What I'm trying to get at with all this palaver is not that mathematics is false or that it is not useful, but that it affords us only a partial view. I am trying to suggest that there are different ways of playing with numbers, different conceptions of what number is, different kinds of mathematics (depending on what you accept can be a number), and real issues about what it is that you can meaningfully measure and calculate.
Perhaps it is not fair to say that 2 + 2 = 4 is meaningless in base 3. But if I were to ask something like show me the number of objects that 23 corresponds to, the answer would be different if it was 23 base 5 or 23 base 10. I'm arguing that the neutrality and universality of mathematics is something we have been trained to believe in, it is not something that is necessarily Real.
Joanna
John Mage wrote:
> John Kozak wrote:
> >>> I don't know him; does he argue that 2+2=4 can be false? If so, I
> >>> like to see the argument; it would be fascinating.
> >> Well, in base 3, the argument wouldn't be false, it would be
> >> nonsensical.
> > But it isn't _in_ base three, any more than your above sentence is in
> > German.
>
> I'm not sure that this aids Joanna's point, but on a more elementary
> level (that is to say i was taught this in elementary school) the truth
> of 2+2=4 is conditioned on the assumption of the density of real
> numbers. Otherwise 2+2=4 is not true by definition. i.e., if 2 (as in "2
> percent of the vote") stands for all values between more than 1.5 and
> less than 2.5, then 2+2=4 will often be false.
>
> john mage
>
>
>
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