Math Forum / Mathematics / Mathematical Logic / July 2005

Tony Orlow seems to think that the set of finite naturals is a finite
set. But consider the following pattern:
  1. There is exactly 1 natural number that is less than 1, namely 0.
  2. There are exactly 2 natural numbers that are less than 2, namely 0

I am pretty new to temporal logic. Browsing the materials
online, I found that sometimes the diamond symbol(<>) is named
"eventually", and in some materials the diamond symbol is
named as "somttimes". Are "eventually" and "somttimes" the

    I am trying to explicitly (not using Church Thesis) cook up a
"universal recursive function".  There are plenty examples of explicit
UTMs, but noone even goes so far as to explicitly state so much as a
numbering for recursives.  Of course it's easy to make a numbering, you

The arguments of current computer theory are really very weak.
All proofs of 'the impossible' are based on diagonalisation, using a formula
X(i) = ANTI ( F(i,i) )
X(i) is naively taken as a valid construction, its not!

This is from mendelson's book:
Let f(x)= 2 if FLT is true; 1 if FLT is false.
Is f primitive recursive?
I admit that the problem has not too much sense to me...

can someone show me an example of recursive function who is not primitive
recursive (other than Ackermann's function)?
Thank you.

David Holland <daj...@sbcglobal.net> casually objected:
S D Rodrian wrote:
 > S D Rodrian wrote:
 >  > The Specific Mechanism of Species Differentiation.

anti-Cantorian David Petry writes:

There is a theorem proved by Cresswell 1967 that for modal
propositional T and S5, if T is complete, then S5 is complete. It also
follows that for any proposition p, if p is S5-valid then it is
T-valid. This, to me, implies that T and S5 are equivalent (i.e. they

The question came up in a discussion between non-logicians.  
Some wanted to refer to valid proofs and or theorems of mathematics as
tautologies.  It was objected that math goes far beyond logic (even
assuming something exists) and tautologies must be true by virtue of

Greetings to everybody.
I have tried to solve this problem about deduction in first order logic
unsuccessfully.
Let G be a the set which comprises the formulas:

Thanks to all who answered 'What isn't a tautology?'
That's all cleared up.  A slightly different question, the status of
definitions, was only partly clarified. I suggested that they are
rules, hence normative rather than true-false.  It is sometimes said

Plesae look at the two statements below:
1) Ironically, this statement is not ironic.
2) Ironically, this statement is ironic.
Now my question is: which of the two  statemenst above, is ironic?

Let us assume that in theory T, statement p has a shortest proof,
called p1.
Also there exists p2, which is the shortest proof that p1 is the
shortest proof for p.

If you deny uncountability, then for me to understand your position, I
should know exactly what it is you deny.
Which of the below, if any, do you deny are theorems from classical first
order logic and Zermelo set: theory?