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Berry's Paradox


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38 replies to this topic

#11 cpotting

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Posted 20 September 2007 - 04:42 PM

The best I could come up with was
Solution
1,177,777
one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables
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#12 Scraff

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Posted 20 September 2007 - 08:25 PM

The best I could come up with was
Solution
1,177,777
one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables


Am I the only one who is reading less than 23 as not meaning equal to 23?
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#13 Writersblock

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Posted 21 September 2007 - 01:52 AM

Scraff,

Not sure what you are missing, but it's supposed to be "not specifiable using less than 23 syllables."

This means that the number cannot be specified if you are using less than 23 syllables. Which means, in turn, that you must use 23 syllables or more. Once we know that, we are looking for the smallest postive whole number that fits the definition. I cannot think of a number that uses 23 syllables or more that is less than 7,777,771.
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#14 Writersblock

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Posted 21 September 2007 - 01:56 AM

1,177,777
one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables



One-mill-ion one-hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = I count 22.

But I realize I am wrong with 7,777,771. It should be 1,777,777.
One-mill-ion sev-en hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = 23.
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#15 Scraff

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Posted 21 September 2007 - 02:12 AM

Scraff,

Not sure what you are missing, but it's supposed to be "not specifiable using less than 23 syllables."

This means that the number cannot be specified if you are using less than 23 syllables. Which means, in turn, that you must use 23 syllables or more.


In what language?

What is the smallest number not specifiable using fewer than twenty-three syllables


How on Earth can you interpret that to mean one should use 23 or more syllables?
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#16 Scraff

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Posted 21 September 2007 - 02:14 AM


1,177,777
one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables



One-mill-ion one-hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = I count 22.

But I realize I am wrong with 7,777,771. It should be 1,777,777.
One-mill-ion sev-en hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = 23.


Who are you quoting? You should use copy and paste to avoid misquoting someone and attempting to prove that someone besides you was wrong.
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#17 Writersblock

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Posted 21 September 2007 - 03:34 AM

That was cpotting's post I quoted. I did use copy and paste. I figured anyone reading through the post would figure that out. Sorry you still aren't getting it Scraff. Think of it this way -- if I say, "give me not less than 23 dimes" how can you make that true? Give me 23 or more.
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#18 Scraff

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Posted 21 September 2007 - 04:10 AM

That was cpotting's post I quoted. I did use copy and paste.


Ahh, sorry 'bout that.


Sorry you still aren't getting it Scraff. Think of it this way -- if I say, "give me not less than 23 dimes" how can you make that true? Give me 23 or more.


And I understand perfectly what that means.

Totally different than, "What is the smallest number not specifiable using fewer than twenty-three syllables".

That is asking for a number that is not specifiable and has fewer than 23 syllables. Not: "What is the smallest specifiable number not using fewer than twenty-three syllables".
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#19 Writersblock

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Posted 21 September 2007 - 05:43 AM

And I understand perfectly what that means.

Totally different than, "What is the smallest number not specifiable using fewer than twenty-three syllables".

That is asking for a number that is not specifiable and has fewer than 23 syllables. Not: "What is the smallest specifiable number not using fewer than twenty-three syllables".



Since there isn't such a thing as a number that is a positive integer which is not specifiable, then the two sentences mean exactly the same thing. It's merely a matter of semantics. I see what you mean, but if you elminate the clause starting with "using" and just try to understand "smallest number not specifiable" then you end up with something that is nonsense. As a matter of language construction, you have to assume that in most cases, absent evidence to the contrary, most people don't mean to communicate nonsense. Therefore the proper contruction of "not specifiable" is to include the clause that follows in order to make sense out of the seeming nonsense. Let's look to see if the nonsense is defined by surrounding clauses. Does "not specifiable using fewer than 23 syllables" change the meaning? Of course it does. Now the nonsense makes sense, even if it is ambiguous, and we have language that most can agree on. Now instead of a nonsensical number that is "not specifiable," we have a number that is not specifiable using fewer than 23 syllables, or in otherwords, specifiable only by using 23 syllables or more.
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#20 bonanova

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Posted 21 September 2007 - 10:37 AM


1,177,777
one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables



One-mill-ion one-hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = I count 22.

But I realize I am wrong with 7,777,771. It should be 1,777,777.
One-mill-ion sev-en hund-red sev-en-ty sev-en thou-sand sev-en hund-red sev-en-ty sev-en = 23.

Bravo, Writersblock.

1,777,777 is the smallest number not specifiable using fewer than twenty-three syllables.
At least, no one has come up with a smaller number. So let's say it is.
You get the prize.

O wait. This is supposed to be a paradox.

ummm, just for the heck of it, count the syllables in red, above.
If the red words specified your answer, then ....
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