Re: Epistemology 201: The Science of Science

From: Wolf Kirchmeir (wwolfkir_at_sympatico.ca)
Date: 02/07/05 

Date: Mon, 07 Feb 2005 12:16:11 -0500

Albert wrote:
> Wolf Kirchmeir wrote:
>
>> Albert wrote:
>> [...]
>>
>>>
>>> Oh, I see. Mathematical jargon. I was hoping for you to tell me how
>>> to count an infinite number.
>>
>>
>>
>> Consider the difference between the set of integers and the set of
>> reals. Both are infinite sets. Integers can be counted. That is, no
>> matter what integer you propose, you can count exactly one more: Given
>> N, you can specify that the next integer N' = N + 1 for any N. So the
>> set is countable. (This is not a rigorous explanation, but it will
>> have to do. It depends on the notion that counting is a step-by-step
>> listing of the elements of a set.)
>>
>> You can't do this with real numbers, since you can't specify what the
>> next real number in the sequence will be: Given R, what is R'? Given
>> any R and R', there will always be an R" such that R < R" <R'. Or, no
>> matter how arbitrarily small you make the difference E between R and
>> R', there will a number R" such (R' - R") < E and (R" - R) < E. So,
>> the set of reals is uncountable.
>>
>> See?
>
>
> Of course, I see. Integers can be *theoretically* counted but not
> *actually* counted. You use the word 'countable' to mean that one could
> count forever. Your definition is only useful in mathematics and is at
> odds with the common meaning of the word. Now do *you* see?

Oh, sure, that's obvious, and I saw that when I first read Cantor -
which was probably before you were born. What you don't seem to see is
that the common meanings of words have no relevance to mathematical
arguments, and I was foolish enough to think you were engaged in a
mathematical discussion. I won't make that mistake again.

And you are using "theoretical" and "actual" in their common meanings,
too, which is pointless in a philosophical discussion, which I presumed
also you were presuming to be a part of. I won't make that mistake
again, either.

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