  We suggest that the inner syntax of Quantum Mechanics is relational logic, a
form of logic developed by C. S. Peirce during the years 1870 - 1880. The
Peircean logic has the structure of category theory, with relation serving as
an arrow (or morphism). At the core of the relational logical system is the law
of composition of relations. This law leads to the fundamental quantum rule of
probability as the square of an amplitude. Our study of a simple discrete
model, extended to the continuum, indicates that a finite number of degrees of
freedom can live in phase space. This "granularity" of phase space is
determined by Planck's constant h. We indicate also the broader philosophical
ramifications of a relational quantum mechanics.
