On 15 Sep 2011, at 04:24, meekerdb wrote:
On 9/14/2011 5:51 PM, Mindey wrote:
"Nothingness" (as absence of things) is more than a concept. It is a
mathematical concept - an empty set. It is easy to give an example of
an empty set
I'm not so sure about that. Usually you would give some definition
like "The present king of France" = { }. But if you think the
universe is infinite and 'everything' exists, then there is a
present king of France...somewhere. Bruno of course would say
something like "The even divisors of three" = { }, but that would be
circular since the definition of three is the successor of the
successor of the successor of { }. And in any case he assumes
arithmetic exists.
Not really. I have define three as the successor of successor of
successor of 0. Which is a primitive symbol. I don't rely on set theory.
Of course I could have use an axiomatic of hereditarily finite sets,
instead of PA, like I could use combinators or java programs, but we
have to stick on the definition, once chosen. Simple sets of numbers
can be handled in PA by arithmetical definition, indeed we can define
in arithmetic all recursively enumerable set, and we can talk about
non recursively enumerable set too, although not always define them.
Also, it is slightly misleading to say that I assume arithmetic
exists. Arithmetic exists like physics exists, like music exists, etc.
What I assume is that arithmetical statements are true independently
of me, and of the physical laws (which is a very common assumption
implicitly used in theoretical physics, analysis, etc.). (and then I
assume the "yes doctor" and Church thesis).
To just understand CT we need at least the believe that the excluded
middle applies on the sigma_1 sentences: a machine stops or does not
stop. I don't need much more.
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
