Dear Brian,
"can be defined ..." implies the necessary existence of something
or process or whatever that does the act of defining the set. Truth
values do not do this, btw. Sets are collections defined in terms of
functions, but numbers in-themselves are not those functions.. Unless
you are considering some other ideas of what sets are... If we are going
to think of set as having ontological primacy we have to have a notion
of a set that does not need a membership function.
On 9/6/2012 10:28 AM, Brian Tenneson wrote:
All numbers can be defined in terms of sets. The question becomes this:
do sets have ontological primacy relative to mankind or are sets
invented or created by mankind?
On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough <[email protected]
<mailto:[email protected]>> wrote:
Hi Stephen P. King
Yes, of course, but I wanted a more obvious, dramatic example.
The philosophy of mathematics says something like the numbers
belong to a static or eternal world, change itself is a property
of geometry.
Numbers and geometry thus belong to the platonic world,
which is forbidden or at least not consistent with the philosophy
of materialism, IMHO.
If numbers are platonic, I wonder what the presumably materialist
Steven Hawkings has to say about their origin in his recent
book on numbers.
Roger Clough, [email protected] <mailto:[email protected]>
9/6/2012
Leibniz would say, "If there's no God, we'd have to invent him
so that everything could function."
----- Receiving the following content -----
*From:* Stephen P. King <mailto:[email protected]>
*Receiver:* everything-list
<mailto:[email protected]>
*Time:* 2012-09-06, 07:53:18
*Subject:* Re: Could we have invented the prime numbers ?
Dear Roger,
Could the mere possibility of being a number (without the
specificity of which one) be considered to be "there from the
beginning"?
--
Onward!
Stephen
http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html
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