[PD] CVs

[Simon Wise]

On 11/05/11 08:16, Chris McCormick wrote:
> On Tue, May 10, 2011 at 12:12:04PM -0400, Mathieu Bouchard wrote:
>> It doesn't mean that those artifacts don't exist in the physical world,
>> it means that we had to invent those concepts by ourselves because we
>> can't perceive them from the physical world.


Numbers are like words, they are part of a language for talking about some kinds 
of things, some kinds of concepts. Rational numbers either exists or not, 
depending on what you mean by exist. Irrational numbers are in the same boat. If 
you want to talk about what number you get when you divide an integer by another 
one, then you won't need irrational numbers and rational ones are just the 
thing. If you want to talk about how far apart two points are then rational 
numbers are inadequate in certain ways ... there are distances that are not 
fully described by dividing two integers, and you can always find a gap between 
any two points on a line described by rational numbers, but irrational numbers 
can describe the points in this gap. Real numbers, that is both rational and 
irrational numbers together, are continuous in a way that rational numbers are 
not. All this is about describing things - making a model which you can work 
with and communicate to others (who know the language you are using) very 
clearly ... and which you may compare with things you observe, and use to help 
understand, interpret and predict these things you observe. If you do it well, 
and remember that it is a description, then this can be very useful indeed.

But what you mean by the word 'exists' will determine whether you say a model 
exists, or a word exists, or a number exists.

Simon