Math Forum / Mathematics / Mathematical Logic / May 2005

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Consider the following (proposed) Arithmetic Principle,
say, "Anti-Induction" [or just "AI"]:
(1) There _exists_ an arithmetic number that we don't know
    if it's even. [I.e. no formalization can assert that it's even]

For some reason people have difficulty accepting the use of Monte Carlo
simulations in Maths proofs.
According to George, if you set the digits of a real number to random
0s and 1s, 0.0000000.... or 0.1111111... are just as likely as

Here is the full text of the newly proposed section of Article I of the
Texas Constitution, proposed by HJR 6, which has been passed by both
chambers:
    Sec. 32. (a) Marriage in this state shall consist only of the union

Hey all,
Here is the second question. Any ideas? This one also is pretty easy.
Just remeber this is only my second week in Logic, so go easy on any
examples, etc. I really want to understand it all 100%.

Here is the first problem we have gotten that has to do with truth
tables. I'm not even sure how you would be able to contruct one on
these boards, but any help/advice would be great. Thanks!
Problem goes like this:

Hi again everyone! I have a new problemset for the weekend that I have
been working on. This is my second week of Logic class. We have moved
on to constructing truth tables, etc. and building sentences in SL.
Anyways, I'll start five different threads, one for for each of the

The LaTeX for Logicians site is at
   http://www.phil.cam.ac.uk/teac hing_staff/Smith/LaTeX/
Its first birthday is a couple of weeks away. I haven't updated it for
a while, but that's because I've not had any info sent to me to add

Here is my last problem for the week. This one involves arguing an
answer, which is nice. Any ideas/thoughts?
5. a)  Suppose that P and Q are truth-functionally indeterminate
sentences.  Does it follow that P&Q is truth functionally

Yet another one using truth tables. Any pointers, advice, answer,
debate?
4.  Say whether each of the following pairs of sentences are
truth-functionally equivalent by constructing a truth-table.  (You may

Ok, this is my last question for this week. Please check what I have
and let me know what is wrong and why! Whoever gives me the most help
on the posts this week will be mailed $1 to supplement the energy they
burned by typing/thinking.

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ABSTRACT
We take 2 random lists of random binary numbers and prove that, given
the diagonal of each list, each list can contain the same diagonal.
This contradicts the notion that the diagonal can be used to ascertain

I've been fiddling with this question on and off for several years now.
I'm at a point where having an answer would actually be quite useful
and I'd be happy to get one from someone who knows the relevant math
better than I do.

Assume that the set of provable statements is recursively enumerable.
For any given statement, whether it is provable or not is the same as
whether it is in this r.e. set.
Now what does that tell us about the statements that we can prove?  For