sci.logic Google Group

Re: What is a logical contradiction?

cmen...@remove-this.tamu.edu (Chris Menzel) — Fri, 09 Jan 2009 20:04:24 UT

You're welcome. :-)

Re: Stuck on modal logic proof

sg...@hotmail.co.uk (Rotwang) — Fri, 09 Jan 2009 19:00:44 UT

Thanks for your reply, but I'm afraid I don't follow. Questions
follow.
I'm with you so far.
Do you mean q here?
Do you mean ~q here? If not then I don't follow. On the other hand, if
so then this shows that there are sets W subset V u {q} and X subset V
u {~q} such that |- &W -> q and |- &X -> ~q. But I don't see how to

Re: Stuck on modal logic proof

sg...@hotmail.co.uk (Rotwang) — Fri, 09 Jan 2009 18:52:30 UT

Ah, I see. I was taking T to mean the trivial statement, i.e. the
statement which satisfies x |= T for any set x, hence my confusion.
Thanks.

Re: What is a logical contradiction?

nom...@invalid (Herbert Newman) — Fri, 09 Jan 2009 18:48:41 UT

:-)
Herb

Re: What is a logical contradiction?

cmen...@remove-this.tamu.edu (Chris Menzel) — Fri, 09 Jan 2009 18:33:54 UT

By asking the question above, presumably. In which case it was out of
place as a response to my most helpful and informative post, as your
intended context had not yet been fixed, let alone agreed upon. A more
appropriate reply would have been "Oh, you're quite correct in general,
but I am assuming a context of classical, non-modal, first-order logic."

Re: The modern mathematical concept of infinity is indefensible

jazzm...@hotmail.com (MoeBlee) — Fri, 09 Jan 2009 18:35:22 UT

To lwal:
I am asking you to retract your lie that I "scared away" zuhair. Here
is what HE said:
"I learned a lot from you actually, indeed more than anyone else in
this usenet. I thank again for your time, in a sense you've been my
teacher here."
As much as I think Rupert and perhaps a couple of other people

Re: The modern mathematical concept of infinity is indefensible

mstem...@walkabout.empros.com (Michael Stemper) — Fri, 09 Jan 2009 18:25:13 UT

As a matter of fact, you can define an axiom system for "djinns",
"metas", and "genie" which is exactly equivalent to the Peano
Postulates, without saying anything about numbers, whether natural
or unnatural.
See _Go:del, Escher, Bach_.

Re: The modern mathematical concept of infinity is indefensible

jazzm...@hotmail.com (MoeBlee) — Fri, 09 Jan 2009 18:20:07 UT

lwal recounts that you took this tack:
Suppose x is infinite. Define a function class F on the power set of x
by:
F(x) = finite cardinality of x, if x is finite
= 0, otherwise.
So the range of F is the set of natural numbers, which is successor
inductive.
Seems right to me. Do you see a problem with it?

Re: The modern mathematical concept of infinity is indefensible

jazzm...@hotmail.com (MoeBlee) — Fri, 09 Jan 2009 18:14:14 UT

WHAT?! zuhair posted a quite warm and appreciative post to me when he
left. I don't mean to boast, but to refute the above nonsense, I
should say that zuhair even warmly called me a "kind of teacher" to
him and made clear that my interaction with him had contributed to his
understanding and that he put a lot of value on our conversations.

Re: The modern mathematical concept of infinity is indefensible

jazzm...@hotmail.com (MoeBlee) — Fri, 09 Jan 2009 17:59:55 UT

So? He didn't there reject proof of non-existence by contradiction.
You're claim is wrong. Albrecht is claiming about ZFC, not just about
"finitist theories".
So what? Newman there didn't there reject proof of non-existence by
contradiction.
You're confusing two things: (1) Whether there is a set that is

Re: The modern mathematical concept of infinity is indefensible

jazzm...@hotmail.com (MoeBlee) — Fri, 09 Jan 2009 17:44:37 UT

I've told you: STOP for just a minute and THINK about what you're
posting before you post it. Your stuff seems to be getting even more
illogical each time you post.
MoeBlee

Re: The modern mathematical concept of infinity is indefensible

jazzm...@hotmail.com (MoeBlee) — Fri, 09 Jan 2009 17:43:27 UT

Then you have no basis to say that ZF-I+~I has all the math he wants
(or however exactly you phrased it).
First, "MoeBlee was right, and Aatu was mistaken" seems to say that I
disagreed with Aatu on this matter. But I never did. I just asked what
the proof is, and Aatu gave it.
Second, Aatu is correct. ZF-I+~I has the theorem "there does not exist

Re: What is a logical contradiction?

nom...@invalid (Herbert Newman) — Fri, 09 Jan 2009 17:38:14 UT

In the context of classical logic we might _define_ "negated predicates"
the following way:
_
P(x) :<-> ~P(x).
In your case we would have, say
___
dog(x) :<-> ~dog(x).
"x is a non-dog"
Then we would get:
___
Ax(dog(x) <-> ~dog(x)).
"For every x: x is a non-dog iff x is not a dog."
Specialization gives, say:

Re: What is a logical contradiction?

nom...@invalid (Herbert Newman) — Fri, 09 Jan 2009 17:39:00 UT

Re: What is a logical contradiction?

nom...@invalid (Herbert Newman) — Fri, 09 Jan 2009 17:26:26 UT

Or rather: What entities/objects fall under the concept /non-dog/.
Well, every entity/object which is not a dog, I'd say.
How would you know? (See the subjectof the tread.)
I mean: Please explain (define) what it means for you "to contradict
oneself".
After formulating your definition, please support your claim "you