  We claim that $M$(atroid) theory may provide a mathematical framework for an
underlying description of $M$-theory. Duality is the key symmetry which
motivates our proposal. The definition of an oriented matroid in terms of the
Farkas property plays a central role in our formalism. We outline how this
definition may be carried over $M$-theory. As a consequence of our analysis we
find a new type of action for extended systems which combines dually the
$p$-brane and its dual $p^{\perp}$-brane.
