Re: Is Validity Just a Hypothetical or Conditional Characteristic?
- From: Jan Burse <janburse@xxxxxxxxxxx>
- Date: Sun, 28 Jan 2007 17:33:08 +0100
herbzet wrote:
Jan Burse wrote:
If you have a proof of the validity of
a sentence, you can look at the proof,
and will learn a lot of about the contribution
of the parts of the sentence to the validity
of the whole sentence.
If you have a valid sentence P -> Q then there is a
sentence P' = P of the form
P1 & P2 & P3 ... & Pn (0 < n)
and there is a sentence Q' = Q of the form
P1 & P2 & P3 ... & Pm (0 < m <= n).
That is, each conjunct of Q' is a conjunct of P'.
Here is a counter example to your above claim.
The following sentence is valid, but I don't
see how you would arrive at your decomposition:
p & ~p -> q
Can you give such a decomposition. Also the
decomposition mentioned by you, has nothing
to do with the method I suggested.
The method I suggested might include an axiom
schema A |- A. But in a proof, this axiom
schema might be applied multiple times, and
not only once.
If we have also weakening in our proof system,
we might see that A & B |- A v C is always
provable. But claiming that any proof of
P |- Q implies that P=A & B and Q=A v C would
be a false jump to conclusions.
Also craig's interpolation theorem says that
for P |- Q there is a formula D, such that
P |- D and D |- Q and D is formulated in the
common language of P and Q. But still this
does not imply some trivial form of D, in
my opinion.
Best Regards
.
- Follow-Ups:
- References:
- Prev by Date: Re: Request for clarification of what is a non first-order definable set.
- Next by Date: Re: Is Validity Just a Hypothetical or Conditional Characteristic?
- Previous by thread: Re: Is Validity Just a Hypothetical or Conditional Characteristic?
- Next by thread: Re: Is Validity Just a Hypothetical or Conditional Characteristic?
- Index(es):
Relevant Pages
|
|
