Robert W. wrote:
>I also mention it because it seems that much of the
>dicussion here is forcing understanding through
There is no way to force understanding.
You know there was a time when people believed that the
5th postulate of Euclide geometry was a consequence of
the four others.
Until Lobachevski shows a mathematical model obeying
to the four first axioms and not the 5th. This shows
the independance (the relative consistency of the negation
of the 5th postulate).
This is exactly what modern logician does. Building structures
for viewing the relative independance or dependance of
In the same way, we know through Kripke models that the
formula K, T, 4, 5, B are mutually independant (and we can
prove semantically that KT45 -> B, because a relation
which is reflexive transitive and euclidian is necessarily
symmetrical, or that KT4B -> 5 because a relation which is
reflexive, transitive and symmetrical is automatically
euclidian, etc. Modern logic help us to forget syntactical
This is liberating the mind.
IMO logic is just a polite way for
helping others (including oneself) to realise they have
The french poet and novelist Paul Valery said it in a
rather forceful manner:
"You have just one choice in life, the choice between war
Robert wrote also
>A lot will be left out. There are many things
>physically observable that defy excluded-middle
>analysis, like much of the phenomenon found in quantum
Intuitionist logic (classical logic minus the
excluded-middle principle "p v -p") and quantum logic
(classical logic minus distributivity axioms)
will find their proper place in the dialog
with the UTM.