Your favorite paradoxes

[Maze1125]

Value n meets the crita of the first number that requires more than fourteen words to describe.

This is where your error in logic lies.
You are assuming that such a number exists.

If you don't assume that, then you don't get any of the problems you describe.

Here's a similar example:

Given the sentence "The first number not equal to one that is not described by this sentence"

The value of 1 is found to not apply. The value of 2 is examined and found to meet the criteria, thus it may be described as the first number not equal to one... The same conundrum arrives. What conclusion do you draw from this situation? Following the EXACT SAME logic we would find that since this cannot apply to any number, all numbers MUST therefore be 1.

I'm sorry, but I don't follow how you reach that conclusion, could you write it up more formerly please.

 

[Ph33nix]

"the first number not nameable in under ten words"

how is this a paradox?

 

[lozfoe444]

I never make statements.

 

[Enigmers]

"All generalizations are false" is my personal favourite - because it's true.

 

[Folsense]

War is Peace.
Freedom is Slavery.

Ignorance is strength

He loved Big Brother.

 

[Folsense]

Is the word "heterological", meaning "not applicable to itself," a heterological word?

Edit: Sorry, double posted.

 

[Artemis923]

"Snake! You've created a time paradox!"

 

[Singularly Datarific]

Pinochio saying "my nose will now grow"

His nose just exploded.

 

[SeanTheSheep]

My personal favourite:
"Get lost I'm asleep" Unless the person actually sleep-talks, then it gets awkward, in that case though it turns into "Get lost I'm dead"

 

[SeanTheSheep]

Since cats allways land on there feet.

1.Get two cats

2.Tie them together (at the feet)

3. and throw them up in the air.

Logically there never going to hit the ground.

There just going to spin around just 6 inches above the ground.

That also works if you tie buttered toast to a cat, weee!

 

[EllaAlle]

"the first number not nameable in under ten words"

how is this a paradox?

Because they named the number in under ten words

 

[Eclectic Dreck]

Formerly, my NEW example, which expresses the same logical flaw as what started this whole ordeal:

Theorm: all numbers are equal to value n (in the original case the theorm is all natural numbers may be described by in fourteen or fewer words)

Condition: Find the first number not equal to n (in the original case, find the first value that requires more than 14 words to describe)

Judging criteria: "the first value that is not equal to n that is not described by this sentence" (originally : "the first number not unambiguously namable in under fourteen words")

1) A value is chosen, n. This value is equal to n and therefore falls outside the juding criteria. n = n therefore the theorm holds.

2) A second value is chosen, n+1. This value is found to NOT be equal to n and is not currently described by my judging criteria. Applying the descriptive sentence results in a contradiction ergo the judgring criteria cannot possibly apply. Therefore N + 1 = N and the theorm holds.

3) An arbitrary value is chosen, n +/- a. This value is found NOT to be equal to n and is not currently described by the judging criteria. Applying the description results in a contradiction and again cannot possibly apply. Therefore n +/- a = n.

Thus:
n = n +/- a where a is any member of the natural number set.

The same logic is used: my judging criteria, though far more blantant, has the same logical flaw. Any value it MIGHT describe it, by definition, CANNOT describe. As such, if it cannot describe ANY value then ALL values must be equal to my chosen value.

It's a common logical flaw really. If you have two options and you know that one is not met is it logical to say that the other MUST have been met? According to my formal education in logic, the answer is, in fact, no.

 

[Merteg]

I like it when people say "unthaw" with a perfectly straight face

yeah, others to add to that list

Pre-heat an oven; how do you heat it up before heating it up?

and

Hot water heater; why are you heating water that is already hot?!?

Note: Maybe by unthaw they mean freeze

The oven is being preheated because you are heating it before, or "pre," the cooking process.

The heater's purpose is to heat. The "hot water" part of it is describing how the heating takes place, not what it does.

Thaw - To lose heat.

Therefore unthaw would be the opposite, thus the prefix. So, as you said, to freeze.

I believe I got those right?

 

[YuheJi]

I love Zeno's paradoxes. If there are infinite points from point A to B, and we can never reach infinity, how could anyone possibly walk from point A to B?

 

[Twitchycat]

Good resident evil game is a hilarious paradox.

 

[Maze1125]

Formerly, my NEW example, which expresses the same logical flaw as what started this whole ordeal:

Theorm: all numbers are equal to value n (in the original case the theorm is all natural numbers may be described by in fourteen or fewer words)

Condition: Find the first number not equal to n (in the original case, find the first value that requires more than 14 words to describe)

Judging criteria: "the first value that is not equal to n that is not described by this sentence" (originally : "the first number not unambiguously namable in under fourteen words")

1) A value is chosen, n. This value is equal to n and therefore falls outside the juding criteria. n = n therefore the theorm holds.

2) A second value is chosen, n+1. This value is found to NOT be equal to n and is not currently described by my judging criteria. Applying the descriptive sentence results in a contradiction ergo the judgring criteria cannot possibly apply. Therefore N + 1 = N and the theorm holds.

3) An arbitrary value is chosen, n +/- a. This value is found NOT to be equal to n and is not currently described by the judging criteria. Applying the description results in a contradiction and again cannot possibly apply. Therefore n +/- a = n.

Thus:
n = n +/- a where a is any member of the natural number set.

The same logic is used: my judging criteria, though far more blantant, has the same logical flaw. Any value it MIGHT describe it, by definition, CANNOT describe. As such, if it cannot describe ANY value then ALL values must be equal to my chosen value.

Ignoring that fact that your proof differs from mine in several key areas, the main problem is that you're disguising two conditions as one.
The condition "Not equal to n." and "Not described by this sentence."
The former can be true or false, the latter is an intrinsic paradox. If you apply it as false to a number it becomes true and if you apply it as true to a number, it becomes false.

Mine is not an intrinsic paradox. Yes, if you take it to be true you get a problem, but it can be false with no contradiction.

If you have two options and you know that one is not met is it logical to say that the other MUST have been met?

No, of course not.
But if you have two options and you know that at least one must be met, and one isn't, then yes, the other must be.

 

[Maze1125]

I love Zeno's paradoxes. If there are infinite points from point A to B, and we can never reach infinity, how could anyone possibly walk from point A to B?

Because being unable to walk an infinite distance is different from being unable to pass through an infinite number of points over a finite distance.

The latter is, in fact, quite possible.

 

[Eclectic Dreck]

Formerly, my NEW example, which expresses the same logical flaw as what started this whole ordeal:

Theorm: all numbers are equal to value n (in the original case the theorm is all natural numbers may be described by in fourteen or fewer words)

Condition: Find the first number not equal to n (in the original case, find the first value that requires more than 14 words to describe)

Judging criteria: "the first value that is not equal to n that is not described by this sentence" (originally : "the first number not unambiguously namable in under fourteen words")

1) A value is chosen, n. This value is equal to n and therefore falls outside the juding criteria. n = n therefore the theorm holds.

2) A second value is chosen, n+1. This value is found to NOT be equal to n and is not currently described by my judging criteria. Applying the descriptive sentence results in a contradiction ergo the judgring criteria cannot possibly apply. Therefore N + 1 = N and the theorm holds.

3) An arbitrary value is chosen, n +/- a. This value is found NOT to be equal to n and is not currently described by the judging criteria. Applying the description results in a contradiction and again cannot possibly apply. Therefore n +/- a = n.

Thus:
n = n +/- a where a is any member of the natural number set.

The same logic is used: my judging criteria, though far more blantant, has the same logical flaw. Any value it MIGHT describe it, by definition, CANNOT describe. As such, if it cannot describe ANY value then ALL values must be equal to my chosen value.

Ignoring that fact that your proof differs from mine in several key areas, the main problem is that you're disguising two conditions as one.
The condition "Not equal to n." and "Not described by this sentence."
The former can be true or false, the latter is an intrinsic paradox. If you apply it as false to a number it becomes true and if you apply it as true to a number, it becomes false.

Mine is not an intrinsic paradox. Yes, if you take it to be true you get a problem, but it can be false with no contradiction.

If you have two options and you know that one is not met is it logical to say that the other MUST have been met?

No, of course not.
But if you have two options and you know that at least one must be met, and one isn't, then yes, the other must be.

The proof differs because it's a different proof. I thought that much was obvious

With regards to the statement that I have two critera - yep this is ENTIRELY true because I didn't want to think of a SINGLE statement that was self-referential.

What continues to surprise me (as my continued refusal to accept your argument must certainly surprise you) is that while you identified the key feature wrong in my proof (that my statement is not self-consistant) you fail to see that the exact same feature is wrong in the proof you offer.

As I have said a dozen times - you can construct any number of examples where your criteria cannot possibly be true and then apply any of a number of tests designed to reach an arbitrary conclusion.

But, what REALLy annoys me about this back and fourth lies simply in the logic being used.

From my perspective, there are a finite number of WORDS available (about a million in English at the moment). We also have a fininite number of spaces for said words for the proof to be true. The proof states that all such words must be "unambiguous" meaning there can be no repition of a specific sequence of words. We also know that we have a set of infinite numbers to deal with. According to your statement, you will take a finite number of possible solutions and unambiguously assign names to an infinite set of numbers. While I may not have graduate degrees in mathematics, I do know enough to be fairly certain that cannot unamiguously assign a finite number of names to an infinite set of values. I am as certain of this as I am certain that not every number in the natural number set is equal to one. In spite of this certainty I'm nevertheless sitting here and being forced to argue with someone who is saying, in effect, one can unambiguously assigin a finite number of names to an infinite set of values.

 

[Maze1125]

What continues to surprise me (as my continued refusal to accept your argument must certainly surprise you) is that while you identified the key feature wrong in my proof (that my statement is not self-consistant) you fail to see that the exact same feature is wrong in the proof you offer.

Except, as I just explained, your claim was a paradox, mine was only inconsistent if you assume it to be true.

That is, in no way, the same problem.

As I have said a dozen times - you can construct any number of examples where your criteria cannot possibly be true and then apply any of a number of tests designed to reach an arbitrary conclusion.

Go on then, using something that is only a problem if you assume it to be true, rather than something that is a problem if it is both true and false.

But, what REALLy annoys me about this back and fourth lies simply in the logic being used.

From my perspective, there are a finite number of WORDS available (about a million in English at the moment). We also have a fininite number of spaces for said words for the proof to be true. The proof states that all such words must be "unambiguous" meaning there can be no repition of a specific sequence of words. We also know that we have a set of infinite numbers to deal with. According to your statement, you will take a finite number of possible solutions and unambiguously assign names to an infinite set of numbers. While I may not have graduate degrees in mathematics, I do know enough to be fairly certain that cannot unamiguously assign a finite number of names to an infinite set of values. I am as certain of this as I am certain that not every number in the natural number set is equal to one. In spite of this certainty I'm nevertheless sitting here and being forced to argue with someone who is saying, in effect, one can unambiguously assigin a finite number of names to an infinite set of values.

Why do you assume there are only a finite number of words in a language? Languages evolve, which leaves the potential as infinite.

And, before, you said that hyphenated words counted as one word.
So if we say 1,003,201 is one-million-three-thousand-two-hundred-and-one that is a system that can describe every single natural number using only one word that looks very much like English.

Not that that is really relevant as proving the conclusion correct by other means does not prove the argument previously used was valid, and this discussion was about the validity of the argument, and not so much the conclusion.

 

[philosophicalbastard]

Everything is possible, thus its possible for something to be impossible.

Try rapping your head around that.