MD Inconsistent Systems

From: gmbbradford@netscape.net
Date: Tue Jan 23 2001 - 06:26:56 GMT


Platt,
OK. The secondary definition of "scientific" you provided convinces
me that it could also be read in the way you suggest.

I'm interested in talking to you about great art, but not just now. I've
suddenly gotten very popular.

David Prince,

  DAVID PRINCE:
  Screw you, Glenn!! Your axioms need to be questioned! What are your axioms?

  1. That logical consistency is necessary for truth!
  2. That language is necessary to express Metaphysical Truth!

These aren't axioms. These are simply necessary rules of the game. Any
system of thought, such as a metaphysics, should be internally consistent
to be worth much. If we accept that A is true and ~A is true by this
system, then anything goes as far as A is concerned. It's like having
your cake and eating it, too. But it only gets worse from here. If new
truths can be deduced from A, and new truths can be deduced from ~A, etc.,
then we soon have a system that's infinitely flexible and suits
every whim. That's what happens if you disobey rule 1.

And yes, a metaphysics is written in a language, but this is unavoidable.
There may very well be truths that can not be expressed by language, but
let's try to get the written ones right first.

  DAVID PRINCE:
  No logical system can be completely consistent! (Godel?)

You seem very excited about this, but it's not true. Perhaps you fell
for my little tongue-in-cheek satire.

  DAVID PRINCE:
  If truth must be logically consistent, and no logical system is
  consistent, then there can be no truth.

Logically this doesn't follow because it's based on a false premise.

  DAVID PRINCE:
  Fuck truth!!!

Taut and incisive, this sums up the general sentiment at moq.org.

3WD,

  3WD:
  But the
  view that everything between their covers must be or should be
  scientifically or literally true for them to be of value is not only
  impossible within the framework of the metaphysics he proposes, it
  really is just plainly impossible within any philosophy.

Agreed. A metaphysics simply needs to be consistent with accepted science.

Jonathan,

  JONATHAN:
  In an earlier post, reference was made to Goedels theorem, which states
  that an infinite number of axioms are needed to make a system absolute.

No, this is not what Godel's theorem states.

  JONATHAN:
  Thus, IMHO the modified version would:
    Truth must be logically consistent.
    No logical system is absolute.
    Therefore, truth is relative.

I can only guess what is meant by an 'absolute' system. I assume it doesn't
mean 'complete', otherwise you'd have just said 'complete'. Truth may
indeed be relative, but it's not proved here. Godel's Thm has nothing to
say about relative truth.

David again,

  DAVID PRINCE:
  I say:
  Truth must be logically consistent.
  No logical system is completely consistent.
  Therefore, there is no truth.

  DAVID PRINCE:
  Or

  Truth exists.
  No logical system used to convey truth is consistent.
  Logical consistency is not required to convey truth.

Neither of the above makes logical sense. You appear to have started with
conclusions you liked, and then worked backwards nonsensically.

  DAVID PRINCE:
  Or?

  The local professor of philosophy(MTSU) says:

  Well, something of the flavor of Gödel's paradox gets through, but you've
  vastly overstated the case: there are plenty of complete AND consistent
  logical systems around (the standard apparatus for conducting what we
  typically call 'propositional logic' or the 'sentential calculus'
  (formalizing truth relations among whole, tenseless sentences) is a case in
  point. The Gödel results are about logical systems stuffed with enough
  axiomatic steroids to express the truths of arithemetic; it turns out that
  any such system is consistent if and only if it is imcomplete (that is, if
  and only if there are truths of the system that the system can express but
  cannot prove); i.e., for artithmetic, there will necessarily always be more
  truths than theorems.

This is exactly correct. I'm glad you asked about it, David. If you or
others still have questions about it, feel free to ask me. While Godel's
actual proof is a real bear, I at least understand the conclusion and have
a good grip on its philosophical and mathematical ramifications.

Also, if you go back over your statements and figure out why they don't
make sense, then you are on the road to becoming a critical thinker. That's
assuming you want to be one, of course.

Glenn
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