On 6/14/2015 12:45 PM, LizR wrote:
On 14 June 2015 at 16:40, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
On 6/13/2015 9:18 PM, LizR wrote:
None of this explain why it works so well anyway.
I don't understand why the effectiveness of mathematics is considered
problematic.
First, we, creatures who evolved in this world, invented it to be useful.
We
invented counting and arithmetic to be used in describing and predicting
things. And
I've given examples where the rules of arithmetic don't work. So the
second point
is that we only apply them where they are effective. Where they are not
effective we
say that's a misapplication and we try to add rules to avoid those
misapplications.
Don't work in what sense? Don't apply to the universe, or are not
self-consistent?
In the sense that we have to be careful how we interpret and apply them and make
approximations and simplifications and THEN they work.
"We invented it to be useful" is not true,
Sure we did. Some
AND it's a non-argument. We invented religion to be useful, and lots of other things,
but we didn't invent maths, we observed the regularities (e.g. conservation of number of
things)
But first we (or more likely evolution) invented the notion of individual things being
members of classes, so that it was useful to count them and manipulate the numbers instead
of trying to think about the individuals. If you've ever taught a little child numbers
(and I assume you have since you're a mother) you know you must start by showing them very
similar things. If you show them a car, an apple, and four people and ask them "How many
are they." you may well get "Four." instead of "Six."
and codified them.
But we did more than codify them. We made up theories about them. Nobody can have
observed that EVERY number has a successor. We invented that because it's simple and it
makes it easier to reason about some things.
So it was something about the world that we discovered, and it works. I'm not making any
metaphysical claims about it, but I don't understand why you feel this need to hand-wave
the effectiveness away. It's just there (so far) -- and to quite a lot of decimal places.
I'm not saying it's ineffective. I'm saying it's not a mystery why it's
effective.
Brent
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