On 06 Sep 2012, at 16:28, 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?
I would say "invented", as many different notion of sets can exist.
You can take sets for the ontology, but it makes everything more
complex, and possibly confusing.
With comp the cardinal ontology is undecidable, and I think it is
simpler to limit to the finite things. If you want set, with comp a
good choice would be the hereditarily finite sets, but it is
equivalent (for the computability and provability) with PA.
A set seems to me to be a typical construction of the mind. Like
physics, analysis, etc.
But comp is consistent with set theory, a priori, so no real problems
here.
Bruno
On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough <rclo...@verizon.net>
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, rclo...@verizon.net
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
Receiver: everything-list
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"?
On 9/6/2012 7:47 AM, Roger Clough wrote:
Hi Stathis Papaioannou
If the prime numbers were there from the beginning, before man,
then I think they were mind-created (platonic) not brain-created
(human creations).
Are the prime numbers an invention by man or one of man's
discoveries ?
I believe that the prime numbers are not a human invention,
they were there from the beginning. Humans can discover
them by brute calculation, but there is a pattern to them
(except for 1, 3 and 5, spaced 6 apart, plus or minus one)
Thus 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 etc.
for n>5, they can be placed +-1 on a grid with a spacing of 6
That spacing seems to me at least to be a priori, out of man's
control.
Roger Clough, rclo...@verizon.net
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: Stathis Papaioannou
Receiver: everything-list
Time: 2012-09-06, 01:24:31
Subject: Re: Sane2004 Step One
On Thu, Sep 6, 2012 at 2:34 PM, Craig Weinberg
<whatsons...@gmail.com> wrote:
>> But you couldn't realise you felt different if the part of your
brain
>> responsible for realising were receiving exactly the same inputs
from
>> the rest of the brain. So you could feel different, or feel
nothing,
>> but maintain the delusional belief that nothing had changed.
>>
>>
>
> That's begging the question. You are assuming that the brain is a
machine
> which produces consciousness. I think that the brain is the three
> dimensional shadow of many levels of experience and it produces
nothing but
> neurochemistry and alterations in our ability to access an
individual set of
> human experiences. The brain does not produce consciousness, it
defines the
> form of many conscious relations.
But you believe that the neurochemicals do things contrary to what
chemists would predict, for example an ion channel opening or closing
without any cause such as a change in transmembrane potential or
ligand concentration. We've talked about this before and it just
isn't
consistent with any scientific evidence. You interpret the existence
"spontaneous neural activity" as meaning that something magical like
this happens, but it doesn't mean that at all.
--
Stathis Papaioannou
--
Onward!
Stephen
http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html
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