Math Forum / Mathematics / Mathematical Logic / January 2004

Giving a number m which is the "code" of a Turing machine, is it possible to
decide if m is such as its associated Turing machine will always go to the
right whatever the entry is ?

With another student from my computer science faculty we are trying to
investigate if logic can be helpful through a logic of questions.
Questions themselves are not true or false, but often they seek for
information that are themselves logical clauses.

Let A be true and B be true then A implies B is true.
So if I'm asked to show that one statement implies another then surely
all I need to do is have them both true?
A = its raining

In the planetmath article on IF-logic, the claim was made that the
2nd order induction axiom of arithmetic can be formalized as the
negation of an IF-logic statement. That means that induction can
be expressed as the claim that a particular game does *not* have

I find myself in a situation where mathematicians seem unwilling to
accept algebra, so I thought it might be interesting to show the
logical outline of the argument, and post both on the sci.math and
sci.logic newsgroups.

In this list below I was wondering what would be the proper relation to
Kant's categories of each. Can someone take a couple of examples from the
list and proceed as if explainning from the perspective of "The Critiques."
After the list I have some links to the background of this ...

Let "r.e." abbreviate "recursively enumberable"
Suppose {B_n : n is a natural number} is a family of r.e. sets.
Is the union of this family also an r.e. set?
My initial thought is "yes" because we can make a "dove-tail" argument

What is the difference between a theorem and a proposition?
qualifications/disclaimers/comments:
1) I mean these in the technical mathematical sense
2) I feel like I've seen (mathematical) papers/books which

I was interested in the matter of self-reference and the famous Liar
example: "This sentence is false".
Someone told me Don Perlis wrote an article on Self-Reference and I am
reading it now:

NC (non computable) + NP (non polinomial) + P (polinomial ) != All
prgrams
What is the class name of the other programs?
Thanks , Denis.

This post presents a topic from intuitionistic logic.
The following statements provide some context for the longer excerpt
that follows.  All excerpts are from "The Blackwell Guide to
Philosophical Logic."

I'm not sure if "soundness" is the standard terminology, but here's
my question:
Let Phi be a formula in the language of PA. We will call Phi "valid"
if it is provable using pure first-order logic (for example:

Does Godel's incompleteness theorems apply to nonboolean logics such
as quantum logic?

Gentlemen, Ladies,
Is this group 'about' the science of Logic?
If the group is indeed concerned with that science, then is it possible
that you (that is, the Gentlemen and Ladies of the group) consider Logic

"How long be a piece of string Maester?" the village idiot asked, knowingly.
"As long as I say it is," Dr Pangloss replied.
"Ah, you'm be right there, Maester but how long be thaat in inches, like?"
"Every immeasurable thing is as long as every other immeasurable thing."