Re: Peterson's Death Sentence

From: Parse Tree (account_at_domain.extension)
Date: 02/01/05 

Date: Tue, 01 Feb 2005 07:37:06 GMT

John Fields wrote:
> On Mon, 31 Jan 2005 02:25:28 GMT, Parse Tree
> <account@domain.extension> wrote:
>
>
>>learner@juno.com wrote:
>>
>>>>On Sun, 30 Jan 2005 08:25:30 GMT, Parse Tree
>>>><account@domain.extension> wrote:
>>>
>>>
>>>
>>>>>Suppose I said that there was an equation such that 4+4=10. Now I can
>>>>>claim that it's not bound by the laws of arithmetic, but that doesn't
>>>>>change the fact that applying the laws of arithmetic results in that
>>>>>equation being impossible.
>>>
>>>You failed to mention that your math only works if you are using base 10
>>>arithmetic.
>>
>>It wasn't necessary.
>
>
> ---
> Yes, it was. Your argument was unspecific enough to be ambiguous,
> which led to its carrying an inherent contradiction.

No, all math is in base 10 by convention unless otherwise specified.

>>>If you change the base of the numbers, you change the rules of the
>>>equation.
>>
>>No, it changes the symbols. The quantities referred to do not change.
>
> ---
> Yes, the quantities _do_ change.
>
> In base 10, "10" means this many periods: ..........
>
> In base 8, "10" means this many: ........
>
> Note that the symbols stayed the same, but the quantities changed.

We're talking about too different things. I'm talking about the inverse,
where the quantities remain the same and the symbols change.

Ie. Changing the equation from base 10 to base 8 by actually changing
the symbols, rather than just writing that it's now in base 8 (without
changing the symbols).

>>Anyway, you can't really specify that equation in another number base
>>without adding semantic info.
>
> ---
> The fact that you _didn't_ specify the base when presenting a logical
> argument led to the ambiguity which led to the contradiction which
> made your statement not true all of the time, which made it false.

Specifying that it was in base 10 was no more necessary than mentioning
that it was written using arabic numerals.

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