Re: completeness what is it exactly

On Jul 9, 7:53 pm, Aatu Koskensilta <aatu.koskensi...@xxxxxx> wrote:
Chris Menzel <cmen...@xxxxxxxxxxxxxxxxxxxx> writes:
On 09 Jul 2008 19:46:33 +0300, Aatu Koskensilta
<aatu.koskensi...@xxxxxx> said:

The more usual definition is that a logic is weakly complete if there
is a deductive system in which all of its validities are provable and
strongly complete if there is a deductive system such that if A is a
logical consequence of B then B is derivable from A.

A from B, of course.

That is an even more usual definition, yes.

--
Aatu Koskensilta (aatu.koskensi...@xxxxxx)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
 - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

Thanks all.

Where i am struggeling with
Completeness seems to presume universal substitution. (every variable
is replaceble with another variable of formula)

While deduction itself doesn't presumes universal substitution

.so i guess
A theory T is complete :<=> forall "A" (T |- A v T |- ~A)

is false

if a is an variable/ contingent neither T |- A nor T |- ~A

or am i mistaken?





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