, but are much closer to each other.  That's about the best edge case I can come up with.

Well, 1=2 if you're doing mod 1 arithmetic.
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Re: Random Stuff Part III
« Reply #2910 on: October 14, 2017, 05:44:18 pm »
0

I am confused, you both say that a statement can only be either true or false, then you say that a statement can also not be properly defined. In the second case, you are agreeing with me.

Well, I'm saying statements can either be true or false or not properly defined (it's obvious that the last category exists – if I say "smoking is good" then that's not properly defined because 'good' doesn't have a distinct meaning). In other words, the only way a statement can be neither true nor false is if it doesn't have a real meaning. I'm not sure if that is disagreeing with you, I got the sense that it's disagreeing with WW at least.

On a separate note, I also wouldn't count "exactly one of these signs is true" as a properly defined statement because it also references itself. By doing that you can always construct paradoxes, like having a sentence A which says "sentence B is true" and a sentence B which says "sentence A is false"; any assignment of truth values is inconsistent. But there's no magic there, it's just the two formulas

A ⇔ B
B ⇔ ¬A

... which contradict.

But that's not the point I was making – the point I was making was that even if the signs had proper statements, there is nothing shown by the story/puzzle, because the statements change when the signs trade positions, and of course different statements mean different things.

pacovf

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Re: Random Stuff Part III
« Reply #2911 on: October 15, 2017, 09:34:11 am »
0

Try asking the first part of the puzzle to anybody that likes logic puzzles. You will see that they will follow the logic in the first puzzle and tell you where the treasure is, because they are implicitly assuming that all statements are either true or false. Changing the signs positions obviously change the nature of the statements, but they will realize that if they try to follow the same logic again, they would be forced to conclude that the treasure is in the other chest now, which obviously makes no sense! And they will have some trouble figuring out what the mistake in their reasoning was, which is that statements can be neither true nor false (improperly defined, as you call them). That’s what the puzzle is attempting to illustrate.
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Awaclus

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Re: Random Stuff Part III
« Reply #2912 on: October 15, 2017, 09:44:28 am »
+1

Try asking the first part of the puzzle to anybody that likes logic puzzles. You will see that they will follow the logic in the first puzzle and tell you where the treasure is, because they are implicitly assuming that all statements are either true or false. Changing the signs positions obviously change the nature of the statements, but they will realize that if they try to follow the same logic again, they would be forced to conclude that the treasure is in the other chest now, which obviously makes no sense! And they will have some trouble figuring out what the mistake in their reasoning was, which is that statements can be neither true nor false (improperly defined, as you call them). That’s what the puzzle is attempting to illustrate.

I have another puzzle:

Assume there's two chests in front of you. One has treasure inside, the other is trapped. In front of the one on the left, there's a sign that says "This treasure is trapped"; in front of the one on the right, there's a sign that says "This treasure is not trapped". Which chest do you open?

Solution:

you open the one on the right because it's not trapped

You follow the logic and decide which chest to open. Yet, just before you open either:

I come in and switch both signs with each other, so that the one that used to be on the left is now on the right, and viceversa.

What do you do now? Which chest do you open?
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pacovf

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Re: Random Stuff Part III
« Reply #2913 on: October 15, 2017, 09:52:36 am »
0

In your case, only making the assumption that statements have to be either true or false, I can’t make any conclusion about where the treasure is in either case, so there is no problem.
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silverspawn

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Re: Random Stuff Part III
« Reply #2914 on: October 15, 2017, 11:14:51 am »
0

Try asking the first part of the puzzle to anybody that likes logic puzzles. You will see that they will follow the logic in the first puzzle and tell you where the treasure is, because they are implicitly assuming that all statements are either true or false. Changing the signs positions obviously change the nature of the statements, but they will realize that if they try to follow the same logic again, they would be forced to conclude that the treasure is in the other chest now, which obviously makes no sense! And they will have some trouble figuring out what the mistake in their reasoning was, which is that statements can be neither true nor false (improperly defined, as you call them). That’s what the puzzle is attempting to illustrate.

It just seems the same to as the much simpler case of 2 chests, 1 sign saying "treasure here" which you then move right before the corresponding chest is opened.

pacovf

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Re: Random Stuff Part III
« Reply #2915 on: October 15, 2017, 11:18:52 am »
+1

It is not. “Treasure here” could be either true or false, so you can’t get any information out of it. In the scenario I describe, if you assume that statements have to be either true or false, then the treasure is necessarily on the left.

I will remember to change the delivery of this puzzle next time.
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silverspawn

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Re: Random Stuff Part III
« Reply #2916 on: October 15, 2017, 11:28:36 am »
+2

Oh now I get it. Your point is that because both assigning "true" and assigning "false" to the signs leads to the same result, so therefore the treasure MUST be left. I was wondering why you'd have to believe any of the signs in the first place.

Ok. In that case my original reply misses the point because misunderstood what you were trying to say.

The actual problem is what I said about self-referencing: "exactly one of us is truthful" depends on itself. It afaik not possible to replicate that effect without having a self-referencing statement.

ConMan

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Re: Random Stuff Part III
« Reply #2917 on: October 15, 2017, 07:30:38 pm »
0

Oh now I get it. Your point is that because both assigning "true" and assigning "false" to the signs leads to the same result, so therefore the treasure MUST be left. I was wondering why you'd have to believe any of the signs in the first place.

Ok. In that case my original reply misses the point because misunderstood what you were trying to say.

The actual problem is what I said about self-referencing: "exactly one of us is truthful" depends on itself. It afaik not possible to replicate that effect without having a self-referencing statement.
Not true. It's difficult, but possible. For example:

"yields negation when preceded by its quotation" yields negation when preceded by its quotation.

Also, in more mathematical terms you can get into stuff like Godel numbering and things which kind of side-step the self-referential problem.
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Kirian

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Re: Random Stuff Part III
« Reply #2918 on: October 15, 2017, 09:34:54 pm »
+3

Try asking the first part of the puzzle to anybody that likes logic puzzles. You will see that they will follow the logic in the first puzzle and tell you where the treasure is, because they are implicitly assuming that all statements are either true or false. Changing the signs positions obviously change the nature of the statements, but they will realize that if they try to follow the same logic again, they would be forced to conclude that the treasure is in the other chest now, which obviously makes no sense! And they will have some trouble figuring out what the mistake in their reasoning was, which is that statements can be neither true nor false (improperly defined, as you call them). That’s what the puzzle is attempting to illustrate.

I have another puzzle:

Assume there's two chests in front of you. One has treasure inside, the other is trapped. In front of the one on the left, there's a sign that says "This treasure is trapped"; in front of the one on the right, there's a sign that says "This treasure is not trapped". Which chest do you open?

Solution:

you open the one on the right because it's not trapped

You follow the logic and decide which chest to open. Yet, just before you open either:

I come in and switch both signs with each other, so that the one that used to be on the left is now on the right, and viceversa.

What do you do now? Which chest do you open?

"They were both poisoned.  I've spent the last few years building up an immunity to iocaine."
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silverspawn

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Re: Random Stuff Part III
« Reply #2919 on: October 16, 2017, 03:55:09 am »
0

Oh now I get it. Your point is that because both assigning "true" and assigning "false" to the signs leads to the same result, so therefore the treasure MUST be left. I was wondering why you'd have to believe any of the signs in the first place.

Ok. In that case my original reply misses the point because misunderstood what you were trying to say.

The actual problem is what I said about self-referencing: "exactly one of us is truthful" depends on itself. It afaik not possible to replicate that effect without having a self-referencing statement.
Not true. It's difficult, but possible. For example:
"yields negation when preceded by its quotation" yields negation when preceded by its quotation.

You'll have to explain that. Negation of what?

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Re: Random Stuff Part III
« Reply #2920 on: October 16, 2017, 05:12:17 am »
+1

Oh now I get it. Your point is that because both assigning "true" and assigning "false" to the signs leads to the same result, so therefore the treasure MUST be left. I was wondering why you'd have to believe any of the signs in the first place.

Ok. In that case my original reply misses the point because misunderstood what you were trying to say.

The actual problem is what I said about self-referencing: "exactly one of us is truthful" depends on itself. It afaik not possible to replicate that effect without having a self-referencing statement.
Not true. It's difficult, but possible. For example:
"yields negation when preceded by its quotation" yields negation when preceded by its quotation.

You'll have to explain that. Negation of what?

Negation of the phrase "yields negation when preceded by its quotation".

Suppose ""yields negation when preceded by its quotation" yields negation when preceded by its quotation" = false. Let's call that entire statement A. If we took the phrase "yields negation when preceded by its quotation", and added its quotation in front of it, we get A, so it's false. But it's also true, because we did indeed get a negation when we preceded the phrase with its own quotation.

By a similar argument, if A is true, then A should be false, because we're supposed to get a negation.
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Re: Random Stuff Part III
« Reply #2921 on: October 16, 2017, 11:56:49 am »
0

The false assumption is that I must open a treasure. Also, that the silly signs are the only means I have to detect a trap (if there even is one) or if there is even any treasure to be had. I can easily elect to not open either chest. I can employ other means of trap/treasure detection. I'd probably just walk away, though. Where does that leave your navel gazing ramblings about logic?
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Re: Random Stuff Part III
« Reply #2922 on: October 16, 2017, 12:07:01 pm »
+4

I wrote a trap in D&D that used the player assumptions against them.

I cannot remember the exact wording of the puzzle, but it basically asked the reader what color was the bear. Options were brown, grey, or black. There were three buttons of those colors.

The thing was that if you pressed the correct answer, that triggered the trap. After all, who is going to guard the entry to his house with an easily solved riddle? Those who examined the buttons saw little notches that were a reminder to the owner of which order to press them.

Friend of mine yelled at me rather vociferously because his character found the notches and conveyed this to everyone else, but they were too focused on the puzzle and simply assumed that getting the puzzle right is the correct course of action.

Silly puzzle traps.
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Re: Random Stuff Part III
« Reply #2923 on: October 16, 2017, 04:37:26 pm »
0

I... still don't get it. What does it mean to "yield a negation?"

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Re: Random Stuff Part III
« Reply #2924 on: October 16, 2017, 07:29:29 pm »
+1

I... still don't get it. What does it mean to "yield a negation?"
Basically, "generates a false statement". It's terrible language, but that's because (a) it's not mine (it's Quine's, I believe), and (b) you have to use slightly awful phrasing to make something that works without being directly self-referential.

Roughly speaking, "yields negation when preceded by its quotation" means "take X, put it in quotes, then put it in again without quotes, and you get a false statement". In other words, it's saying that for some phrase X, the sentence "X", X is false. It just so happens that the phrase we chose to test is itself.
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