On 1/23/2014 3:42 PM, LizR wrote:
On 24 January 2014 11:51, meekerdb <[email protected] <mailto:[email protected]>>
wrote:
On 1/23/2014 2:40 PM, LizR wrote:
This appears to be the fundamental "bone of contention" between you and
Brent. He
appears to believe arithmetic is a human invention which relates to reality
because, well, (waves hands, and cunningly slips "AR" hat on) ... it just
does,
somehow.
It relates to reality as we experience it because we invented arithmetic by
abstracting and generalizing from that experience.
If we abstract and generalise something from experience, I would say the standard usage
is to say that we have discovered something, rather than invented it. For example, Isaac
Newton invented an equation which he called "the law of gravitation". He did so by
abstracting and generalising from observations of the world. However, most people
(outside philosophy departments) would say that his equation describes (or attempts to
describe) a feature of the world that is genuinely "out there".
But notice that is failed "out there". Elliptical orbits are still true in 1/r
potentials, but it turned out those are idealized approximations.
Similarly, if we abstracted and generalised in order to invent "2", presumably we did so
in order to describe something we discovered, something that is genuinely "out there"...
Sure, it describes a relationship between countable sets. But I don't think that
justifies reifying it. "Bigger" also describes a relationship between objects that is
"out there", but we don't reify it.
I would say most people use "invented" to mean that something had no counterpart in
reality, in any sense (abstract or otherwise) until someone brought it into existence.
So in that sense, I would claim we didn't "invent" arithmetic or gravity. Do you agree,
or would you say that arithmetic is an invention, in this standard usage? (Or did you
have some other sense of "invent" in mind that I've missed?)
I think we invent theories and descriptions and we may hope and intend that they apply to
reality, but we can't know that. And some mathematical inventions were not intended to
apply to anything realistic, they were just generalizations that occurred to a
mathematician. Of course we may say we discover a relation in something even though we
invented it. Just because we invent something (like Peano's axioms) it doesn't follow
that we know all the consequences. We certainly invented chess, but nobody knows whether
white can always win following a Ruy Lopez opening.
It's not surprising that our ideas relate to what we experience.
You seem to be trying to have this both ways. Or maybe it's just me not getting quite
where you're coming from. Is arithmetic a genuine feature of reality that we have
discovered, or is it not?
I'd say a finitist form of arithmetic is a good description of some aspects of reality -
but don't try to add raindrops or build Hilbert's Hotel.
Brent
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