Re: Mathematical Logic, Podnieks'page ...

2004-07-01 Thread Kory Heath
At 03:25 PM 6/30/2004, CMR wrote (quoting www.fact-index.com):
Mathematical realism holds that mathematical entities exist independently
of the human mind. Thus humans do not invent mathematics, but rather
discover it, and any other intelligent beings in the universe would
presumably do the same. The term Platonism is used because such a view is
seen to parallel Plato's belief in a heaven of ideas, an unchanging
ultimate reality that the everday world can only imperfectly approximate.
This is a perfect example of what I'm complaining about. The quote implies 
that the term Platonism can be used as just another term for 
mathematical realism, but then it immediately provides a definition that 
goes beyond simple mathematical realism. The belief that mathematical 
entities exist independently of the human mind - that humans discover 
mathematics rather than invent it - does not automatically entail the 
belief that there's a heaven of ideas containing (say) the Essence of 
Horseness which everyday horses only imperfectly approximate. These two 
ideas are logically distinct, and it seems sensible to call them by two 
different names. I prefer mathematical realism and essentialism, or 
maybe Platonic essentialism. I'd prefer not to use the term Platonism 
all by itself, but if I had to use it, I'd use it to refer to Platonic 
essentialism, not mathematical realism.

-- Kory



Re: Mathematical Logic, Podnieks'page ...

2004-07-01 Thread Hal Ruhl
Re the discussion on mathematical realism etc. I ask for comments on 
whether or not definition that is the division of ALL in to two parts 
is a mathematical process.

To me definition seems arbitrary but some definitions result in 
mathematical concepts such as the one I use which results in the concepts 
of incompleteness and inconsistency.

Hal



Re: Mathematical Logic, Podnieks'page ...

2004-07-01 Thread John M
Hal,
I agree (whatever it is worth) with the (empty or not) 'set' being
'something' in the nothing.
(I started my 'naive otology (1991) with 'nothingNESS', which is also more
than (your) nothing: containing an ontological qualifier, so it became
SOMETHINGNESS which was the startup of the world.
(Never mind that now, just reminiscence). - )
I had no 'smart'(?) ideas on what moves, but had some headaches with the
vacuum energy (I read about it by D. Bohm) and concluded that it may be a
physicistical quantizing of the (OOPS!) creation: the
vacuumenergy-amount of allegedly 10^124 times that of the total energy
content of the material universe - contained in 1 ml of vacuum (I did not
make that up) - was assigned in my mind to the 'work' to make 'nothing' into
'something'. (Just for the fun of it.)
Silly idea but at that time I had no better one - nor do I have now.
^
To your more recent post upon Kory's rather technical complaints to CMR's
quote:
(Mathematical realism holds that mathematical entities exist
independently of the human mind...)
I have a principal complaint: How do we learn about things existing
independently of our mind? by some 'unidentifiable' input how it is
interpreted by the mind (the essence of 1st person ideas). So it is our mind
that 'makes up' the mathematical concepts which may exist in the natural
world quite differently. Our response.
As I recall I mentioned D. Bohm's remark that numbers do not exist in
nature, they are human inventions or something of that kind, and as I
remember it was CMR who retorted (correct me if I remember wrong) that your
mind is part of the world and the numbers exist in it, how can you maintain
Bohm's statement? [quote approximate].
Discounting what came first WE may conclude that if mathematics
came from nature - it came from our interpretation. An inventive
discovery.
Just like the space-time coordination which led to motion.

Sorry for the common sense rambling

John Mikes


- Original Message -
From: Hal Ruhl [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Wednesday, June 30, 2004 2:38 PM
Subject: Re: Mathematical Logic, Podnieks'page ...


 Hi Stephen:


 At 01:14 PM 6/30/2004, you wrote:
 Dear Hal,
 
  Could the Nothing be a generalization of the notion of the Null or
Empty
 set?

 I think the Null or Empty sets are more particular than my Nothing since
 they include all the underpinnings supporting the idea of set.

  One question that I have is what moves? It seems that I am merely
 re-asking Zeno's question...
 
  How is motion, whether it is the UD moving infinitely slowly from
string
 to string or your example of a shackwave, what is the reason MOTION
 exists? What necessitates motion and change a priori?

 In our universe we identify something called a vacuum energy.  I see the
 incompleteness of the Nothing as such a prime mover if you will.  The
 initiator is sort of a symmetry breaking when the Nothing must answer a
 meaningful question.  Once this starts it acts rather like a formal system
 attempting to complete itself - an empty quest.  This provides the
 motivator for the evolution of the particular metaverse associated with
 this particular symmetry breaking.  I do see the evolution process as
 digital so there is no motion as we usually interpret it.  A universe
 just winks out between successive states.  In this case relativity and
 quantum mechanics seem to me to be simple consequences.

 Hal