  We propose partial measurements as a conceptual tool to understand how to
operate with counterfactual claims in quantum physics. Indeed, unlike standard
von Neumann measurements, partial measurements can be reversed
probabilistically. We first analyze the consequences of this rather unusual
feature for the principle of superposition, for the complementarity principle,
and for the issue of hidden variables. Then we move on to exploring non-local
contexts, by reformulating the EPR paradox, the quantum teleportation
experiment, and the entanglement-swapping protocol for the situation in which
one uses partial measurements followed by their stochastic reversal. This leads
to a number of counter-intuitive results, which are shown to be resolved if we
give up the the idea of attributing reality to the wavefunction of a single
quantum system.
