  We argue that the double-slit experiment can be understood much better by
considering it as an experiment whereby one uses electrons to study the set-up
rather than an experiment whereby we use a set-up to study the behaviour of
electrons. We also show how the concept of undecidability can be used in an
intuitive way to make sense of the double-slit experiment and the quantum rules
for calculating coherent and incoherent probabilities. We meet here a situation
where the electrons always behave in a fully deterministic way (following
Einstein's conception of reality), while the detailed design of the set-up may
render the question about the way they move through the set-up experimentally
undecidable (which follows more Bohr's conception of reality). We show that the
expression $\psi_{1} + \psi_{2}$ for the wave function of the double-slit
experiment is numerically correct, but logically flawed. It has to be replaced
in the interference region by the logically correct expression $\psi'_{1} +
\psi'_{2}$, which has the same numerical value as $\psi_{1} + \psi_{2}$, such
that $\psi'_{1} + \psi'_{2} = \psi_{1} + \psi_{2}$, but with $\psi'_{1} =
{\psi_{1} +\psi_{2}\over{\sqrt{2}}} \,e^{\imath {\pi\over{4}}} \neq \psi_{1}$
and $\psi'_{2} = {\psi_{1} +\psi_{2}\over{\sqrt{2}}}\,e^{-\imath
{\pi\over{4}}}\neq \psi_{2}$. Here $\psi'_{1}$ and $\psi'_{2}$ are the correct
contributions from the slits to the total wave function $\psi'_{1} +
\psi'_{2}$. We have then $p = |\psi'_{1} + \psi'_{2}|^{2} = |\psi'_{1}|^{2} +
|\psi'_{2}|^{2} = p_{1}+p_{2} $ such that the paradox that quantum mechanics
(QM) would not follow the traditional rules of probability calculus disappears.
