Robert W. wrote: >I also mention it because it seems that much of the >dicussion here is forcing understanding through >symbolic logic.

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 statements. 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 symbolic derivations. This is liberating the mind. IMO logic is just a polite way for helping others (including oneself) to realise they have prejudices. 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 and logic". 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 >mechanics. 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. Bruno