On 1/7/2015 7:23 PM, 'Chris de Morsella' via Everything List wrote:
-----Original Message-----
From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of meekerdb
Sent: Wednesday, January 07, 2015 12:12 PM
To: everything-list@googlegroups.com
Subject: Re: Why is there something rather than nothing? From quantum theory to
dialectics?
On 1/7/2015 3:22 AM, Bruno Marchal wrote:
On 06 Jan 2015, at 20:21, meekerdb wrote:
On 1/6/2015 1:48 AM, Bruno Marchal wrote:
On 03 Jan 2015, at 06:05, 'Roger' via Everything List wrote:
Even if the word "exists" has no use because everything exists, it
seems important to know why everything exists.
But everything does not exist. At the best, you can say everything
consistent or possible exist.
Anyway, as I said, the notion of nothing and everything, which are
conceptually equivalent, needs a notion of thing. That notion of
thing will need some thing to be accepte
It is often ambiguous in this thread if people talk about every
physical things, every mathematical things, every epistemological things, every
theological things, ...
So, we cannot start from nothing.
We light try the empty theory: no axioms at all. But then its
semantics will be all models, and will needs some set theory (not
nothing!) to define the models. The semantics of the empty theory is a theory
of everything, but in a sort of trivial way.
Computationalism makes this clear, I think. We need to assume 0 (we
can't prove its existence from logic alone, we need also to assume
logic, if only to reason about the things we talk about, even when they do not
exist).
What does it mean to "assume 0". Is it to assume a collection of
things
No. If we assume a collection, we would do set theory, or something.
We might assume some intended collection at the metalevel, but if we
build a formal theory (a machine), we will not assume a collection at the base
level.
such that every element has a unique successor (per some ordering
relation) and there is one element that is not the successor of any other
element, which we call zero?
That seems to assume things too.
Assuming zero means here that we add a symbol ("0") in the language
alphabet, and we assume some logical formula. The non logical symbol
that we have introduced are "0, s, + and *", and we assume some formula like:
~(0 = s(x)), for any x (the x are always supposed to denote the
object of our universe, here the intended standard natural numbers)
also:
0 + x = x
0 * x = 0
We don't assume anything else (about zero).
So 0 is just a mark on paper, a symbol that is not a symbol "of" anything such
as the empty set.
I get the feeling that '0' has a lot more meaning for Bruno than merely being a
vertically oriented oval drawn on a paper (or computer screen), that it is a
symbolic notational reference to a rather profound concept, which eluded the
world for much of its recorded history. It wasn't until the fifth century A.D.
in India that mathematicians fully conceived of it giving it conceptual
existence, though it was used earlier as a kind of decimal place holder as far
back as 300BC or thereabouts -- in Babylon. It was the Italian mathematician
Fibonacci who introduced the concept back into the church darkened intellectual
deserts of Europe in 1200 AD. Placeholder type zero's -- to differentiate an
empty number column seems to have been adopted in ancient Sumer. It is only
however much later that the concept of zero was really understood.
As a place holder is meant "no units" or "no tens"; it meant none of some specific
category. You imply that "the concept is really understood" differently now, but I have
my doubts. Bruno reifies all the natural numbers and all of arithmetic; which is fine as
a theory, but it's not a proof of existence.
Brent
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
