Math Forum / Mathematics / Mathematical Logic / February 2008

I was hoping somebody could help me understand a remark in Lawvere and
Schanuel's book *Conceptual Mathematics*.
On p180, the authors say that one can investigate a large category X
by considering the mappings between X and a small category C.  To

mathematicians  say .999999 [BAR] = 1
http://mathforum.org/dr.math/faq/faq.0.9999.html
the australian philosopher colin leslie dean  shows you it does not
another example that maths ends in meaninglessness

The australian philosopher colin leslie dean points out that mathematics is
not a rigourous discipline but is no more than an ad hoc sham
3 examples
Colin leslie dean-the first person in 76 years - points out that Godel in

Indiana University Bloomington chemists have designed an organic
molecule   [http://www.theanalystmagazine.com/pr/7010228.htm]  that
binds negatively charged ions, a feat they hope will lead to the
development of a whole new molecular toolbox for biologists, chemists

The  Burali-Forti paradox makes ZFC inconsistent thus proving colin leslie
deans claim that mathematics ends in meaninglessness
http://en.wikipedia.org/wiki/Burali-Forti_paradox
suppose that we associate with each well-ordering an object called its

I said that "order" was no more than a memorable array and that
"disorder" was an indiscernible array. A problem with that idea, of
course, is that it seems to deny the role of relationship in presenting
order. For example, a totality is related to and constituted of its

Does the law of excluded middle say anything about P and notP both
being true?
Law states: "Either P or not P is true." (according to Aristotlean
classical logic).

A monad announces only itself, while an object can announce its
neighbours. The distinction is ignored or not noted in the formal
sciences, but was initially described by Kant (after Liebniz) and
later independently formulated by Wittgenstein.

If w1 is not provable in PA then is it possible that after I add axiom
~w1 that I will then be able to prove w1?
C-B

A little Cantor puzzle
Let's have a binary number Y with the starting value Y = 0.1
Now consider the well-known sequence of real numbers
0.1

The australian philosopher colin leslie dean has brought mathematics to the
threshold of a new era
1)His proof that godels incompleteness theorem-what godel did - is
invalid

Gian Aldo Antonelli states in 'Conceptions and Pardoxes of Sets'
http://orion.uci.edu/~aldo/papers/PM-sets.pdf
that Platomism and the naïve comprehesion axiom are inconsistent,
which is revealed by the set teoretic paradoxes.

There is neither order nor disorder in nature. Mathematics also does not
present order or disorder, even in sequences. Order and disorder are not
properties of systems or their objects.
There are merely memorable arrays. Arrays that are memorable are called

Can number-theoretic results be proven in weaker systems than Peano
Arithmetic, and if so how weak?  It has been common to look at systems
with weakened induction:  for instance Q, which does not assume it at
all; and then various sub-systems of Second-Order Arithmetic

The following notations is the closest to what is present in the print
for FOL.
\-/ : Universal quantifier
-] : Existential quantifier.