Berry's Paradox

[bonanova]

Considering only positive integers, 7 is unambiguously specified by the phrase the smallest number not specifiable using fewer than two syllables.

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

How many syllables does the smallest number not specifiable using fewer than twenty-three syllables have?

[Guest]

Possible

Using your prompt, 7,777,777 would make sense.

[Guest]

What does 'not specifiable' mean? Seven has two syllables. Eight has one. I'm obviously not getting something.

[unreality]

"se-ven" is the only one digit number with more than one syllable... so you'll get more syllable per smaller number, so to speak

[Guest]

Possible

Using your prompt, 7,777,777 would make sense.

That has 24 syllables. 7,777,778 has 23. One trillion one has 4 syllables. I'm not gettin' it.

[unreality]

this should clear it up:

the smallest number

we want the smallest number thats 23 syllables... so it would be 777,777,778 or whatever you said.

[Guest]

OH MY GOD!

23!

2/3 equals 0.666!

[Guest]

we want the smallest number thats 23 syllables

No, we don't. We want "the smallest number not specifiable (whatever that means) using fewer than twenty-three syllables".

[Guest]

Exactly.

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

It's written kind of ambigously, but it means that the number must be:

specifiable

using MORE than 23 syllables and no less

the smallest such number to fit the definition

and from the prompt

Considering only positive integers

It must be a positive integer.

EDIT:

Even as I wrote this, I disagreed with myself.

not specifiable using fewer than twenty-three syllables

This would allow 23 syllables and therefore it would be 7,777,771.

[Guest]

It's written kind of ambigously, but it means that the number must be:

specifiable

The OP said, "not specifiable". And I still don't know what that means.

not specifiable using fewer than twenty-three syllables

This would allow 23 syllables and therefore it would be 7,777,771.

You're saying 23 is less than 23? 1 is less than 23. I think that would make the answer: 1. Although I'm not sure if the 'not specifiable' part cahanges the answer.

[Guest]

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

[Guest]

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?

[Guest]

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.

[Guest]

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.

[Guest]

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?

[Guest]

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.

[Guest]

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.

[Guest]

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".

[Guest]

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.

[bonanova]

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 ....

[bonanova]

proving that ...

[1] the smallest number not specifiable in fewer than 23 syllables can be specified in 22 syllables.

[2] there are only a finite number of numbers.

[bonanova]

Hmmm....

Ok; so there is a finite number of numbers.

No biggie, I guess.

After all, there is also only a finite number of textbooks to be re-written.

[Guest]

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.

Well, well, well. You are right. My first reaction was to say "no, it is pronounced mill-ee-un , so it is three syllables, not two", but I thought I had better look it up first. I am not near my trusty Oxford (the only real dictionary), but I did use the the Cambridge online dictionary, and I see that I have been mispronouncing this word - it is mil-yun - two syllables.

In my defense, I found the following:

In standard English, it is pronounced with an l-sound followed by a y-glide. However, as other languages use a fully palatalized 'l' in this word (such as Italian spells by 'gl'), some English-speakers have picked up this pronunciation, which does not occur elsewhere in the English language but in words of this model.

I guess that latter part refers to me.

I have to catch a flight, but this gives me something to do while sitting at 10,000 metres. If I come up with a number, I'll post when I am back home tonight.

[bonanova]

1,177,777

one million, one hundred seventy seven thousand, seven hundred seventy seven = 23 syllables

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 ....

Oh ... we never got to the paradox. Let's try again:

ummm, just for the heck of it, count the syllables in red, above.

the smal-lest num-ber not spe-ci-fi-a-ble us-ing few-er than twen-ty-three syl-la-bles.

If the red words specified the answer, then ....

The smallest number not specifiable using fewer than twenty-three syllables has just been specified using fewer than twenty-three syllables.

Which leads to the conclusion that there is only a finite number of natural numbers.

Good old Berry ...

[Guest]

the smal-lest num-ber not spe-ci-fi-a-ble us-ing few-er than twen-ty-three syl-la-bles. <== 22 syllables.

If the red words specified the answer, then ....

The smallest number not specifiable using fewer than twenty-three syllables has just been specified using fewer than twenty-three syllables.

I did count the number of syllables, but I completely missed the fact that this creates a paradox.

Very good.

[Which leads to the conclusion that there is only a finite number of natural numbers.

I don't see the path to this conclusion. Care to elaborate?

BTW: I am home now and have consulted my Oxford, which gives the pronounciation of million as "-yon". I am utterly defeated.