sci.logic Google Group

Re: In a Consistent System, Can a True Sentence Imply a False One?

namducngu...@shaw.ca (Nam Nguyen) — Fri, 30 Jul 2010 02:19:26 UT

Why was I the one who got confused when a) even you yourself only assumed
(not asserted) "disprovable" would mean "refutable" and b) somebody else
introduced (CM) or defined (AS) the term here which face-value seems to
be ridiculous because the context is in an inconsistent system where
*all formulas* are _provable_ by sheer technical definition, or consequences

Re: details re Z-R |- PA consistent

herb...@gmail.com (herbzet) — Fri, 30 Jul 2010 02:07:59 UT

Officer, arrest that man!

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Re: What are space and time?

n...@droffats.ten (John Stafford) — Thu, 29 Jul 2010 21:00:03 UT

In article
<efe6a582-9984-46e0-8243-90c97 97ac...@x21g2000yqa.googlegrou ps.com>,
Well, that is that. Impossible. Moving on, then...

Re: What are space and time?

federation2...@netzero.com (Rock Brentwood) — Thu, 29 Jul 2010 20:41:42 UT

It was not Einstein, but his teacher, Minkowski who "merged them". But
even this is wrong. It was Galileo who merged them -- what counts is
that the appearance of a mixed space-time symmetry. That's what
marries space and time. The marriage was already in place when the
extra "space-time" term in the transformation law appeared under

Re: What are space and time?

federation2...@netzero.com (Rock Brentwood) — Thu, 29 Jul 2010 20:36:25 UT

Place a stationary shell around a spherical region of space and then
let it go. Its volume will contract with an acceleration given by 4 pi
G M, where M is the mass contained within the region. Once it gets
moving, the equation for the volume contraction will also involve the
first derivative of the volume contraction. Both cases are instances

Re: cube = inside sphere + hyperboloid Re: strip-geometry-building as reversal of Calculus #4.30 & #245 Correcting Math & Atom Totality

plutonium.archime...@gmail.com (Archimedes Plutonium) — Thu, 29 Jul 2010 19:01:28 UT

It is a shame, perhaps in math history that the Recalculus was not
borne first and only later
would the Calculus be borne, but if we look at technology we
understand instantly why Recalculus is borne later, because strip
making technology is sophisticated. To make wine
barrels out of strips of oak wood; to make baskets out of strips of

Re: In a Consistent System, Can a True Sentence Imply a False One?

je...@phiwumbda.org (Jesse F. Hughes) — Thu, 29 Jul 2010 18:44:26 UT

Probably because he's confusing "disprovable" (which I assume means
"refutable") with "not provable".
In fact, here's what he says in reply:
Because in a T if A is provable but ~A is "disprovable" then T
should be consistent. "Provable" means having a proof and
"disprovable" means otherwise, in the context of discussing

Re: In a Consistent System, Can a True Sentence Imply a False One?

namducngu...@shaw.ca (Nam Nguyen) — Thu, 29 Jul 2010 18:29:22 UT

Because in a T if A is provable but ~A is "disprovable" then T should
be consistent. "Provable" means having a proof and "disprovable" means
otherwise, in the context of discussing (in)consistency of a system.
And Alan was making the definition for an inconsistent theory where all
formulas are supposed to be _provable_ (not disprovable).

Re: details re Z-R |- PA consistent

fredjeffr...@gmail.com (FredJeffries) — Thu, 29 Jul 2010 17:55:08 UT

I apologize that my language was too strong here (instead of dashing
things off, I need to wait until I have time to think things through
more thoroughly) -- I meant something more on the lines of your "One
could argue that..."

Re: WHY SCIENCE IS NOT PART OF CULTURE

chazwy...@yahoo.com (Chazwin) — Thu, 29 Jul 2010 17:34:32 UT

If science were not part of culture then it would be part of nature.
As science is actually the study of nature then it is not nature per
se.
Therefore as culture and nature are often see as mutually exclusive
terms, science must be included as part of culture.
In fact science fulfills most definitions of of culture. From wiki....

Re: details re Z-R |- PA consistent

aatu.koskensi...@uta.fi (Aatu Koskensilta) — Thu, 29 Jul 2010 16:46:31 UT

No, no ordinal is a model of ZFC. V_kappa for a large cardinal kappa is
a model of ZFC.
It follows from the existence of a large cardinal that ZFC is consistent
but it is consistent with ZFC that ZFC is inconsistent.

Re: details re Z-R |- PA consistent

ross.finlay...@gmail.com (Ross A. Finlayson) — Thu, 29 Jul 2010 16:32:18 UT

But wouldn't a large cardinal be a model of ZFC? *
Here that's where the cardinal as an ordinal would model the
cumulative hierarchy of ZFC, but then it would have the other
properties of being a model of ZFC. So, having a large cardinal
supports the features of a model of ZFC, i.e., a sufficiently larger

Re: In a Consistent System, Can a True Sentence Imply a False One?

cmen...@remove-this.tamu.edu (Chris Menzel) — Thu, 29 Jul 2010 15:10:39 UT

Obviously not. Since the question has such an obvious answer, I'm
guessing that your intention here is to imply that Alan's answer leads
to the absurd conclusion that a system can be simultaneously consistent
and inconsistent. It doesn't, of course, but why do you think it does?

Re: In a Consistent System, Can a True Sentence Imply a False One?

namducngu...@shaw.ca (Nam Nguyen) — Thu, 29 Jul 2010 14:30:07 UT

I do need some coffee: there was a typo. The formula I meant is cGC, not pGC.
Sorry.