On 19/05/11 12:59, Chris McCormick wrote:
On Fri, May 13, 2011 at 12:38:37PM -0400, Mathieu Bouchard wrote:
On Wed, 11 May 2011, 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.
At the very least they exist physically encoded in the brain chemistry
of somebody who is thinking about those concepts. Brains are part of
physical reality, right?
Yeah, but the map is not the territory.
I am not convinced they are different in the case of things that "we can't perceive
... from the physical world."
Which numbers can be perceived in some way that isn't a mathematical model?
That is which numbers are directly perceivable, without some more abstract
mathematical mapping to guide us?
Certainly most people can look at four matches on a table and see that there are
four, without doing any counting at all. There are a few people who can tip a
matchbox full of matches onto a table and see immediately that there are 51, or
53, or whatever in the same way ... no counting involved. There must be some
point where this is no longer possible for anyone ... is 1,549,364 anything
other than word in the language of mathematics?
In some languages, where mathematics hasn't become part of the language, and the
words for numbers are pre-mathematics, counting goes something like "one, two,
three, four, many" so I guess that backs up the idea that the first few integers
are perceived directly, but every other number - counting numbers past that,
zero, negative integers, the rest of the rational numbers, the rest of the real
numbers, the rest of the complex numbers, ... and so forth are all just
constructs in the language of mathematics which all happen to have some quite
useful mappings to things we can observe around us. Most integers do not have
any more 'existence' (however that may be defined) than complex numbers.
Simon
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