Re: Did prime numbers evolve?
- From: Entertained by my own EIMC <eimc@xxxxxxxxxxxxxxxx>
- Date: Fri, 18 Apr 2008 13:34:38 -0400 (EDT)
Alan Meyer wrote:
On Apr 11, 1:28 pm, dkomo <dkomo...@xxxxxxxxxxx> wrote:
Yes, of course they did. Prime numbers are concepts in human....
brains, and human brains obviously evolved. Prime numbers have
no independent existence outside of human minds. If humans
went extinct, prime numbers would go extinct along with them.
Your conversation piece here is indeed intriguing. I can't help
but take the bait and join in.
Unfortunately, I am not versed in the philosophy of mathematics.
I know that some truly heavyweight thinkers have weighed in on
this topic and anyone attempting to add anything to the
discussion should read them and understand them before voicing
arguments that have, in fact, been demolished hundreds or
thousands of years ago.
But, after all, we are discussing this on the Internet where
ignorance is _de rigeur_. So I'll plow right ahead.
I incline towards the realist school (that numbers exist without
our having to entertain them in our minds.) There is more about
"inclination" at the end.
I will begin by asserting, in blissful ignorance, that material
objects are one category of reality, but not the only one.
Consider such objects as "facts", "propositions", "scientific
laws", "physical relationships", "properties", and possibly some
others.
We can say A is above B meaning that B is closer to the center of
the earth and A is along the same radius line, but further from
the center of the earth. I don't think we have any trouble
saying that the relationship exists even though it itself, i.e.,
the relationship, is not a physical object.
Or consider properties. We can give reasonable physical
interpretations to properties like "heavy", "red", "dense",
"loud", and many others. Although living beings have specific
perceptions of those properties that may be somewhat
idiosyncratic to the the species or even the individuals, the
properties themselves have a demonstrably independent existence
and can be described in terms that don't necessarily appeal to
particular sensations.
Now if "red" is a property, what about "circular", a mathematical
property, or at least a property whose description is
mathematical?
If that's admitted, it seems to me a short step to talk about
numbers as physical properties of collections of objects. Water
is a collection of 3 atoms. Carbon has 6 protons and 6
electrons. If we grant that the protons and electrons are real,
then why not admit the 3's and 6's. After all, there were 3
atoms in water and 6 protons and electrons in carbon long before
humans arrived on the scene - which can be demonstrated by
examining ancient water in the earth and ancient carbon in coal
or wherever. If we admit the numbers, again, there are very
short steps to admitting the properties of numbers, such as
primeness.
I think maybe we're on a slippery slope. Tilt it one way and we
slide towards admitting the reality of all sorts of abstract
objects. Tilt it the other way and we wind up denying the
reality of a lot more than we meant to.
Personally, I'm tilting towards realism rather than the
alternative ("nominalism"?, "subjectivism"?) Tomorrow, I might
incline the other way.
Alan
It is just that realism is problematic in that Reality (that which
realists prefer to spend their exhaustible mental resources on
recognizing and attending - or, more generally and EPTly put,
"actending" - to) is an infinite whilst in some difficult-to-dissect
sense self-limiting process. To me that is _the_ "definitely ultimate
holistic" and EPT answer to why we and Reality exist.
Apropos which: String/M-theoretical physicists are currently pursuing
some details of how this ultimate infinity is self-limiting. ;-)
.
- References:
- Did prime numbers evolve?
- From: dkomo
- Re: Did prime numbers evolve?
- From: Alan Meyer
- Did prime numbers evolve?
- Prev by Date: Re: Did prime numbers evolve?
- Next by Date: Re: A new theory of humor
- Previous by thread: Re: Did prime numbers evolve?
- Next by thread: Re: Did prime numbers evolve?
- Index(es):
Relevant Pages
|
