Continuity was necessary for Leibniz's infinitesimal calculus.
Although at first it might seem to rule out QM, and it would be problematic for
atomic structures, but in these it only applies to particles. The
quantum wave field is a probability field which is smooth and continuous.
"Principle of Continuity
According to Leibniz, there are “two famous labyrinths where our reason very
often goes astray.”
(G VI 29/H 53) The first concerns human freedom, the latter the composition of
Leibniz, however, thought that he had found the way out of each labyrinth, and
to the problem of the continuum is related ultimately to a maxim or law that
he employs not
only in his mathematical writings but also in his metaphysics. As he puts it in
the Preface to
the New Essays, “Nothing takes place suddenly, and it is one of my great and
maxims that nature never makes leaps.” (A VI vi 56/RB 56) More exactly, Leibniz
that this law or principle implies that any change passes through some
and that there is an actual infinity in things. The Principle of Continuity
will be employed to
show that no motion can arise from a state of complete rest and that
arise by degrees from ones which are too minute to be noticed.” (ibid.)"
Dr. Roger B Clough NIST (ret.) [1/1/2000]
See my Leibniz site at
http://independent.academia.edu/RogerClough- Roger Clough
DreamMail - Your mistake not to try it once, but my mistake for your leaving
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