On 15 Jan 2014, at 21:03, Chris de Morsella wrote:
Stephen -- I like how he derives the natural numbers from some basic
set operations on an empty set. One question though how does the
empty set itself arise.
Arithmetic is equivalent to finite set theory (hereditary finite set
theory, HFST). Of course, like RA and PA assumes the existence of 0,
and HFST has to assume the empty set.
Now set theory assumes also an infinite set.
While an empty set contains; it is not the same thing as nothing. It
is a container; it envelopes, contains, encompasses.
OK.
Even if something exists that contains nothing it is itself
something – a minimal something perhaps – but never the less it is
not a formless nothing, but rather it is a conceptual entity that
contains nothing.
Not trying to be obdurate, driven by curiosity to understand.
Yes. "Nothing" would be more like an empty model. But in first order
logic, we usually suppose that the model are not empty. We suppose
that we are talking on something. That is why AxP(x) -> ExP(x) is a
predicate "tautology".
Nothing type of theories have to define "things" which presuppose some
non trivial axioms. Usually it leans, like in comp, non physical
things. But you need still a Turing complete theory, to have computer,
for example.
Bruno
Cheers,
Chris
From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com
] On Behalf Of Stephen Paul King
Sent: Saturday, January 11, 2014 6:48 AM
To: everything-list@googlegroups.com
Subject: A different take on the ontological status of Math
Dear Friends,
I highly recommend Louis H. Kauffman's new blog. His latest post
speaks to the Becoming interpretation of mathematics that I advocate:
http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/
--
Kindest Regards,
Stephen Paul King
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