Is this a paradox?

[oe39]

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In a discussion I recently had in a class that dealt with Zeno's paradox of infinity (or one of them, anyway) we seemed to discover something interesting. Or at least I did; perhaps others already knew it.

Anyway, this is what we found. Most people, including you the OP, fall into problems because they think of infinity as Being, in other words, as a unifiable concept. While what infinity really is, I would now argue, is Becoming. This makes sense: something that is infinite by definition has no end; and if there is no end, there is no smallest number.

Your friend said there isn't enough time to cite an infinite number of numbers. He's right and he's wrong. We will never have enough time because no amount of time would be enough. Infinity is a perpetual stretching, if you will.

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i don't understand what this has to do with the thread.

[PairTheBoard]

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But once all humans are dead, once there can be no more referencing, there is a smallest one. Doesnt "the smallest number that will never be referenced by a human (past, present or future)" refer to an actual number? There wouldnt be a problem if a martian said it, would there? He could even name it explicitly without generating a paradox.

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It's a self referencing and self contradictory statement like;

"This statement is false".

You could simplify the idea to take a closer look at it by just defining the "smallest number that will not be referenced in the first 50 posts of this thread". Call that statement S. Call the number it turns out to reference N. Then N is referenced by S in the first 50 posts of this thread. Yet S defines N as not being referenced in the first 50 posts of this thread. Contradiction. The problem is that besides referencing a number, the statement S makes reference to the statement S, just like "This statement is False" does.

PairTheBoard

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What I find interesting though is that the statement itself isnt self-contradictory. It only becomes so if a human says it. If a martian wants to make the statement, the number is well defined and there is no paradox.

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The statement refers to statements made by humans, so it is self referencing exactly when a human says it. Statements which refer to the speaker of the statement can be either true or false depending on who speaks them. For example, "I am a male".

PairTheBoard

[evolvedForm]

After posting it I realized it has nothing to do with the the thread.

[CrayZee]

I'm not sure what you're trying to get at, but how about asking a smart historian about this?

From what I understand, people have used numbers as a means to impress. For example, a city with 200,000 people would be said to have a million. Of course, we supposedly have better means of reference to check these facts now.

Political pollsters like to manipulate numbers, for example.

People seem to like the "concreteness" of absolute numbers, well at least 72.42% of people.

Also, isn't the number 1 the smallest natural number? [img]/images/graemlins/wink.gif[/img]

[reup]

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Given that, it seemed to me that there must be a smallest natural number which will never be referenced by a human being.

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There is much yet that remains unexplored!! Onward Brothers onward!!

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Having said that, havent I just referenced it?

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[censored]

[borisp]

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People make reference to numbers all the time in everyday speech, in articles, journals and so on (not references to a class as in "all odd numbers" but individually like "17", "a googol", "the smallest perfect number greater than 1000", etcetera). Someone made the comment to me the other day that not all numbers will be referenced by a human being, there just isnt enough time to cite an infinite number of numbers. Given that, it seemed to me that there must be a smallest natural number which will never be referenced by a human being. Having said that, havent I just referenced it?

Anyone know if this has a name (or if I'm just making a simple thing complicated - I've been mulling it over for days now and I'm all confused...)

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There is such a number. However, it is not computable.

Proving the existence of an object that satisfies certain properties is different from giving a method for finding that object. For (a bad but well known) example, it is true that two people in NYC have the same number of hairs on their body, but it is another thing altogether to find them.

Put another way...is there a smallest number that will never be explicitly referenced by a human being? Yes. Will a human being ever explicitly compute this number? No.

There is no paradox if one accepts that a number can be simultaneously known to exist and impossible to compute. This is technically different from the distinction between the "reference to an object vs. the object itself," but intuitively it is the same idea.

[oe39]

SSSHHHHH!!!!!! every time we reference it, we drive it up

[XxGeneralxX]

This is the last guy who tried to find the smallest number imaginable. The poor guy just kept dividing by two...... he was so damn close.

[vanwely]

141,695,524 was in the lead, but I just blew it.

Vanwely