Math Forum / Mathematics / Mathematical Logic / November 2008

Logic and mathematics are studies founded entirely on the discrete, the
reidentifiable, the object. A number is one such object, a set and a
proposition are others ...
Too much is asked of the discrete. For example, numbers are expected to

Vaguely connected to the intuitionist topic.
Parallel to the intuitionist's loathing of the concept of
"either this or that must be true, but we don't know which".
I was told this example by Thomas Forster;

On 20 Nov., 13:31, William Hughes <wpihug...@hotmail.com> wrote:

Not in a binary tree that completely exists. The order of quantifiers
is important if a set does not completely exist, like the potentially

Below is a dialogue arguing that traditionals view of objects,
endurance, perdurance in philosophy and logic are incorrect. I would
be interested to hear your comments, whether you see flaws in its
argument or what the extensions of it may be. Sigmund.

In the latest (here) episode of "House",
there was a definite example of "Russell diagnosis",
on the part of Dr House.  As always, the resolution
could easily be achieved by minimal attention to

[Goes like this:]
There can be friends.
There can be enemies.
The friend of my friend is my enemy?

I paraphrase (using my own notation and variables) exercise 22 on page
158 of Enderton's 'Elements Of Set Theory':
[Let 'U' stand for the unary union operation and 'AC' for the axiom of
choice.]

Oneness of pair (equator of self-contradiction), is simultaneity of
cause and effect, and the Abolute Logic of self-creation of Spacetime-
continuum.-Aiya-Oba(Poet/Philosopher)
  Hence, 2(c^2)  +  2(e^2)   =    (c + e)^2

It's at least credible that there is a standard or intended model for
Peano Arithmetic.  For instance, in Godel Escher Bach, Douglas
Hofstadter studies a sentence G with the standard meaning:
"this sentence has no formal proof in PA".

I just saw some information about something called the
"QED Project" which apparently had as its goal, creating
a repository (in computer readable form) of existing
mathematical knowledge. Apparently the QED Project is

INTRODUCTION
The ontological perspective of maths and logic places objects in a
'domain', whose objects are particular to that domain only.* I argue
that Godel selectively employs the object-domain distinction.

Some time ago, Barendregt claimed that he had calculated/estimated the
length of the Goedel sentence (of, say, PA), and that it was larger than
the number of atoms in the universe.
Does anyone know a reference for this? Or of some related results

Is there any account of why IRV is flawed, but plurality rule voting
is somehow okay? (Plurality rule means that whoever gets the MOST
votes wins, regardless of whether or not they have a majority.)

1. the good: Why do we do evil? / Socrates
2. Being and non-being: What is real? / Parmenides of Elea
3. Change, conflict and harmony: How does the cosmos work? /
Heraclitus of Ephesus

This is reposted essentially as is from sci.physics etc. Now,  I wonder
if "logic" can provide any interesting insights into the problem:
Here's my humorous take on science and politics, modified from my recent
posts to NG alt.fan.rawilson and Backreaction blog: