Math Forum / Mathematics / Mathematical Logic / October 2008

Suppose T is a theory of first-order logic. Further suppose P -> Q is
proved using RAA. Now the truth table for P -> Q is:
P   Q    P->Q
0    0    1

As I see it, WM has clearly made the point that there is a pairing
procedure able to produce a one-one application between nodes and
paths AS the construction of the binary tree goes on. For instance:
                           # (1)

A path in an infinite binary tree is the representation of a real
number of the interval [0, 1]. (Terminating rational numbers have two
representations each.)
Two paths A and B in the infinite binary tree can be distinguished by

1. A(x)(Human(x) -> Mortal(x))
2. E(x)(Human(x) -> Philosopher(x)) /:. E(x)(Human(x) -> (Mortal(x) ^
Philosopher(x)))
Is this equivalent to what would be in category logic:

Is this argument valid, or even a WFF:
1. A(x)(Cat(x) -> (Cute(x) ^ Eats(x, salmon)))
2. Cat(Chloe) /:. Cute(Chloe) ^ Eats(Chloe, salmon)
What about this one:

is it not true that understanding and common interpretation are
necessary for progress?

PROPOSAL
We know that mathematics employs powerful metaphors to bring us ideas
that otherwise might seem alien to us. But is this a misrepresentation
of the role of metaphor in mathematics? Isn't it more the case that

The usual clueless objection to Cantor's Theorem is to say that you
can just add
the anti-diagonal to the list..  The fact that this results NOT  (as
the newbies mistakenly

There's no left or right in a string of beads. And the middle of a
string of beads is only dependent on our being able to ascertain left
and right. But the string itself doesn't have a left or right: thus, a
middle doesn't belong to a string.

This is a disproof of the "diagonal argument" by induction, although
I'd rather call it a proof of unsoundness: yet another one, that is.
It's actually a shortened version of an argument I have presented in
the thread "A consideration concerning the diagonal argument of G.

Logical, computer and mechanical operations are not comprised of STEPS.
Steps refer to a task or argument. Rather, such operations are comprised
of discrete, independent, isolated EVENTS. Each event is both a new
start and a finish, with no powers of task representation. It is ...

I want to know  why we cannot express omega={ {},{{}},{{},{{}}},...}
in a first order language?
If you know any references (in this case), please let me know.
Regards,

Time is the included middle (equator) of the self-contradiction (pair)
of Space.
               -Aiya-Oba (Poet/Philosopher).
Thus,

Hi, I'm new to boolean algebra and am having a lot of problems
figuring out which identities to use to solve this problem. any help
would be grately appreciated.
Given that:

It seems to me that I can create within FOL a predicate that determines
whether a finite set has a particular finite cardinality.
Lets define C_0 being a wff that states a set A is of cardinality zero as:
C_0(A) = (def) a={}